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.caption-partial-url{-webkit-flex:1;-ms-flex:1;flex:1;background:url('data:image/svg+xml;base64,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') no-repeat 6px;background-position:center;padding:16px 0 16px 0;min-width:62px;max-width:62px;} @media (min-width:768px){.brzlt .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{padding:16px 0 17px 0;min-width:52px;max-width:52px;}} @media (min-width:992px){.brzlt .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{padding:15px 0 17px 0;min-width:60px;max-width:60px;}} .brzlt .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url:hover{-webkit-text-decoration:none;text-decoration:none;} .brzlt .floats-partial-section .floats-partial-footer .floats-partial-caption-text{font-size:14px;padding:0px 18px 17px 22px;} @media (min-width:768px){.brzlt .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:0px 15px 15px 18px;}} @media (min-width:992px){.brzlt .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:0px 18px 19px 21px;}} .brzlt .floats-partial-section .floats-partial-footer .floats-partial-caption-text figcaption{margin:0;padding:0;} .brzlt .floats-partial-section .floats-partial-footer .floats-partial-caption-text svg{max-width:100%;} .brzlt ol{font-size:16px;padding-left:32px;font-family:STIXGeneral-Regular;line-height:24px;margin:15px 0;} .brzlt ol li{margin:10px 0;padding-left:10px;word-break:normal;} .brzlt ol li a{word-break:break-all;} .brzlt ol li .reflinks{display:block;} .brzlt ol li .reflinks a{color:#4D8A17;-webkit-text-decoration:none;text-decoration:none;cursor:pointer;} .brzlt ol li .reflinks a:hover{-webkit-text-decoration:underline;text-decoration:underline;} .brzlt ol li .reflinks .sep{color:#000000;} .brzlt .table-wrapper{width:auto;overflow-x:auto;} .brzlt .table-wrapper::-webkit-scrollbar{-webkit-appearance:none;width:5px;height:5px;} .brzlt .table-wrapper::-webkit-scrollbar-thumb{border-radius:5px;background-color:rgba(0,0,0,.5);-webkit-box-shadow:0 0 1px rgba(255,255,255,.5);} @media (min-width:768px){.brzlt .table-wrapper{overflow-x:auto;width:auto;-webkit-break-word:word-break;break-word:word-break;margin:0 auto;}} @media (min-width:992px){.brzlt .table-wrapper{width:auto;}} @media (min-width:1324px){.brzlt .table-wrapper{width:auto;}} @media (min-width:320px){.brzlt{margin-bottom:33px;padding:0;}} @media (min-width:992px){.brzlt{padding:0;}} @media (min-width:1325px){} .brzlt .owl-stage{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;} .brzlt .floats-partial-middle--thumbs{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;} .brzlt .floats-partial-middle--thumbs .partial-carousel-dot svg{fill:#4D8A17;} .brzlt .floats-partial-middle--thumbs .partial-carousel-dot strong{color:#4D8A17;font-weight:500;} .brzlt .floats-partial-middle--thumbs .partial-carousel-dot.active strong{color:#007B8B;} .brzlt .floats-partial-middle--thumbs .partial-carousel-dot.active svg{fill:#007B8B;} .brzlt 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img{width:100%;max-height:239px;height:auto;} @media (min-width:767.5px){.brzlt .partial-carousel--single-image img{max-height:357px;}} @media (min-width:991.5px){.brzlt .partial-carousel--single-image img{max-height:417px;}} .brzlt .partial-carousel--single-image strong{font-size:11px;padding-top:12px;} @media (min-width:767.5px){.brzlt .partial-carousel--single-image strong{font-size:16px;}} .brzlt .owl-nav,.brzlt .owl-dots{display:none;} .brzlt .partial-carousel-wrapper .owl-loaded{position:relative;height:auto;max-height:287px;} @media (min-width:767.6px){.brzlt .partial-carousel-wrapper .owl-loaded{max-height:414px;}} @media (min-width:767.5px){.brzlt .partial-carousel-wrapper .owl-loaded{max-height:477px;}} .brzlt .partial-carousel-wrapper .floats-partial-content,.brzlt .owl-stage-outer,.brzlt .owl-stage{max-height:287px;height:auto;} @media (min-width:767.6px){.brzlt .partial-carousel-wrapper .floats-partial-content,.brzlt .owl-stage-outer,.brzlt .owl-stage{max-height:414px;}} @media (min-width:767.5px){.brzlt .partial-carousel-wrapper .floats-partial-content,.brzlt .owl-stage-outer,.brzlt .owl-stage{max-height:477px;}} .brzlt .partial-carousel-wrapper .floats-partial-content::after,.brzlt .owl-stage-outer::after,.brzlt .owl-stage::after{background:transparent;} .brzlt .partial-carousel-wrapper .floats-partial-middle--thumbs{width:100%;overflow-x:auto;-webkit-align-items:self-start;-webkit-box-align:self-start;-ms-flex-align:self-start;align-items:self-start;} @media (min-width:767.5px){.brzlt .partial-carousel-wrapper .floats-partial-middle--thumbs{width:calc(100% - 110px);}} .brzlt .partial-carousel-wrapper .floats-partial-middle--nav{width:100%;position:relative;} @media (min-width:767.5px){.brzlt .partial-carousel-wrapper .floats-partial-middle--nav{width:20%;}} .brzlt .floats-partial-middle{position:relative;} .brzlt .partial-carousel-wrapper 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height="24"><span class="text">提交</年代p一个n></年代p一个n><span class="sc-htoDjs kNoiZu sc-dqBHgY cQgXqt fileArrow icon-colored undefined icon-themeable" title="" font-size="16"></span></a> <div class="sc-krDsej ezTxjV hide__submenu journalSubmenuCheck" id="journalnav__submenu"> <button class="sc-itybZL kdvWPs journalSubmenuCheck"><span class="sc-htoDjs gvAGTV sc-fzsDOv hAFFGk journalSubmenuCheck icon-colored _1CwL9R82TPl2HxDleeYGDR icon-themeable" title="" font-size="9"></span></button> </div> <div class="sc-dTdPqK lkWWFY hide__submenu journal__nav__desktop" id="journalnav__submenudesktop"> <div order="0" class="sc-jVODtj LnqHR"> <div class="sc-gPWkxV sTano"></div> <div class="sc-gPWkxV sTano"></div> <div class="sc-gPWkxV sTano"></div> <div class="sc-gPWkxV sTano"></div> </div> </div> </nav> </div> <div class="sc-crNyjn hnRKrw breadcrumb__wrapper journal_article__BreadCrumbStyle-sc-t08z80-2 iSqwbI article"> <a class="sc-htpNat bUhGXt link sc-cpHetk jUUanO breadCrumb" href="//www.newsama.com/journals/aor/" aria-label="Advances in Operations Research">行动研究进展</一个>/<gydF4y2Ba一个cl作为年代=”年代c-htpNat bUhGXt link sc-cpHetk jUUanO breadCrumb" href="//www.newsama.com/journals/aor/contents/year/2011/" aria-label="2011">2011年</一个>/<gydF4y2Ba年代p一个ncl作为年代=”年代c-nrwXf drSekm">文章</年代p一个n></div> <div class="threeColumn__ThreeColumnWrapper-sc-1crxfky-0 jeKbHB threeColumnWrapper"> <div class="threeColumn__LeftWrapper-sc-1crxfky-1 cCYREf leftWrapper"> <button type="button" class="sc-ePZHVD kXdKQA section__button " id="sectionButton"><span class="sc-htoDjs diutvq icon__dots dots__detector icon-colored _3n-7Ho7DlfjMlZbrRr9Q4a icon-themeable" title="" font-size="22"></span>文章部分</gydF4y2Babutton> <div class="sc-jtRlXQ dncNEX static_contents__section_links links__hidden "> <div id="leftSectionMenu" class="sc-cbkKFq prcY sc-jeCdPy eVPlap left_section_menu"> <p>在这一页上</p><年代p一个ncl作为年代=”年代c-bEjcJn iLzNBj grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-bGbJRg ihXRQF" href="#abstract" aria-label="">文摘</一个></年代p一个n><年代pan class="sc-bEjcJn iLzNBj grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-bGbJRg ihXRQF" href="#introduction" aria-label="">介绍</一个></年代p一个n><年代pan class="sc-bEjcJn iLzNBj grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-bGbJRg ihXRQF" href="#conclusions" aria-label="">结论</一个></年代p一个n><年代pan class="sc-bEjcJn iLzNBj grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-bGbJRg ihXRQF" href="#acknowledgments" aria-label="">确认</一个></年代p一个n><年代pan class="sc-bEjcJn iLzNBj grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-bGbJRg ihXRQF" href="#references" aria-label="">引用</一个></年代p一个n><年代pan class="sc-bEjcJn iLzNBj grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-bGbJRg ihXRQF" href="#copyright" aria-label="">版权</一个></年代p一个n><年代pan class="sc-bEjcJn iLzNBj grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-bGbJRg ihXRQF" href="#related-articles" aria-label="">相关文章</一个></年代p一个n></div> </div> </div> <div class="threeColumn__ContentWrapper-sc-1crxfky-3 ibxgRv contentWrapper"> <div class="threeColumn__Content-sc-1crxfky-4 bPvmyp content"> <div class="articleContent__ArticleContentsWrapper-sc-phk71o-0 dentpz article_contents"> <div class="articleContent__ArticleContentsSectionsWrapper-sc-phk71o-1 lnYIEU article_contents__sections_wrapper"> <div class="articleContent__ArticleWrapper-sc-phk71o-2 LalmI"> <div class="sc-iBEsjs kOIDmJ article_header_class"> <p class="sc-fcdeBU jSVooP article_type">研究文章|<gydF4y2Ba!-- -->开放获取</p><gydF4y2Badiv class="sc-gmeYpB edbFGD article_citation"> 体积<gydF4y2Ba!-- --> 2011年<gydF4y2Ba!-- --> <span class="sc-RcBXQ euBwsC">|</年代p一个n>文章的ID<gydF4y2Ba!-- --> 269239年<gydF4y2Ba!-- --> <span class="sc-RcBXQ euBwsC">|</年代p一个n><一个cl作为年代=”年代c-htpNat bUhGXt link sc-iSDuPN kDGfWF" href="https://doi.org/10.1155/2011/269239" aria-label="Doi-link">https://doi.org/10.1155/2011/269239</一个></div> <div class="sc-jKVCRD kVmHSX article_full_citation"> <div class="sc-LKuAh eHdRBi isHide"> <p>威利Semmler Hideaki青山,Lars Grune,耀西藤原,Wataru苏马病<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> ”<年代p一个ncl作为年代=”一个djust-article-svg-size">公司规模的波动在长期和双峰分布</年代p一个n>”,<gydF4y2Ba!-- --><i>行动研究进展</我>,<ggydF4y2BaydF4y2Ba!-- --> 卷。<gydF4y2Ba!-- -->2011年<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> 文章的ID<gydF4y2Ba!-- -->269239年<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> 21<gydF4y2Ba!-- -->   页面<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> 2011年<gydF4y2Ba!-- -->。<gydF4y2Ba!-- --> https://doi.org/10.1155/2011/269239</p></gydF4y2Badiv> <button class="sc-hSdWYo etauus sc-kaNhvL hZfccF" color="">显示引用</gydF4y2Babutton> </div> <h1 class="sc-iRbamj jZOxOO sc-kZmsYB hgeJsC article_title adjust-article-svg-size heading-title">公司规模的波动在长期和双峰分布</gydF4y2Bah1> </div> <div class="sc-kQsIoO ilXkOX article_authors"> <hr class="sc-iQtOjA bpnzQO hr__author"> <span class="">Hideaki青山<gydF4y2Ba!-- -->,<年代up>1</gydF4y2Ba年代up></年代p一个n><年代pan class="">佬司Grune<gydF4y2Ba!-- -->,<年代up>2</gydF4y2Ba年代up></年代p一个n><年代pan class=""><b>威利Semmler</gydF4y2Bab><a class="sc-htpNat bUhGXt link" href="mailto:" aria-label="Mail Option"><span class="sc-htoDjs kNoiZu sc-gPzReC kIRihs icon-colored _2zt-1j0LmaF8UjTQAM413G icon-themeable" title="" font-size="16"></span></a>,<年代up>3</gydF4y2Ba年代up></年代p一个n><年代pan class="">耀西藤原<gydF4y2Ba!-- -->,<年代up>3</gydF4y2Ba年代up>和</年代p一个n><年代p一个ncl作为年代="">Wataru苏马病<年代up>4</gydF4y2Ba年代up></年代p一个n><div class="sc-iybRtq hqlWOa isHide"> <p><sup>1</年代up><年代p一个n>研究生院科学,京都大学,吉田,Sakyo, 606 - 8501年《京都议定书》,日本</年代p一个n></p><p><sup>2</年代up><年代p一个n>法兰克福大学数学系,罗伯特·迈耶街8 - 10,60054年法兰克福,德国</年代p一个n></p><p><sup>3</年代up><年代p一个n>中心实证宏观经济学,33615比勒费尔德,德国和新学校大学,纽约,纽约10011,美国</年代p一个n></p><p><sup>4</年代up><年代p一个n>一个TR人类信息科学实验室,619 - 0288年《京都议定书》,日本</年代p一个n></p></div> <button class="sc-hSdWYo etauus sc-hjRWVT erRKjF" color="">显示更多</gydF4y2Babutton> </div> <div class="articleContent__EditorWrapper-sc-phk71o-3 faJNbX"> <div class="articleContent__TextWrapper-sc-phk71o-8 dsGtgx"> <b>学术编辑器:</gydF4y2Bab>沃尔特·j·Gutjahr</gydF4y2Badiv> <div class="articleContent__PublicationTimeLineWrapper-sc-phk71o-4 hoUdUJ"> <div class="articleContent__PublcationCol-sc-phk71o-5 bwbOqE notPublished"> <span class="articleContent__PublicationField-sc-phk71o-6 jrHvLY">收到了</年代p一个n><年代p一个ncl作为年代="articleContent__PublicationValue-sc-phk71o-7 GvnvP">03年4月2011年</年代p一个n></div> <div class="articleContent__PublcationCol-sc-phk71o-5 bwbOqE notPublished"> <span class="articleContent__PublicationField-sc-phk71o-6 jrHvLY">接受</年代p一个n><年代p一个ncl作为年代="articleContent__PublicationValue-sc-phk71o-7 GvnvP">2011年6月27日</年代p一个n></div> <div class="articleContent__PublcationCol-sc-phk71o-5 bwbOqE isPublished"> <span class="articleContent__PublicationField-sc-phk71o-6 jrHvLY">发表</年代p一个n><年代p一个ncl作为年代="articleContent__PublicationValue-sc-phk71o-7 GvnvP">05年9月2011年</年代p一个n></div> </div> </div> <article class="sc-hzDEsm brzlt article_body "> <div> <div class="xml-content"> <h4 class="header" id="abstract">文摘</gydF4y2Bah4> <p>我们研究经验和分析经济增长和波动的大小分布。实证分析是进行我们的数据集公司大小,与强调一次性分配以及经济增长概率分布。帕累托法则和Gibrat定律通常用于研究公司大小分布。讨论他们的理论关系,表明他们是complementable双峰分布的公司规模。我们介绍经济机制,建议公司大小的双峰分布。我们学习的机制已经知道在经济长期以来文学。然而,他们并没有在一个动态的背景下研究公司的决策问题。允许这些机制从而将引起企业对某些特征的异质性。然后我们展示不同类型的测试数据对我们公司大小标明公司规模的双峰分布。</p><年代p一个ncl作为年代=”end-abs"></span> <h4 id="introduction">1。介绍</gydF4y2Bah4> <p>最近的统计研究公司大小分布在不同的国家和时间(见Gibrat [<一个href="#B13">1</一个>),藤原et al。<一个href="#B10">2</一个>和Mantegna和斯坦利<一个href="#B19">3</一个>]。)表明,公司规模的分布遵循一个权力法律事务所规模的各种措施,如总资产和员工人数。大小分布非正态的公司一直是一个长期有争议的问题在工业组织文学。一个重要的早期研究公司大小分布发现,它遵循Gibrat定律(<一个href="#B13">1</一个>]。</p><p>gydF4y2Ba看经验数据,指出,公司发展不均衡。公司大小变化或波动。看这一个定量的方法是看概率分布函数(pdf)的增长率,这被定义为第二年的比率的值和第一年的价值。在这方面有一些研究[<一个href="#B11">4</一个>),再次上尾巴,导致确认Gibrat定律(<一个href="#B13">1</一个>),即第一年增长率pdf条件的价值从第一年的独立价值。换句话说,第一年的增长率是独立的价值,当后者很大。</p><p>gydF4y2Ba这两个法律的事实,帕累托定律和Gibrat定律,观察共存提出深之间的关系。事实上,这样一个关系被发现时,细致平衡定律,即同时pdf的价值和第二年的第一年价值交换的两个变量是对称的。这也会导致一个理论关系的正增长的pdf和增长率相同的负增长一边,被确认的数据。</p><p>gydF4y2Ba整体最近的实证研究发现,第一,公司的大小分布的上尾帕累托定律认为(这也可能是符合Gibrat定律,超过一定最小大小公司的增长率是独立的大小),第二,的方差公司的增长率是独立于大小超过某一最小大小,第三,上下移动的频率大小的类也是大致相同的一定规模以上的类。</p><p>gydF4y2Ba然而,所有三个结果似乎与事实一致,上部尺寸类行为独特从较低的大小类和中型类是“变薄。“因此,可能有一个倾向twin-peak分布与不同的上下大小类的行为。实证研究可能要处理公司大小类的事实组织不同,有双峰分布的大小类从长远来看。(最近其他文献也发现了双峰公司大小分布;看到Bottazzi和西奇(<一个href="#B5">5</一个>)和Bottazzi et al。<一个href="#B6">6</一个>]。)我们还提供了一种分析讨论帕累托法则的关系和Gibrat定律。但由于这种关系的推导,而技术、细节提出了本研究在附录<一个href="#sec6">一个</一个>。分析公司的尾巴上下大小分布通过帕累托法则和Gibrat定律是辅以实证研究,解决了问题“稀疏”的中间,公司规模的双峰分布的问题。</p><p>gydF4y2Ba大小分布的统计研究以来,公司不给我们提供了很多见解的潜在机制,我们也关注公司大小分布的动态给统计结果的一些理论基础。我们介绍和研究经济机制可以解释公司规模和公司增长的动力。我们表明,有一个悠久的传统经济理论,尤其是在过去的五十年的产业组织文学指出一些主要机制为什么确实期望一个企业在长期的双峰大小分布。在部分<一个href="#sec2">2</一个>和<一个href="#sec3">3</一个>的上下文中,我们将展示这些机制的动态投资模型公司。在理论研究中,我们认为公司可能是异构的大小,因为他们接触到的一些后续机制。</p><p>gydF4y2Ba我们想排除一些武断的行为的公司,因此假定所有公司追求相同的动态投资策略旨在最大化他们的未来支付的现值。当然,还有其他影响公司整体需求增长等,行业需求,成本和技术冲击和复杂的融资实践。但我们想只关注一些经济理论的主要机制,研究了长期以来,面对隐含预测公司大小动态实证研究的结果。</p><p>gydF4y2Ba本文的其余部分组织如下。在部分<一个href="#sec2">2</一个>和<一个href="#sec3">3</一个>我们引入机制,可能导致某些公司的大小分布的性质,特别是twin-peak分配公司的大小。节<一个href="#sec4">4</一个>,然后会显示我们的实证结果证明确实有一个倾向twin-peak大小分布的公司从长远来看。部分<一个href="#sec5">5</一个>总结了纸。附录<一个href="#sec6">一个</一个>介绍了帕累托定律的技术关系的推导和Gibrat法与上下大小类。</p><gydF4y2Bah4 id="modeling-the-dynamics-of-firm-size-distribution">2。公司大小分布的动力学建模</gydF4y2Bah4> <p>我们在这里介绍一些机制,可能会引来一些动力学向twin-peak大小分布的公司。第一个重要的机制,我们想研究是基于本地规模收益递增。这个想法的本地文学中存在规模收益递增自马歇尔(<一个href="#B20">7</一个>]。最近,它已经广泛被受雇于亚瑟(<一个href="#B2">8</一个>- - - - - -<一个href="#B4">10</一个>)表明,各种各样的正反馈,如学习利用,规模经济,并增加返回信息和技能是如果一个公司享有,例如,通过历史事故,一些规模优势。特此,局部增加回报可能是近似的凸凹形生产函数像斯科巴提出的还<一个href="#B24">11</一个>)和布鲁克Milliaris (<一个href="#B8">12</一个>]。</p><p>gydF4y2Ba第二个机制是基于调整资本成本一直受雇于投资理论自从艾斯纳和Stroz [<一个href="#B9">13</一个>卢卡斯],[<一个href="#B18">14</一个>),古尔德(1968)。我们将探索二次以及更一般的调整资本成本和研究到什么程度会生成一个尺度依赖的动态。我们尤其感兴趣的大小对调整成本的影响,将是大公司的优势。(调整成本的进一步讨论和调查文献中给出了加藤et al。<一个href="#B17">15</一个>]。)</p><p>gydF4y2Ba第三个机制可以看到起源于成本和缓解信贷(或密度)。重要贡献这条线的研究可以发现在汤森(<一个href="#B25">16</一个>),伯南克et al。<一个href="#B7">17</一个>],Grune et al。<一个href="#B15">18</一个>]。此文献假定借款和贷款关系中的信息不对称和代理成本。这可能,Gertler和吉尔(<一个href="#B12">19</一个>)表明,尤其适用于小型企业。我们在这里画的洞察力文学昂贵的状态验证(这个文学起源于汤森(的开创性工作<一个href="#B25">16</一个>]。),银行必须支付成本为了观察借款人的意识到回报。这激发了抵押信贷的使用。假定计费抵押借款支付风险溢价超过抵押借款或自筹经费。风险溢价来自破产的威胁即从成本由审计、会计、法律费用以及损失的资产带来的资产清算。所以,希望对不同类型的公司不同,因此信贷风险溢价水平分布在公司已经默顿(<一个href="#B22">20.</一个>已经证明。</p><p>gydF4y2Ba据推测,风险溢价之间借款人的预期回报和无风险利率为零,在极限情况下,当债务接近零。一个合适的函数这种溢价,将在下面介绍。然而,即使信贷成本是endogenized传播,可能有外部借贷约束公司财政投资。</p><p>gydF4y2Ba我们可以指定一个一般模型的公司<年代vg height="9.9250002" id="M1" style="vertical-align:-0.13794pt;width:4.9875002px;" version="1.1" viewbox="0 0 4.9875002 9.9250002" width="4.9875002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.925)"> <g transform="translate(72,-64.06)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>这可能是暴露于上述机制。让我们定义公司的动态决策问题<年代vg height="9.9250002" id="M2" style="vertical-align:-0.13794pt;width:4.9875002px;" version="1.1" viewbox="0 0 4.9875002 9.9250002" width="4.9875002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.925)"> <g transform="translate(72,-64.06)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>的脸。除了索引<年代vg height="9.9250002" id="M3" style="vertical-align:-0.13794pt;width:4.9875002px;" version="1.1" viewbox="0 0 4.9875002 9.9250002" width="4.9875002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.925)"> <g transform="translate(72,-64.06)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,提出了决策问题如下:<年代p一个ncl作为年代=”equation" id="EEq1"> <svg height="94.849998" id="M4" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 94.849998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,94.85)"> <g transform="translate(72,3.88)"> <text transform="matrix(1,0,0,-1,114.51,54.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.077898" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.241398" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.018023" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.657356" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.697746" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.812912" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.364243" y="0"> x</t年代p一个n></text> <text transform="matrix(1,0,0,-1,167.75,46.53)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,184.3,46.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,191.3,68.19)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-1.25" y="25.530001"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,201.98,54.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,207.55,59.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.572416" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,221.37,54.16)"> <tspan style="font-size: 12.50px; " x="-89.800003" y="28.48"> ̇</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-160.78999" y="51.700001"> ̇</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.515023" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.678522" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.54315" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.706648" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.620087" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.859085" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.072834" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.774685" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.938183" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.85162" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.015121" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.25412" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="75.905716" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="79.819153" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="243.38" y="0.1"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="247.5435" y="0.1"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="253.795" y="0.1"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="256.92075" y="0.1"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="263.17224" y="0.1"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-95.599998" y="31.209999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-86.747879" y="31.209999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-82.584373" y="31.209999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-78.670937" y="31.209999"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-71.031609" y="31.209999"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-59.003719" y="31.209999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-51.301872" y="31.209999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-47.138371" y="31.209999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-43.224934" y="31.209999"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-36.285767" y="31.209999"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-24.945547" y="31.209999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-17.606285" y="31.209999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-8.7416592" y="31.209999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-4.5781598" y="31.209999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-0.66472101" y="31.209999"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.5867791" y="31.209999"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.752918" y="31.209999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.617544" y="31.209999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.781044" y="31.209999"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.032543" y="31.209999"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.671879" y="31.209999"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.712265" y="31.209999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.488892" y="31.209999"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="243.38" y="31.209999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="247.5435" y="31.209999"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="253.795" y="31.209999"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="256.92075" y="31.209999"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="263.17224" y="31.209999"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-168.27" y="54.240002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-156.99229" y="54.240002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-152.8288" y="54.240002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-148.91536" y="54.240002"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-141.27602" y="54.240002"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-129.23564" y="54.240002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-115.11974" y="54.240002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-110.95625" y="54.240002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-102.09162" y="54.240002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-97.928123" y="54.240002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-94.014687" y="54.240002"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-87.763184" y="54.240002"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-82.561935" y="54.240002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-71.271729" y="54.240002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-67.108231" y="54.240002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-63.19479" y="54.240002"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-59.031288" y="54.240002"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-52.092125" y="54.240002"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-40.751904" y="54.240002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-36.588406" y="54.240002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-26.060879" y="54.240002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-21.897379" y="54.240002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-13.032752" y="54.240002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-8.8692532" y="54.240002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-4.9558139" y="54.240002"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="1.283183" y="54.240002"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.4969339" y="54.240002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.198782" y="54.240002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.362282" y="54.240002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.275721" y="54.240002"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.439219" y="54.240002"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.378384" y="54.240002"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.718605" y="54.240002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.620502" y="54.240002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.784" y="54.240002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.697437" y="54.240002"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.860939" y="54.240002"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.112434" y="54.240002"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="86.27858" y="54.240002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="97.568787" y="54.240002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="101.73228" y="54.240002"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="107.98379" y="54.240002"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="115.62312" y="54.240002"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="127.651" y="54.240002"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,357.74,-3.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,362.61,-0.08)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="102.14" y="-0.15000001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="106.3035" y="-0.15000001"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="112.555" y="-0.15000001"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="115.68075" y="-0.15000001"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="121.93225" y="-0.15000001"> )</t年代p一个n></text> </g> </g> </svg></span></p> <p>公司的决策问题是其现值最大化<年代vg height="13.45" id="M7" style="vertical-align:-2.21957pt;width:27.987499px;" version="1.1" viewbox="0 0 27.987499 13.45" width="27.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1892252" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.129351" y="0"> )</t年代p一个n></text> </g> </g> </svg>,(<一个href="#EEq1">2。1</一个>),使用投资<年代vg height="12.675" id="M8" style="vertical-align:-2.34499pt;width:7.1374998px;" version="1.1" viewbox="0 0 7.1374998 12.675" width="7.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.675)"> <g transform="translate(72,-61.86)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>选择变量。(后来,我们搁置时间指数)。这个术语下的积分(<一个href="#EEq1">2。1</一个>)是贴现回报,<年代vg height="13.6125" id="M9" style="vertical-align:-2.34499pt;width:40.275002px;" version="1.1" viewbox="0 0 40.275002 13.6125" width="40.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9391651" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.87929" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.080538" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.944204" y="0"> )</t年代p一个n></text> </g> </g> </svg>,公司的净收益折现率折现<年代vg height="10.7375" id="M10" style="vertical-align:-0.13794pt;width:8.3125px;" version="1.1" viewbox="0 0 8.3125 10.7375" width="8.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。方程(<一个href="#EEq1">2。2</一个>)代表资本存量的运动定律,<年代vg height="10.7375" id="M11" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="6.9875002" id="M12" style="vertical-align:-0.13794pt;width:9.3000002px;" version="1.1" viewbox="0 0 9.3000002 6.9875002" width="9.3000002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,6.9875)"> <g transform="translate(72,-66.41)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>一个表示资本存量的折旧系数。方程(<一个href="#EEq1">2。3</一个>)表示的发展公司的债务,<年代vg height="10.325" id="M13" style="vertical-align:-0.0pt;width:11.625px;" version="1.1" viewbox="0 0 11.625 10.325" width="11.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。注意,我们允许负投资利率<年代vg height="13.6125" id="M14" style="vertical-align:-2.34499pt;width:33.412498px;" version="1.1" viewbox="0 0 33.412498 13.6125" width="33.412498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3269978" y="0"> <</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.367388" y="0"> 0</t年代p一个n></text> </g> </g> </svg>这是可逆的投资为简单起见。(模型也可以解释为用劳动效率;因此,<年代vg height="6.9875002" id="M15" style="vertical-align:-0.13794pt;width:9.3000002px;" version="1.1" viewbox="0 0 9.3000002 6.9875002" width="9.3000002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,6.9875)"> <g transform="translate(72,-66.41)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>能代表资本折旧率的总和和外生技术变革的速度)。在(<一个href="#EEq1">2。3</一个>),这个词<年代vg height="13.45" id="M16" style="vertical-align:-2.21957pt;width:50.037498px;" version="1.1" viewbox="0 0 50.037498 13.45" width="50.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.915119" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.078618" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.855244" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.056492" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.758579" y="0"> )</t年代p一个n></text> </g> </g> </svg>代表了信贷成本取决于公司的净资产,和<年代vg height="7.1875" id="M17" style="vertical-align:-0.13794pt;width:7.3874998px;" version="1.1" viewbox="0 0 7.3874998 7.1875" width="7.3874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1875)"> <g transform="translate(72,-66.25)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>可以被视为股息支付(或资产持有者的消费流),将这里视为外生。(如何endogenized进一步指定Grune et al。<一个href="#B15">18</一个>]。)</p><p>gydF4y2Ba允许调整的成本,<年代vg height="16.612499" id="M18" style="vertical-align:-2.34499pt;width:36.012501px;" version="1.1" viewbox="0 0 36.012501 16.612499" width="36.012501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6125)"> <g transform="translate(72,-58.71)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.34,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.18,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n></text> </g> </g> </svg>,是由公司的净收入<年代p一个ncl作为年代=”equation" id="EEq4"> <svg height="18.375" id="M19" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.375)"> <g transform="translate(72,-57.3)"> <text transform="matrix(1,0,0,-1,138.23,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.515023" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.678522" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.455149" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.6689" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.282745" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.909576" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.949966" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.239452" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.402954" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.179581" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.118744" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="89.458961" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="97.110802" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="108.45102" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,252.3,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,257.68,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,264.46,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,275.4,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="189.35001" y="-0.41999999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="193.5135" y="-0.41999999"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="199.765" y="-0.41999999"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="202.89075" y="-0.41999999"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="209.14224" y="-0.41999999"> )</t年代p一个n></text> </g> </g> </svg></span>公司的收入<年代vg height="13.55" id="M20" style="vertical-align:-2.29482pt;width:26.75px;" version="1.1" viewbox="0 0 26.75 13.55" width="26.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.201488" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.141613" y="0"> )</t年代p一个n></text> </g> </g> </svg>是来自资本存量,通过生产函数,定义如下。所以,总的来说,投资,<年代vg height="12.675" id="M21" style="vertical-align:-2.34499pt;width:7.1374998px;" version="1.1" viewbox="0 0 7.1374998 12.675" width="7.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.675)"> <g transform="translate(72,-61.86)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,进行以最大化净收益的现值(<一个href="#EEq4">2。4</一个>)考虑到调整资本成本<年代vg height="16.612499" id="M22" style="vertical-align:-2.34499pt;width:36.012501px;" version="1.1" viewbox="0 0 36.012501 16.612499" width="36.012501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6125)"> <g transform="translate(72,-58.71)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.34,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.18,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n></text> </g> </g> </svg>在(<一个href="#EEq4">2。4</一个>)。请注意,<年代vg height="11.0625" id="M23" style="vertical-align:-0.30096pt;width:36.5px;" version="1.1" viewbox="0 0 36.5 11.0625" width="36.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.802592" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.842981" y="0"> 0</t年代p一个n></text> </g> </g> </svg>,<年代vg height="11.0625" id="M24" style="vertical-align:-0.30096pt;width:36.137501px;" version="1.1" viewbox="0 0 36.137501 11.0625" width="36.137501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.515023" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.555412" y="0"> 0</t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.55" id="M25" style="vertical-align:-2.29482pt;width:36.049999px;" version="1.1" viewbox="0 0 36.049999 13.55" width="36.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.440005" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.480394" y="0"> 1</t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.6125" id="M26" style="vertical-align:-2.34499pt;width:35.262501px;" version="1.1" viewbox="0 0 35.262501 13.6125" width="35.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8148546" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.855244" y="0"> 0</t年代p一个n></text> </g> </g> </svg>是常数。为<年代vg height="13.4875" id="M27" style="vertical-align:-2.34499pt;width:63.362499px;" version="1.1" viewbox="0 0 63.362499 13.4875" width="63.362499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.440005" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.480394" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.307751" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.348141" y="0"> </t年代p一个n></text> </g> </g> </svg>,二次调整的成本。</p><p>gydF4y2Ba作为生产函数,<年代vg height="13.55" id="M28" style="vertical-align:-2.29482pt;width:26.75px;" version="1.1" viewbox="0 0 26.75 13.55" width="26.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.201488" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.141613" y="0"> )</t年代p一个n></text> </g> </g> </svg>,我们可能需要一个生产函数凸凹形像斯科巴提出了还<一个href="#B24">11</一个>),指定以下给我们第一个机制整合进我们的模型。我们也可以使用柯布-道格拉斯生产函数<年代vg height="14.15" id="M29" style="vertical-align:-2.29482pt;width:69.25px;" version="1.1" viewbox="0 0 69.25 14.15" width="69.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.15)"> <g transform="translate(72,-60.68)"> <text transform="matrix(1,0,0,-1,-71.95,63.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.201488" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.141613" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.768442" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.80883" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.085339" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-22.08,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和压力调整资本成本与规模效应。这将提供我们的第二个变体模型。</p><p>gydF4y2Ba自净收益(<一个href="#EEq4">2。4</一个>),减少股息流<年代vg height="7.1875" id="M30" style="vertical-align:-0.13794pt;width:7.3874998px;" version="1.1" viewbox="0 0 7.3874998 7.1875" width="7.3874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1875)"> <g transform="translate(72,-66.25)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>可以是负的,临时预算约束需要进一步从信贷市场贷款,如果有积极的净收益,减少股息,债务可以退休了。</p><p>gydF4y2Ba注意,在上面的一般情况下的调整成本<年代vg height="16.612499" id="M31" style="vertical-align:-2.34499pt;width:36.012501px;" version="1.1" viewbox="0 0 36.012501 16.612499" width="36.012501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6125)"> <g transform="translate(72,-58.71)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.34,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.18,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n></text> </g> </g> </svg>在(<一个href="#EEq4">2。4</一个>),如果我们把<年代vg height="13.55" id="M32" style="vertical-align:-2.29482pt;width:36.049999px;" version="1.1" viewbox="0 0 36.049999 13.55" width="36.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.440005" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.480394" y="0"> 2</t年代p一个n></text> </g> </g> </svg>和<年代vg height="13.6125" id="M33" style="vertical-align:-2.34499pt;width:35.262501px;" version="1.1" viewbox="0 0 35.262501 13.6125" width="35.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8148546" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.855244" y="0"> 0</t年代p一个n></text> </g> </g> </svg>,我们有标准模型与二次调整投资成本。当我们使用本地收益递增的生产函数,凸凹形生产函数,我们将把调整的成本项<年代vg height="16.612499" id="M34" style="vertical-align:-2.34499pt;width:36.012501px;" version="1.1" viewbox="0 0 36.012501 16.612499" width="36.012501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6125)"> <g transform="translate(72,-58.71)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.34,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.18,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n></text> </g> </g> </svg>,还在布鲁克和Milliaris [<一个href="#B8">12</一个>]。</p><p>gydF4y2Ba代表我们的第三个机制,我们假定信贷成本<年代vg height="13.45" id="M35" style="vertical-align:-2.21957pt;width:50.037498px;" version="1.1" viewbox="0 0 50.037498 13.45" width="50.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.915119" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.078618" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.855244" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.056492" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.758579" y="0"> )</t年代p一个n></text> </g> </g> </svg>在(<一个href="#EEq1">2。3</一个>)可能依赖于状态,根据资本存量,<年代vg height="10.7375" id="M36" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和债务水平<年代vg height="10.325" id="M37" style="vertical-align:-0.0pt;width:11.625px;" version="1.1" viewbox="0 0 11.625 10.325" width="11.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>与<年代vg height="14.7125" id="M38" style="vertical-align:-3.2316pt;width:47.525002px;" version="1.1" viewbox="0 0 47.525002 14.7125" width="47.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61.03,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-52.32,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n></text> </g> </g> </svg>和<年代vg height="14.6" id="M39" style="vertical-align:-3.13504pt;width:49.650002px;" version="1.1" viewbox="0 0 49.650002 14.6" width="49.650002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61.03,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-50.62,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n></text> </g> </g> </svg>。但是请注意,如果我们假设信用差价反向取决于净资产和净资产等于资本存量的价值,我们得到我们的模型的一个特例,当只有无风险利率决定了信贷成本。然后我们有一个信贷成本,只取决于一个外生利率和状态方程等债务的进化<年代p一个ncl作为年代=”equation" id="EEq5"> <svg height="17.7125" id="M40" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 17.7125" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.7125)"> <g transform="translate(72,-57.83)"> <text transform="matrix(1,0,0,-1,101.18,64.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̇</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-7.48" y="2.53"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.810209" y="2.53"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9737082" y="2.53"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.887147" y="2.53"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.513977" y="2.53"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.554365" y="2.53"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.105938" y="2.53"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.396149" y="2.53"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.559647" y="2.53"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.473083" y="2.53"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.412247" y="2.53"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="75.752472" y="2.53"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="86.279999" y="2.53"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="90.443497" y="2.53"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="99.308121" y="2.53"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="103.47162" y="2.53"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="107.38506" y="2.53"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="113.62406" y="2.53"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="118.83781" y="2.53"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="130.12802" y="2.53"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="134.29152" y="2.53"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="138.20496" y="2.53"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="142.36845" y="2.53"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="148.60745" y="2.53"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="163.78609" y="2.53"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="175.0638" y="2.53"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="179.22729" y="2.53"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="185.47881" y="2.53"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="193.11813" y="2.53"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="205.15852" y="2.53"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,315.05,58.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,319.92,61.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="144.83" y="-0.15000001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="148.9935" y="-0.15000001"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="155.245" y="-0.15000001"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="158.37074" y="-0.15000001"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="164.62225" y="-0.15000001"> )</t年代p一个n></text> </g> </g> </svg></span>在这种情况下,我们只会考虑横截性条件<年代vg height="17.6875" id="M41" style="vertical-align:-3.21404pt;width:134.35001px;" version="1.1" viewbox="0 0 134.35001 17.6875" width="134.35001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.6875)"> <g transform="translate(72,-57.85)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9516678" y="0"> 米</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-51.1,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.1922078" y="0"> →</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="13.749392" y="0"> ∞</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-26.66,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-21.09,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.572416" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-7.27,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.7020884" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.865587" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.779026" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.405855" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.446243" y="0"> 0</t年代p一个n></text> </g> </g> </svg>随着债务nonexplosiveness条件,关闭模型(<一个href="#EEq1">2。1</一个>)- (<一个href="#EEq1">2。3</一个>)。</p><p>gydF4y2Ba一般来说,我们定义的极限<年代vg height="13.45" id="M42" style="vertical-align:-2.21957pt;width:26.299999px;" version="1.1" viewbox="0 0 26.299999 13.45" width="26.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.7020884" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.865587" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.779026" y="0"> )</t年代p一个n></text> </g> </g> </svg>等于<年代vg height="13.45" id="M43" style="vertical-align:-2.21957pt;width:27.987499px;" version="1.1" viewbox="0 0 27.987499 13.45" width="27.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1892252" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.129351" y="0"> )</t年代p一个n></text> </g> </g> </svg>这里代表的现值借贷约束定义为曲线,而不是一个点。现值<年代vg height="13.45" id="M44" style="vertical-align:-2.21957pt;width:27.987499px;" version="1.1" viewbox="0 0 27.987499 13.45" width="27.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1892252" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.129351" y="0"> )</t年代p一个n></text> </g> </g> </svg>代表公司的债务的能力。在上述情况下,要解决的问题是如何计算最优投资策略和现值<年代vg height="13.45" id="M45" style="vertical-align:-2.21957pt;width:27.987499px;" version="1.1" viewbox="0 0 27.987499 13.45" width="27.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1892252" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.129351" y="0"> )</t年代p一个n></text> </g> </g> </svg>的公司。</p><p>gydF4y2Ba如果利率<年代vg height="13.45" id="M46" style="vertical-align:-2.21957pt;width:93.462502px;" version="1.1" viewbox="0 0 93.462502 13.45" width="93.462502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.014903" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.055292" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.970409" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.133911" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.910538" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.124287" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.826374" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.989876" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.465706" y="0"> </t年代p一个n></text> </g> </g> </svg>是常数(在上述计算未来净收益的现值,我们不需要假设一个特定的固定利率,但现值,<年代vg height="13.45" id="M47" style="vertical-align:-2.21957pt;width:27.987499px;" version="1.1" viewbox="0 0 27.987499 13.45" width="27.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1892252" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.129351" y="0"> )</t年代p一个n></text> </g> </g> </svg>,将最优投资决策,进入信贷成本函数作为参数<年代vg height="13.45" id="M48" style="vertical-align:-2.21957pt;width:97.625px;" version="1.1" viewbox="0 0 97.625 13.45" width="97.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.915119" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.078618" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.855244" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.018744" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.932182" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.09568" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.296928" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.486153" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.649654" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.426277" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.589779" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.50322" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.666718" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="73.830215" y="0"> )</t年代p一个n></text> </g> </g> </svg>在(<一个href="#EEq5">2。5</一个>),那么很容易看到,<年代vg height="13.45" id="M49" style="vertical-align:-2.21957pt;width:27.987499px;" version="1.1" viewbox="0 0 27.987499 13.45" width="27.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1892252" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.129351" y="0"> )</t年代p一个n></text> </g> </g> </svg>是事实上的现值<年代vg height="10.7375" id="M50" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg><span class="equation" id="EEq6"> <svg height="94.849998" id="M51" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 94.849998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,94.85)"> <g transform="translate(72,3.88)"> <text transform="matrix(1,0,0,-1,114.51,54.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.077898" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.241398" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.018023" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.657356" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.697746" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.812912" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.364243" y="0"> x</t年代p一个n></text> <text transform="matrix(1,0,0,-1,167.75,46.53)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,184.3,46.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,191.3,68.19)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-1.25" y="25.530001"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,201.98,54.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,207.55,59.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.572416" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,221.37,54.16)"> <tspan style="font-size: 12.50px; " x="-82.860001" y="28.48"> ̇</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.515023" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.678522" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.54315" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.706648" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.620087" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.859085" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.072834" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.774685" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.938183" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.85162" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.015121" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.25412" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="75.905716" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="79.819153" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="243.38" y="0.1"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="247.5435" y="0.1"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="253.795" y="0.1"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="256.92075" y="0.1"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="263.17224" y="0.1"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-107.42" y="31.209999"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-102.55634" y="31.209999"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-99.43058" y="31.209999"> t</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-95.95475" y="31.209999"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-88.660004" y="31.209999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-79.807877" y="31.209999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-75.644379" y="31.209999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-71.730942" y="31.209999"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-64.091606" y="31.209999"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-52.051216" y="31.209999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-44.36187" y="31.209999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-40.198372" y="31.209999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-36.284931" y="31.209999"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-29.345768" y="31.209999"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-17.993044" y="31.209999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-10.653783" y="31.209999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-1.801659" y="31.209999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="2.36184" y="31.209999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.275279" y="31.209999"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.526779" y="31.209999"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.692919" y="31.209999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.557545" y="31.209999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.721043" y="31.209999"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.972546" y="31.209999"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.611877" y="31.209999"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.652267" y="31.209999"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,294.8,19.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,299.68,22.95)"> <tspan style="font-size: 12.50px; " x="-218.75" y="20.49"> ̇</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="165.07001" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="169.23351" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="175.485" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="178.61075" y="0"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="184.86224" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-226.23" y="23.030001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-214.9523" y="23.030001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-210.78879" y="23.030001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-206.87535" y="23.030001"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-199.23602" y="23.030001"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-187.19563" y="23.030001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-180.64406" y="23.030001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-169.35385" y="23.030001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-165.19035" y="23.030001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-161.27692" y="23.030001"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-154.33775" y="23.030001"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-142.99753" y="23.030001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-138.83403" y="23.030001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-128.3065" y="23.030001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-124.14301" y="23.030001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-115.29088" y="23.030001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-111.12738" y="23.030001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-107.21394" y="23.030001"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-100.96244" y="23.030001"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-95.748695" y="23.030001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-84.470985" y="23.030001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-80.307487" y="23.030001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-76.394051" y="23.030001"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-72.230553" y="23.030001"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-65.278877" y="23.030001"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-53.93866" y="23.030001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-46.036762" y="23.030001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-41.873264" y="23.030001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-37.959827" y="23.030001"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-33.796326" y="23.030001"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-27.557329" y="23.030001"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-12.378688" y="23.030001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-1.100982" y="23.030001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.0625169" y="23.030001"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3140173" y="23.030001"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.95335" y="23.030001"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.993738" y="23.030001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,337.38,-3.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,342.26,-0.08)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="122.49" y="-0.15000001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="126.6535" y="-0.15000001"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="132.905" y="-0.15000001"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="136.03075" y="-0.15000001"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="142.28224" y="-0.15000001"> )</t年代p一个n></text> </g> </g> </svg></span>与<年代vg height="13.45" id="M54" style="vertical-align:-2.21957pt;width:26.8125px;" version="1.1" viewbox="0 0 26.8125 13.45" width="26.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.7766261" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.940125" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.191626" y="0"> )</t年代p一个n></text> </g> </g> </svg>和<年代vg height="13.45" id="M55" style="vertical-align:-2.21957pt;width:29.225px;" version="1.1" viewbox="0 0 29.225 13.45" width="29.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.7020884" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.865587" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.117086" y="0"> )</t年代p一个n></text> </g> </g> </svg>的初始值<年代vg height="10.7375" id="M56" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="10.325" id="M57" style="vertical-align:-0.0pt;width:11.625px;" version="1.1" viewbox="0 0 11.625 10.325" width="11.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。</p><p>gydF4y2Ba这样,然而,当信贷成本是内生的,因此,当我们有<年代vg height="13.45" id="M58" style="vertical-align:-2.21957pt;width:50.037498px;" version="1.1" viewbox="0 0 50.037498 13.45" width="50.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.915119" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.078618" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.855244" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.056492" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.758579" y="0"> )</t年代p一个n></text> </g> </g> </svg>,然后现值本身变得难以治疗。Pontryagin的最大原则是不适合与内生信用成本,解决这个问题,因此我们需要使用动态规划求解的现值和投资策略。我们一步使用动态规划是制定一个模型(<一个href="#EEq1">2。1</一个>)- (<一个href="#EEq1">2。3</一个>)和(<一个href="#EEq6">2。6</一个>)- (<一个href="#EEq6">2。8</一个>)作为Hamilton-Jacobi-Bellman HJB方程。如何做到这一点的一个例子如附录所示<一个href="#sec7">B</一个>。</p><p>gydF4y2Ba的上下文模型,探讨了风险溢价的角色和信贷传播公司大小不均的原因,我们也可以研究“天花板”债务合同的影响及其对公司的影响大小。事实上,信贷限制可能影响投资决策。(假设表单的“天花板”<年代vg height="13.45" id="M59" style="vertical-align:-2.21957pt;width:57.424999px;" version="1.1" viewbox="0 0 57.424999 13.45" width="57.424999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.7020884" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.865587" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.779026" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.405855" y="0"> <</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.446243" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="10.6125" id="M60" style="vertical-align:-0.15048pt;width:11.8625px;" version="1.1" viewbox="0 0 11.8625 10.6125" width="11.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6125)"> <g transform="translate(72,-63.51)"> <text transform="matrix(1,0,0,-1,-71.95,63.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>一个常数,<年代vg height="9.125" id="M61" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。天花板已经明显影响投资动力。要么<年代vg height="13.45" id="M62" style="vertical-align:-2.21957pt;width:57.862499px;" version="1.1" viewbox="0 0 57.862499 13.45" width="57.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.852844" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.893232" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.082458" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.245956" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.022583" y="0"> )</t年代p一个n></text> </g> </g> </svg>,然后天花板太高,因为债务人可能会移动然后破产如果接近上限<年代vg height="13.45" id="M63" style="vertical-align:-2.21957pt;width:58.262501px;" version="1.1" viewbox="0 0 58.262501 13.45" width="58.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.165419" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.205809" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.395033" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.558533" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.335159" y="0"> )</t年代p一个n></text> </g> </g> </svg>。如果<年代vg height="13.45" id="M64" style="vertical-align:-2.21957pt;width:57.862499px;" version="1.1" viewbox="0 0 57.862499 13.45" width="57.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.852844" y="0"> <</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.893232" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.082458" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.245956" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.022583" y="0"> )</t年代p一个n></text> </g> </g> </svg>,那么该公司可能无法通过最优投资决策发展完整的增长潜力。)</p><p>gydF4y2Ba在所有三个cases-locally规模收益递增,非线性调整成本的资本和信贷和信贷约束传播(后两个因信用风险)——最优投资策略和该公司的增长取决于公司的初始大小。我们允许异构企业对他们是如何的方式暴露于上述三个机制。</p><p>gydF4y2Ba我们将表明,阈值,独立的解决路径<年代vg height="13.45" id="M65" style="vertical-align:-2.21957pt;width:27.987499px;" version="1.1" viewbox="0 0 27.987499 13.45" width="27.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1892252" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.129351" y="0"> )</t年代p一个n></text> </g> </g> </svg>不同领域的吸引力。较低的企业资本股票和接触的一个高于机制但是低于某个阈值将是最佳的公司合同,而大公司高于某个阈值可以选择一个投资策略扩大。此外,我们在研究中可以承认各种路径股息支付,<年代vg height="7.1875" id="M66" style="vertical-align:-0.13794pt;width:7.3874998px;" version="1.1" viewbox="0 0 7.3874998 7.1875" width="7.3874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1875)"> <g transform="translate(72,-66.25)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>、投资策略和现值的影响曲线<年代vg height="13.45" id="M67" style="vertical-align:-2.21957pt;width:27.987499px;" version="1.1" viewbox="0 0 27.987499 13.45" width="27.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1892252" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.129351" y="0"> )</t年代p一个n></text> </g> </g> </svg>我们的不同的模型变体。(后者方面研究了Grune et al。<一个href="#B15">18</一个>]。)</p><gydF4y2Bah4 id="numerical-study-on-the-dynamics-of-firm-size-distribution">3所示。公司大小分布的数值研究动态</gydF4y2Bah4> <p>接下来,我们目前的数值结果不同规格的生产功能,调整成本的资本,不完善的资本市场。在本节中,我们指定参数<年代vg height="11.1" id="M68" style="vertical-align:-0.17555pt;width:56.037498px;" version="1.1" viewbox="0 0 56.037498 11.1" width="56.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1)"> <g transform="translate(72,-63.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.802592" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.842981" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.094481" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.22023" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.471729" y="0"> 5</t年代p一个n></text> </g> </g> </svg>和<年代vg height="13.6125" id="M69" style="vertical-align:-2.34499pt;width:46.987499px;" version="1.1" viewbox="0 0 46.987499 13.6125" width="46.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8148546" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.855244" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.106745" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.232494" y="0"> 3</t年代p一个n></text> </g> </g> </svg>。其他参数将下面的模型具体指定。当然,(注意,我们可以选择另一个来源的异质性企业,即企业通过假设不同的技术参数。这可能是另一个的研究我们不会追求。除非另外注明,我们使用的股息流<年代vg height="13.45" id="M70" style="vertical-align:-2.21957pt;width:49.112499px;" version="1.1" viewbox="0 0 49.112499 13.45" width="49.112499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.188745" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3522444" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.265683" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.892513" y="0"> ≡</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.932903" y="0"> 0</t年代p一个n></text> </g> </g> </svg>在我们的实验中放松Grune et al。<一个href="#B15">18</一个>]。</p><p>gydF4y2Ba至于数值程序,我们使用两种算法。第一是一个动态规划算法在Grune et al。<一个href="#B15">18</一个>),应用于Grune Semmler (<一个href="#B14">21</一个>]。下面的例子是计算不同<年代vg height="10.8875" id="M71" style="vertical-align:-0.13794pt;width:19.987499px;" version="1.1" viewbox="0 0 19.987499 10.8875" width="19.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8875)"> <g transform="translate(72,-63.29)"> <text transform="matrix(1,0,0,-1,-71.95,63.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.7766261" y="0"> ′</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.389993" y="0"> </t年代p一个n></text> </g> </g> </svg>在紧凑的时间间隔<年代vg height="13.125" id="M72" style="vertical-align:-1.95624pt;width:32.674999px;" version="1.1" viewbox="0 0 32.674999 13.125" width="32.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.125)"> <g transform="translate(72,-61.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.414999" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.616247" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.867746" y="0"> ]</t年代p一个n></text> </g> </g> </svg>在控制范围<年代vg height="13.8" id="M73" style="vertical-align:-2.34499pt;width:77.675003px;" version="1.1" viewbox="0 0 77.675003 13.8" width="77.675003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.8)"> <g transform="translate(72,-60.96)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3269978" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.367388" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.530886" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.782387" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.996136" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.247639" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.373386" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.624886" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.876389" y="0"> ]</t年代p一个n></text> </g> </g> </svg>。(在所有的实验中,更大的控制范围并不会产生不同的结果。)为了解决这个问题(<一个href="#EEq6">2。6</一个>)- (<一个href="#EEq6">2。8</一个>),一个动态算法被用于计算时间步长<年代vg height="11.1" id="M74" style="vertical-align:-0.17555pt;width:55.887501px;" version="1.1" viewbox="0 0 55.887501 11.1" width="55.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1)"> <g transform="translate(72,-63.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.677562" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.717951" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.969452" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.0952" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.346703" y="0"> 5</t年代p一个n></text> </g> </g> </svg>与39节点和一个初始网格。最后适应网格由130个节点。控制的范围值是使用101 equidistributed离散值。</p><p>gydF4y2Ba第二个算法,计算域的吸引力问题(<一个href="#EEq1">2。1</一个>)- (<一个href="#EEq1">2。3</一个>),我们使用了时间步<年代vg height="11.1" id="M75" style="vertical-align:-0.17555pt;width:48.0625px;" version="1.1" viewbox="0 0 48.0625 11.1" width="48.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1)"> <g transform="translate(72,-63.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.677562" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.717951" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.969452" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.0952" y="0"> 5</t年代p一个n></text> </g> </g> </svg>,为了生成离散时间模型,我们使用一个高度精确的外推法。对于这个算法,控制的范围值是使用51 equidistributed离散值。域覆盖的网格被选为<年代vg height="13.125" id="M76" style="vertical-align:-1.95624pt;width:82.175003px;" version="1.1" viewbox="0 0 82.175003 13.125" width="82.175003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.125)"> <g transform="translate(72,-61.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.414999" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.616247" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.867746" y="0"> ]</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.806911" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.597" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.760502" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.012001" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.213249" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.464748" y="0"> ]</t年代p一个n></text> </g> </g> </svg>,上面的价值<年代vg height="15.7125" id="M77" style="vertical-align:-0.17555pt;width:38.825001px;" version="1.1" viewbox="0 0 38.825001 15.7125" width="38.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.7125)"> <g transform="translate(72,-59.43)"> <g> <path d="m -71.95,70.71 9.2,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.665539" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.705929" y="0"> 3</t年代p一个n></text> </g> </g> </svg>伴随着价值<年代vg height="11.75" id="M78" style="vertical-align:-0.17555pt;width:40.9375px;" version="1.1" viewbox="0 0 40.9375 11.75" width="40.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.75)"> <g transform="translate(72,-62.6)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.14,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.59,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 3</t年代p一个n></text> </g> </g> </svg>为了实现使用限制<年代vg height="15.75" id="M79" style="vertical-align:-4.06421pt;width:106.7px;" version="1.1" viewbox="0 0 106.7 15.75" width="106.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.75)"> <g transform="translate(72,-59.4)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.863667" y="0"> u</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.115167" y="0"> p</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-50.42,60.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7393761" y="0"> ≥</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7344961" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-34.72,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.7020884" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.865587" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.779026" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.405855" y="0"> <</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.446243" y="0"> ∞</t年代p一个n></text> </g> </g> </svg>。与1024个细胞初始网格被选中,而最终适应网格由大约100000到500000个细胞根据例子。对于这个算法,下面的数字总是显示设置<年代vg height="14.2375" id="M80" style="vertical-align:-3.13504pt;width:18.325001px;" version="1.1" viewbox="0 0 18.325001 14.2375" width="18.325001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.02,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Γ</t年代p一个n></text> </g> </g> </svg>接近现值的曲线<年代vg height="13.45" id="M81" style="vertical-align:-2.21957pt;width:27.987499px;" version="1.1" viewbox="0 0 27.987499 13.45" width="27.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1892252" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.129351" y="0"> )</t年代p一个n></text> </g> </g> </svg>。回想一下,这组的宽度给空间离散化误差的估计。</p><p>gydF4y2Ba我们首先开始数值例子与常见的二次调整成本的投资和规模收益不变。这给了我们通常情况下的一个独特的(积极的)稳态和哪些公司规模预测是正态分布。在接下来的例子中,我们建立了上面提到的三个机制引起多个域的吸引力,因此公司规模的多峰分布。</p><gydF4y2Bah5 id="sec3.1">3.1。规模收益不变与二次调整成本</gydF4y2Bah5> <p>常见的情况通常发现在文学,以及代表(<一个href="#EEq6">2。6</一个>)- (<一个href="#EEq6">2。8</一个>),我们假设一个凹生产函数<年代vg height="14.15" id="M82" style="vertical-align:-2.29482pt;width:69.25px;" version="1.1" viewbox="0 0 69.25 14.15" width="69.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.15)"> <g transform="translate(72,-60.68)"> <text transform="matrix(1,0,0,-1,-71.95,63.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.201488" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.141613" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.768442" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.80883" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.085339" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-22.08,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="11.0625" id="M83" style="vertical-align:-0.30096pt;width:63.349998px;" version="1.1" viewbox="0 0 63.349998 11.0625" width="63.349998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.7148314" y="0"> <</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.75522" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.282745" y="0"> <</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.323135" y="0"> 1</t年代p一个n></text> </g> </g> </svg>和二次调整的成本。模型参数,我们指定<年代vg height="11.1" id="M84" style="vertical-align:-0.17555pt;width:47.862499px;" version="1.1" viewbox="0 0 47.862499 11.1" width="47.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1)"> <g transform="translate(72,-63.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.515023" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.555412" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.806911" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.932661" y="0"> 5</t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.55" id="M85" style="vertical-align:-2.29482pt;width:36.049999px;" version="1.1" viewbox="0 0 36.049999 13.55" width="36.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.440005" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.480394" y="0"> 2</t年代p一个n></text> </g> </g> </svg>,<年代vg height="11.1" id="M86" style="vertical-align:-0.17555pt;width:46.400002px;" version="1.1" viewbox="0 0 46.400002 11.1" width="46.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1)"> <g transform="translate(72,-63.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3397408" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.380131" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.63163" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.75738" y="0"> 5</t年代p一个n></text> </g> </g> </svg>,<年代vg height="11.0375" id="M87" style="vertical-align:-0.27588pt;width:54.712502px;" version="1.1" viewbox="0 0 54.712502 11.0375" width="54.712502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.7398367" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.780226" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.031727" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.157476" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.408978" y="0"> 9</t年代p一个n></text> </g> </g> </svg>,<年代vg height="10.9125" id="M88" style="vertical-align:-0.17555pt;width:47.237499px;" version="1.1" viewbox="0 0 47.237499 10.9125" width="47.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.014903" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.055292" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.306791" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.432543" y="0"> 1</t年代p一个n></text> </g> </g> </svg>。这指定最简单的动态决策问题与调整成本经常被用于经济和可以显示只展示一个积极的稳态平衡<年代vg height="11.7875" id="M89" style="vertical-align:-0.13794pt;width:14.9375px;" version="1.1" viewbox="0 0 14.9375 11.7875" width="14.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.7875)"> <g transform="translate(72,-62.57)"> <text transform="matrix(1,0,0,-1,-71.95,62.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.17,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> </g> </g> </svg>和正态分布公司大小。代表公司在这里的现值只是由净收益流的现值的公司,因为我们假设一个常数信贷成本所示(<一个href="#EEq6">2。8</一个>)。</p><p>gydF4y2Ba计算最优投资策略和公司价值,我们可以使用我们的第一个程序,动态规划(DP)算法。公司价值是由最优值函数图<一个href="//www.newsama.com/journals/aor/2011/269239/fig1/" target="_blank">1</一个>和动态决策问题的解决路径,(例如,在Gruene和Semmler [<一个href="#B14">21</一个>]。)的投资决策,因此最优增长(或收缩)的公司是由最优控制图<一个href="//www.newsama.com/journals/aor/2011/269239/fig1/" target="_blank">1</一个>。(独特的)积极的稳定状态<年代vg height="11.9625" id="M90" style="vertical-align:-0.27588pt;width:61.674999px;" version="1.1" viewbox="0 0 61.674999 11.9625" width="61.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.9625)"> <g transform="translate(72,-62.43)"> <text transform="matrix(1,0,0,-1,-71.95,62.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.17,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.62,62.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.405136" y="0"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.656635" y="0"> 5</t年代p一个n></text> </g> </g> </svg>资本存量,低于公司将增长,上面是适合该公司缩减资本存量。允许冲击的大小公司,公司规模的正态分布。</p><gydF4y2Badiv class="floats-partial-section partial-carousel-wrapper" data-section="fig1"> <div class="floats-partial-content fig-content-fig1"> <div class="partial-carousel--single-image"> <img alt="" name="269239.fig.001" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.001.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图1</年代p一个n><一个一个ria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/aor/2011/269239/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 二次调整资本成本。</t一个ble> </div> </div> </div> <h5 id="sec3.2">3.2。规模收益递增和调整成本与规模效应</gydF4y2Bah5> <p>接下来,我们数值求解规模收益递增的情况下,调整成本与规模效应。虽然,见Grune et al。<一个href="#B15">18</一个>),这是两个独立的原因产生多个域的吸引力,我们将演示两种机制在一个单一的数值。我们假设(<一个href="#EEq1">2。1</一个>)- (<一个href="#EEq1">2。3</一个>),但我们仍然认为公司面临着持续的信贷成本<年代vg height="13.45" id="M91" style="vertical-align:-2.21957pt;width:89.125px;" version="1.1" viewbox="0 0 89.125 13.45" width="89.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.915119" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.078618" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.855244" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.056492" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.758579" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.397915" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.438301" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.989876" y="0"> </t年代p一个n></text> </g> </g> </svg>在(<一个href="#EEq6">2。8</一个>)。我们再次可以使用DP算法为了解决贴现无限视界问题(<一个href="#EEq1">2。1</一个>)- (<一个href="#EEq1">2。3</一个>)。图<一个href="//www.newsama.com/journals/aor/2011/269239/fig2/" target="_blank">2</一个>给出了相应的最优值函数的现值代表典型的公司,<年代vg height="13.45" id="M92" style="vertical-align:-2.21957pt;width:27.987499px;" version="1.1" viewbox="0 0 27.987499 13.45" width="27.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1892252" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.129351" y="0"> )</t年代p一个n></text> </g> </g> </svg>(图上)和相关的最优控制,投资决策,反馈形式(低图);参见图<一个href="//www.newsama.com/journals/aor/2011/269239/fig2/" target="_blank">2</一个>。</p><gydF4y2Badiv class="floats-partial-section partial-carousel-wrapper" data-section="fig2"> <div class="floats-partial-content fig-content-fig2"> <div class="partial-carousel--single-image"> <img alt="" name="269239.fig.002" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.002.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图2</年代p一个n><一个一个ria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/aor/2011/269239/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 最优值函数和最优投资。</t一个ble> </div> </div> </div> <p>对于我们的参数,该模型并不一定有一个独特的积极的稳态平衡。可以有多个域的吸引企业暴露于收益递增和/或调整成本与规模效应。一个特定的公司的命运,当暴露在规模收益递增和/或调整成本与规模效应,然后将取决于初始资本存量大小,<年代vg height="10.7375" id="M93" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。有一个阈值,<年代vg height="7.1875" id="M94" style="vertical-align:-0.13794pt;width:7px;" version="1.1" viewbox="0 0 7 7.1875" width="7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1875)"> <g transform="translate(72,-66.25)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,在<年代vg height="12.6625" id="M95" style="vertical-align:-0.17555pt;width:71.262497px;" version="1.1" viewbox="0 0 71.262497 12.6625" width="71.262497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.6625)"> <g transform="translate(72,-61.87)"> <text transform="matrix(1,0,0,-1,-71.95,62.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.17,67.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.21,62.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.291889" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.417639" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.66914" y="0"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.920639" y="0"> 7</t年代p一个n></text> </g> </g> </svg>清晰可见的最优投资策略,这是不连续的。</p><p>gydF4y2Ba因此,公司面临着一个不连续的动态决策问题。公司的资本存量的初始值<年代vg height="15.2125" id="M96" style="vertical-align:-2.21957pt;width:62.799999px;" version="1.1" viewbox="0 0 62.799999 15.2125" width="62.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.2125)"> <g transform="translate(72,-59.83)"> <text transform="matrix(1,0,0,-1,-71.95,62.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.7766261" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.940125" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.191626" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.818455" y="0"> <</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.858845" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-28.31,67.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</t年代p一个n></text> </g> </g> </svg>,它是最佳的收缩资本存量<年代vg height="11.8375" id="M97" style="vertical-align:-0.17555pt;width:42.137501px;" version="1.1" viewbox="0 0 42.137501 11.8375" width="42.137501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.8375)"> <g transform="translate(72,-62.53)"> <text transform="matrix(1,0,0,-1,-71.95,62.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.17,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.62,62.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n></text> </g> </g> </svg>资本存量的初始值<年代vg height="15.2125" id="M98" style="vertical-align:-2.21957pt;width:62.799999px;" version="1.1" viewbox="0 0 62.799999 15.2125" width="62.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.2125)"> <g transform="translate(72,-59.83)"> <text transform="matrix(1,0,0,-1,-71.95,62.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.7766261" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.940125" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.191626" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.818455" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.858845" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-28.31,67.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</t年代p一个n></text> </g> </g> </svg>最优投资将导致吸引力的领域<年代vg height="11.9625" id="M99" style="vertical-align:-0.27588pt;width:75.212502px;" version="1.1" viewbox="0 0 75.212502 11.9625" width="75.212502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.9625)"> <g transform="translate(72,-62.43)"> <text transform="matrix(1,0,0,-1,-71.95,62.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.17,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.5772958" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-52.05,62.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.405136" y="0"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.656635" y="0"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.908134" y="0"> 6</t年代p一个n></text> </g> </g> </svg>。总之,投资公司的左边<年代vg height="12.6125" id="M100" style="vertical-align:-0.13794pt;width:16.7125px;" version="1.1" viewbox="0 0 16.7125 12.6125" width="16.7125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.6125)"> <g transform="translate(72,-61.91)"> <text transform="matrix(1,0,0,-1,-71.95,62.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.17,67.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</t年代p一个n></text> </g> </g> </svg>低于<年代vg height="10.7375" id="M101" style="vertical-align:-0.13794pt;width:17.775px;" version="1.1" viewbox="0 0 17.775 10.7375" width="17.775" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.3267579" y="0"> </t年代p一个n></text> </g> </g> </svg>,使资本存量减少,而投资公司的权利<年代vg height="12.6125" id="M102" style="vertical-align:-0.13794pt;width:16.7125px;" version="1.1" viewbox="0 0 16.7125 12.6125" width="16.7125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.6125)"> <g transform="translate(72,-61.91)"> <text transform="matrix(1,0,0,-1,-71.95,62.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.17,67.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</t年代p一个n></text> </g> </g> </svg>大于<年代vg height="10.7375" id="M103" style="vertical-align:-0.13794pt;width:17.775px;" version="1.1" viewbox="0 0 17.775 10.7375" width="17.775" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.3267579" y="0"> </t年代p一个n></text> </g> </g> </svg>并让资本存量增加。在<年代vg height="12.6125" id="M104" style="vertical-align:-0.13794pt;width:16.7125px;" version="1.1" viewbox="0 0 16.7125 12.6125" width="16.7125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.6125)"> <g transform="translate(72,-61.91)"> <text transform="matrix(1,0,0,-1,-71.95,62.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.17,67.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</t年代p一个n></text> </g> </g> </svg>、投资公司然后跳跃。在这种情况下,多个域的吸引力存在双峰分布的公司有不同的增长率预计将不同大小的类。(的上尾分布可能会表现出帕累托分布(幂律),而下方会显示(日志)正态分布)。</p><gydF4y2Bah5 id="sec3.3">3.3。资本市场和信贷传播</gydF4y2Bah5> <p>可以获得相似的结果如果有不同的信用差价,和公司必须支付的风险溢价,或可能会有信贷约束公司的投资。这也可能导致多个域的吸引力。让我们假定信贷成本<年代vg height="13.45" id="M105" style="vertical-align:-2.21957pt;width:50.037498px;" version="1.1" viewbox="0 0 50.037498 13.45" width="50.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.915119" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.078618" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.855244" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.056492" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.758579" y="0"> )</t年代p一个n></text> </g> </g> </svg>是内生取决于净资产。</p><p>gydF4y2Ba之前,我们已经假定风险溢价是积极相关违约成本和逆相关借款人资产净值。净资产被定义为公司的抵押品的价值(流动性)资本存量少代理的杰出的义务。在伯南克et al。<一个href="#B7">17</一个>),我们衡量风险溢价之间的反向关系和净资产等功能<年代p一个ncl作为年代=”equation" id="EEq9"> <svg height="37.950001" id="M106" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 37.950001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,37.95)"> <g transform="translate(72,-41.64)"> <text transform="matrix(1,0,0,-1,96.43,57.3)"> <tspan style="font-size: 12.50px; " x="133.28" y="-9.1400003"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.115887" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.144012" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.307512" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.220951" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.459949" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.673698" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.963909" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.127407" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.040848" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="70.204346" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="77.843681" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,236.76,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <g> <path d="m 187.51,60.42 96.33,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,187.51,43.74)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,200.41,43.13)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,208.06,46.26)"> <tspan style="font-size: 12.50px; " x="64.099998" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.193544" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.357044" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.270481" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.50948" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.985313" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.849941" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.013439" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.92688" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,278.01,53.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,285.03,57.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.5515718" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.829279" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.992777" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.906216" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.157715" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="179.72" y="3.6099999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="183.8835" y="3.6099999"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="190.13499" y="3.6099999"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="193.26074" y="3.6099999"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="199.51225" y="3.6099999"> )</t年代p一个n></text> </g> </g> </svg></span>与<年代vg height="13.45" id="M107" style="vertical-align:-2.21957pt;width:80.637497px;" version="1.1" viewbox="0 0 80.637497 13.45" width="80.637497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.915119" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.078618" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.855244" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.018744" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.932182" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.09568" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.296928" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.999016" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.162518" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.075954" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.239452" y="0"> )</t年代p一个n></text> </g> </g> </svg>信贷成本取决于净资产,<年代vg height="13.45" id="M108" style="vertical-align:-2.21957pt;width:115.7125px;" version="1.1" viewbox="0 0 115.7125 13.45" width="115.7125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.640053" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.803552" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.716991" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.343821" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.384209" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.160835" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.324333" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.237774" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.176937" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.517159" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="80.219246" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="84.382744" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="88.296188" y="0"> )</t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.45" id="M109" style="vertical-align:-2.21957pt;width:23.9px;" version="1.1" viewbox="0 0 23.9 13.45" width="23.9" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.7766261" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.940125" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.853564" y="0"> )</t年代p一个n></text> </g> </g> </svg>资本存量和<年代vg height="13.45" id="M110" style="vertical-align:-2.21957pt;width:26.299999px;" version="1.1" viewbox="0 0 26.299999 13.45" width="26.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.7020884" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.865587" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.779026" y="0"> )</t年代p一个n></text> </g> </g> </svg>随着债务。的参数是<年代vg height="14.6" id="M111" style="vertical-align:-3.13504pt;width:79.6875px;" version="1.1" viewbox="0 0 79.6875 14.6" width="79.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.9,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.02,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-47.76,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-42.89,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.291409" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.331799" y="0"> 0</t年代p一个n></text> </g> </g> </svg>,<年代vg height="10.7375" id="M112" style="vertical-align:-0.13794pt;width:8.3125px;" version="1.1" viewbox="0 0 8.3125 10.7375" width="8.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是无风险利率。在下面的分析和数值模型的研究中,我们假定的风险溢价将是零<年代vg height="13.45" id="M113" style="vertical-align:-2.21957pt;width:71.887497px;" version="1.1" viewbox="0 0 71.887497 13.45" width="71.887497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.640053" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.803552" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.716991" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.343821" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.384209" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.160835" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.324333" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.237774" y="0"> )</t年代p一个n></text> </g> </g> </svg>,因此,在极限情况下,<年代vg height="13.45" id="M114" style="vertical-align:-2.21957pt;width:53.5px;" version="1.1" viewbox="0 0 53.5 13.45" width="53.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.7020884" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.865587" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.779026" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.405855" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.446243" y="0"> 0</t年代p一个n></text> </g> </g> </svg>,借款利率是无风险利率。虽然这可能发生小规模公司,借贷利率接近于无风险利率更可能保持大规模的公司。(见Gertler和吉尔<一个href="#B12">19</一个>]。)</p><p>gydF4y2Ba一般来说,不可能把上述问题转化为一个标准的无限的地平线最优控制问题对于我们公司的原型;因此,我们将使用我们的第二个过程中,该算法的计算域的景点Grune et al。<一个href="#B15">18</一个>),并进行实验不同形状的信贷成本函数。</p><p>gydF4y2Ba内生信用成本函数(<一个href="#EEq9">3.1</一个>),我们指定<年代vg height="13.55" id="M115" style="vertical-align:-2.29482pt;width:36.849998px;" version="1.1" viewbox="0 0 36.849998 13.55" width="36.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.077658" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.118048" y="0"> 2</t年代p一个n></text> </g> </g> </svg>。考虑到我们想要的<年代vg height="10.7375" id="M116" style="vertical-align:-0.13794pt;width:8.3125px;" version="1.1" viewbox="0 0 8.3125 10.7375" width="8.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>无风险利率,我们获得的条件<年代vg height="17.887501" id="M117" style="vertical-align:-3.13504pt;width:103.45px;" version="1.1" viewbox="0 0 103.45 17.887501" width="103.45" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8875)"> <g transform="translate(72,-57.69)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.9,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.02,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-45.33,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-37.68,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.591721" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-15.92,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-7.57,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代p一个n></text> </g> </g> </svg>,因此<年代vg height="17.887501" id="M118" style="vertical-align:-3.13504pt;width:91.300003px;" version="1.1" viewbox="0 0 91.300003 17.887501" width="91.300003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8875)"> <g transform="translate(72,-57.69)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.9,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.55,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.191385" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-33.3,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-25.65,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.591721" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-3.89,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>。请注意,对于<年代vg height="11.0375" id="M119" style="vertical-align:-3.13504pt;width:57.875px;" version="1.1" viewbox="0 0 57.875 11.0375" width="57.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,66.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.9,63.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.47,66.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> →</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.12911" y="0"> ∞</t年代p一个n></text> </g> </g> </svg>和<年代vg height="12.3" id="M120" style="vertical-align:-1.29163pt;width:66.0625px;" version="1.1" viewbox="0 0 66.0625 12.3" width="66.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.3)"> <g transform="translate(72,-62.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.7148314" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.75522" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.933144" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.97353" y="0"> </t年代p一个n></text> </g> </g> </svg>,一个获得<年代vg height="13.45" id="M121" style="vertical-align:-2.21957pt;width:89.125px;" version="1.1" viewbox="0 0 89.125 13.45" width="89.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.915119" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.078618" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.855244" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.056492" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.758579" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.397915" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.438301" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.989876" y="0"> </t年代p一个n></text> </g> </g> </svg>从一节,即模型。为了比较这两个模型变异我们用公式<年代vg height="19.0375" id="M122" style="vertical-align:-4.22832pt;width:133.6875px;" version="1.1" viewbox="0 0 133.6875 19.0375" width="133.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.0375)"> <g transform="translate(72,-56.77)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.915119" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.078618" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.855244" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.056492" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.758579" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.397915" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.438301" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.601803" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-5.29,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-0.42,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,10.11,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.21"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,14.98,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.715071" y="0"> </t年代p一个n></text> </g> </g> </svg>为<年代vg height="10.9375" id="M123" style="vertical-align:-0.30096pt;width:38.862499px;" version="1.1" viewbox="0 0 38.862499 10.9375" width="38.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9375)"> <g transform="translate(72,-63.25)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.165419" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.205809" y="0"> </t年代p一个n></text> </g> </g> </svg>。(小的值<年代vg height="10.925" id="M124" style="vertical-align:-3.13504pt;width:15.0375px;" version="1.1" viewbox="0 0 15.0375 10.925" width="15.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.9,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>,事实证明,现值曲线满足<年代vg height="13.45" id="M125" style="vertical-align:-2.21957pt;width:55.849998px;" version="1.1" viewbox="0 0 55.849998 13.45" width="55.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1892252" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.129351" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.75618" y="0"> <</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.79657" y="0"> </t年代p一个n></text> </g> </g> </svg>;因此,这种变化的公式没有影响<年代vg height="13.45" id="M126" style="vertical-align:-2.21957pt;width:27.987499px;" version="1.1" viewbox="0 0 27.987499 13.45" width="27.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1892252" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.129351" y="0"> )</t年代p一个n></text> </g> </g> </svg>。)</p><p>gydF4y2Ba图<一个href="//www.newsama.com/journals/aor/2011/269239/fig3/" target="_blank">3</一个>展示了各自的现值曲线<年代vg height="13.45" id="M127" style="vertical-align:-2.21957pt;width:27.987499px;" version="1.1" viewbox="0 0 27.987499 13.45" width="27.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1892252" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.129351" y="0"> )</t年代p一个n></text> </g> </g> </svg>条件下<年代vg height="15.75" id="M128" style="vertical-align:-4.06421pt;width:106.7px;" version="1.1" viewbox="0 0 106.7 15.75" width="106.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.75)"> <g transform="translate(72,-59.4)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.863667" y="0"> u</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.115167" y="0"> p</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-50.42,60.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7393761" y="0"> ≥</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7344961" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-34.72,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.7020884" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.865587" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.779026" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.405855" y="0"> <</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.446243" y="0"> ∞</t年代p一个n></text> </g> </g> </svg>为<年代vg height="14.6" id="M129" style="vertical-align:-3.13504pt;width:94.337502px;" version="1.1" viewbox="0 0 94.337502 14.6" width="94.337502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.9,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.55,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.530886" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.782387" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.996136" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.247639" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.499138" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.712887" y="0"> 1</t年代p一个n></text> </g> </g> </svg>(从上到下)和相应的<年代vg height="17.887501" id="M130" style="vertical-align:-3.13504pt;width:91.300003px;" version="1.1" viewbox="0 0 91.300003 17.887501" width="91.300003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8875)"> <g transform="translate(72,-57.69)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.9,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.55,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.191385" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-33.3,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-25.65,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.591721" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-3.89,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>。</p><gydF4y2Badiv class="floats-partial-section partial-carousel-wrapper" data-section="fig3"> <div class="floats-partial-content fig-content-fig3"> <div class="partial-carousel--single-image"> <img alt="" name="269239.fig.003" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.003.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图3</年代p一个n><一个一个ria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/aor/2011/269239/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="13.45" id="M131" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 27.987499 13.45" width="27.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1892252" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.129351" y="0"> )</t年代p一个n></text> </g> </g> </svg> <svg height="10.925" id="M132" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 15.0375 10.925" width="15.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.9,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg> <table> 现值曲线gydF4y2Ba为不同的gydF4y2Ba。</t一个ble> </div> </div> </div> <p>为<年代vg height="14.6" id="M133" style="vertical-align:-3.13504pt;width:57.862499px;" version="1.1" viewbox="0 0 57.862499 14.6" width="57.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.9,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.55,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.530886" y="0"> 0</t年代p一个n></text> </g> </g> </svg>的轨迹曲线<年代vg height="13.45" id="M134" style="vertical-align:-2.21957pt;width:27.987499px;" version="1.1" viewbox="0 0 27.987499 13.45" width="27.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1892252" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.129351" y="0"> )</t年代p一个n></text> </g> </g> </svg>显示几乎相同的行为最优轨迹在前一节中:存在一个阈值(现在<年代vg height="12.6625" id="M135" style="vertical-align:-0.17555pt;width:63.450001px;" version="1.1" viewbox="0 0 63.450001 12.6625" width="63.450001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.6625)"> <g transform="translate(72,-61.87)"> <text transform="matrix(1,0,0,-1,-71.95,62.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.17,67.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.21,62.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.291889" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.417639" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.66914" y="0"> 2</t年代p一个n></text> </g> </g> </svg>)和两个稳定的吸引域<年代vg height="11.8375" id="M136" style="vertical-align:-0.17555pt;width:42.137501px;" version="1.1" viewbox="0 0 42.137501 11.8375" width="42.137501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.8375)"> <g transform="translate(72,-62.53)"> <text transform="matrix(1,0,0,-1,-71.95,62.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.17,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.62,62.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n></text> </g> </g> </svg>和<年代vg height="11.9625" id="M137" style="vertical-align:-0.27588pt;width:67.400002px;" version="1.1" viewbox="0 0 67.400002 11.9625" width="67.400002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.9625)"> <g transform="translate(72,-62.43)"> <text transform="matrix(1,0,0,-1,-71.95,62.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.17,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.5772958" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-52.05,62.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.405136" y="0"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.656635" y="0"> 9</t年代p一个n></text> </g> </g> </svg>。我们的数值解表明,减少的值<年代vg height="14.6" id="M138" style="vertical-align:-3.13504pt;width:57.862499px;" version="1.1" viewbox="0 0 57.862499 14.6" width="57.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.9,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.55,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.530886" y="0"> 0</t年代p一个n></text> </g> </g> </svg>的阈值<年代vg height="12.6125" id="M139" style="vertical-align:-0.13794pt;width:16.7125px;" version="1.1" viewbox="0 0 16.7125 12.6125" width="16.7125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.6125)"> <g transform="translate(72,-61.91)"> <text transform="matrix(1,0,0,-1,-71.95,62.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.17,67.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</t年代p一个n></text> </g> </g> </svg>(即第一次增加。,米oves to the right) and the stable domain of attraction<年代vg height="11.7875" id="M140" style="vertical-align:-0.13794pt;width:20.6625px;" version="1.1" viewbox="0 0 20.6625 11.7875" width="20.6625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.7875)"> <g transform="translate(72,-62.57)"> <text transform="matrix(1,0,0,-1,-71.95,62.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.17,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.5772958" y="0"> ∗</t年代p一个n></text> </g> </g> </svg>减少(即。,米oves to the left) until they meet at about<年代vg height="14.6" id="M141" style="vertical-align:-3.13504pt;width:50.049999px;" version="1.1" viewbox="0 0 50.049999 14.6" width="50.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.9,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.55,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> 1</t年代p一个n></text> </g> </g> </svg>。较小的值<年代vg height="10.925" id="M142" style="vertical-align:-3.13504pt;width:15.0375px;" version="1.1" viewbox="0 0 15.0375 10.925" width="15.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.9,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>,存在一个平衡<年代vg height="11.8375" id="M143" style="vertical-align:-0.17555pt;width:42.137501px;" version="1.1" viewbox="0 0 42.137501 11.8375" width="42.137501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.8375)"> <g transform="translate(72,-62.53)"> <text transform="matrix(1,0,0,-1,-71.95,62.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.17,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.62,62.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n></text> </g> </g> </svg>所有资本存量规模稳定。</p><p>gydF4y2Ba后者的离散值<年代vg height="14.6" id="M144" style="vertical-align:-3.13504pt;width:50.049999px;" version="1.1" viewbox="0 0 50.049999 14.6" width="50.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.9,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.55,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代p一个n></text> </g> </g> </svg>没有阈值可观测的,存在唯一的吸引域<年代vg height="11.8375" id="M145" style="vertical-align:-0.17555pt;width:42.137501px;" version="1.1" viewbox="0 0 42.137501 11.8375" width="42.137501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.8375)"> <g transform="translate(72,-62.53)"> <text transform="matrix(1,0,0,-1,-71.95,62.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.17,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.62,62.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n></text> </g> </g> </svg>这是稳定的。这种行为的原因在于,对于这样一个小<年代vg height="10.925" id="M146" style="vertical-align:-3.13504pt;width:15.0375px;" version="1.1" viewbox="0 0 15.0375 10.925" width="15.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.9,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>、信贷变得更昂贵;因此,对于这个小<年代vg height="10.925" id="M147" style="vertical-align:-3.13504pt;width:15.0375px;" version="1.1" viewbox="0 0 15.0375 10.925" width="15.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.9,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>,它不再是最优的任何规模企业——资本股票借大量增加资本存量对于一个给定的初始大小的公司;相反,它是缩小最优资本存量为零。因此,用小<年代vg height="10.925" id="M148" style="vertical-align:-3.13504pt;width:15.0375px;" version="1.1" viewbox="0 0 15.0375 10.925" width="15.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.9,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>,因此大型借贷成本,它是任何公司的尺寸,这是对于任何初始资本存量,优化缩减资本存量,公司将表现出负增长率。</p><gydF4y2Bah5 id="sec3.4">3.4。资本市场和信贷约束</gydF4y2Bah5> <p>另一方面,经常有对公司的投资决策债务上限,定义为资本存量的一小部分。这是当一个公司的借贷约束。对于一个特定的<年代vg height="13.45" id="M149" style="vertical-align:-2.21957pt;width:50.037498px;" version="1.1" viewbox="0 0 50.037498 13.45" width="50.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.915119" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.078618" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.855244" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.056492" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.758579" y="0"> )</t年代p一个n></text> </g> </g> </svg>从(<一个href="#EEq9">3.1</一个>债务上限),我们可以测试什么影响对公司增长和公司价值。我们强加的限制<年代vg height="13.45" id="M150" style="vertical-align:-2.21957pt;width:81.074997px;" version="1.1" viewbox="0 0 81.074997 13.45" width="81.074997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.7020884" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.865587" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.779026" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.942526" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.41836" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.194984" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.358482" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.271923" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.898754" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.93914" y="0"> </t年代p一个n></text> </g> </g> </svg>为一个常数<年代vg height="7.1875" id="M151" style="vertical-align:-0.13794pt;width:7.3874998px;" version="1.1" viewbox="0 0 7.3874998 7.1875" width="7.3874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1875)"> <g transform="translate(72,-66.25)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。再一次,我们使用的算法来解决这个问题数值计算领域的吸引力。图<一个href="//www.newsama.com/journals/aor/2011/269239/fig4/" target="_blank">4</一个>曲线显示了各自的现值<年代vg height="10.9125" id="M152" style="vertical-align:-0.17555pt;width:51.775002px;" version="1.1" viewbox="0 0 51.775002 10.9125" width="51.775002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.515023" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.555412" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.806911" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.058411" y="0"> 0</t年代p一个n></text> </g> </g> </svg>。只有一个低风险溢价,但信贷约束,一个公司<年代vg height="11.0375" id="M153" style="vertical-align:-0.17555pt;width:45.537498px;" version="1.1" viewbox="0 0 45.537498 11.0375" width="45.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,63.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.6520758" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.692465" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.943966" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.069715" y="0"> 6</t年代p一个n></text> </g> </g> </svg>不会充分生长。</p><gydF4y2Badiv class="floats-partial-section partial-carousel-wrapper" data-section="fig4"> <div class="floats-partial-content fig-content-fig4"> <div class="partial-carousel--single-image"> <img alt="" name="269239.fig.004" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.004.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图4</年代p一个n><一个一个ria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/aor/2011/269239/fig4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="13.45" id="M154" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 27.987499 13.45" width="27.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1892252" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.129351" y="0"> )</t年代p一个n></text> </g> </g> </svg> <svg height="13.45" id="M155" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 50.037498 13.45" width="50.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.915119" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.078618" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.855244" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.056492" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.758579" y="0"> )</t年代p一个n></text> </g> </g> </svg> <a href="#EEq9">3.1</一个><t一个ble> 现值曲线gydF4y2Ba债务上限,gydF4y2Ba从()gydF4y2Ba。</t一个ble> </div> </div> </div> <p>潜在的高价值曲线可以达到没有信贷约束<年代vg height="10.9125" id="M156" style="vertical-align:-0.17555pt;width:66.175003px;" version="1.1" viewbox="0 0 66.175003 10.9125" width="66.175003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.7020884" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.177922" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.168539" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.208927" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.460426" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.586178" y="0"> 2</t年代p一个n></text> </g> </g> </svg>。然而,对于<年代vg height="11.0375" id="M157" style="vertical-align:-0.17555pt;width:45.537498px;" version="1.1" viewbox="0 0 45.537498 11.0375" width="45.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,63.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.6520758" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.692465" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.943966" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.069715" y="0"> 6</t年代p一个n></text> </g> </g> </svg>目前的价值曲线<年代vg height="13.45" id="M158" style="vertical-align:-2.21957pt;width:27.987499px;" version="1.1" viewbox="0 0 27.987499 13.45" width="27.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1892252" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.129351" y="0"> )</t年代p一个n></text> </g> </g> </svg>伴随着“限制曲线”<年代vg height="13.45" id="M159" style="vertical-align:-2.21957pt;width:64.224998px;" version="1.1" viewbox="0 0 64.224998 13.45" width="64.224998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.7020884" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.865587" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.642214" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.269043" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.309433" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.498177" y="0"> </t年代p一个n></text> </g> </g> </svg>。在这种情况下,曲线<年代vg height="13.45" id="M160" style="vertical-align:-2.21957pt;width:53.387501px;" version="1.1" viewbox="0 0 53.387501 13.45" width="53.387501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.940125" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.141373" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.330599" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.494097" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.270721" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.434223" y="0"> )</t年代p一个n></text> </g> </g> </svg>不再是不变的动力;也就是说,每一个轨迹<年代vg height="13.45" id="M161" style="vertical-align:-2.21957pt;width:26.299999px;" version="1.1" viewbox="0 0 26.299999 13.45" width="26.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.7020884" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.865587" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.779026" y="0"> )</t年代p一个n></text> </g> </g> </svg>与<年代vg height="13.45" id="M162" style="vertical-align:-2.21957pt;width:88.862503px;" version="1.1" viewbox="0 0 88.862503 13.45" width="88.862503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.7020884" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.865587" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.779026" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.405855" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.446243" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.635471" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.798969" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.575596" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.739094" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.652534" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.816032" y="0"> )</t年代p一个n></text> </g> </g> </svg>叶子的曲线<年代vg height="13.45" id="M163" style="vertical-align:-2.21957pt;width:53.387501px;" version="1.1" viewbox="0 0 53.387501 13.45" width="53.387501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.940125" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.141373" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.330599" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.494097" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.270721" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.434223" y="0"> )</t年代p一个n></text> </g> </g> </svg>并最终<年代vg height="13.45" id="M164" style="vertical-align:-2.21957pt;width:26.299999px;" version="1.1" viewbox="0 0 26.299999 13.45" width="26.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.7020884" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.865587" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.779026" y="0"> )</t年代p一个n></text> </g> </g> </svg>趋向于0。债务是可控的,但公司价值向下移动,和增长是有限的<年代vg height="11.0375" id="M165" style="vertical-align:-0.17555pt;width:45.537498px;" version="1.1" viewbox="0 0 45.537498 11.0375" width="45.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,63.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.6520758" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.692465" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.943966" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.069715" y="0"> 6</t年代p一个n></text> </g> </g> </svg>;也就是说,相应的轨迹曲线<年代vg height="13.45" id="M166" style="vertical-align:-2.21957pt;width:27.987499px;" version="1.1" viewbox="0 0 27.987499 13.45" width="27.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1892252" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.129351" y="0"> )</t年代p一个n></text> </g> </g> </svg>并最终<年代vg height="13.45" id="M167" style="vertical-align:-2.21957pt;width:26.299999px;" version="1.1" viewbox="0 0 26.299999 13.45" width="26.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.7020884" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.865587" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.779026" y="0"> )</t年代p一个n></text> </g> </g> </svg>倾向于零。(模拟停止为零,但如果继续,我们要报告<年代vg height="13.45" id="M168" style="vertical-align:-2.21957pt;width:26.299999px;" version="1.1" viewbox="0 0 26.299999 13.45" width="26.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.7020884" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.865587" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.779026" y="0"> )</t年代p一个n></text> </g> </g> </svg>曲线变得消极。)</p><p>gydF4y2Ba这意味着信贷约束公司无法承担足够高投资和将以较低的速度增长。他们将无法实现其增长潜力,因此潜在的现值,他们能够获得没有信用约束。我们可以观察到,在借贷限制,即使对最优投资策略,不同大小类的企业预计将如果有严格的借贷限制的公司。</p><gydF4y2Bah4 id="dynamics-of-firm-size-distribution-in-the-long-run">4所示。公司大小分布的动力学</gydF4y2Bah4> <p>上述机制长期走势的预测,人们预计增长率和大小分布的企业集群为特征的企业上游地区的大小类以及类的低端大小。此外,人们所预料的,中间大小类是“减少”,可能导致长期twin-peak公司大小的分布。</p><p>gydF4y2Ba我们想提供一些经验证据可以证实一些动力学对公司规模的长期twin-peak分布由上述模型隐含的变体。经验来解决这个问题,我们专注于公司大小分布在美国制造业。</p><p>gydF4y2Ba以下实证研究的数据来自<我>p年代t一个r</我>数据集用于b·w·霍尔和r·e·霍尔(<一个href="#B16">22</一个>]。数据集包含23个变量量化的某些特征,如投资,我们公司的股票价格,或资产的价值在制造业时期1960年到1991年。我们使用的变量<我>netc一个p</gydF4y2Ba我>这是定义为账面价值的资产,调整通货膨胀的影响,代表资本存量。在接下来的净资本规范化的所有公司的平均净资本将被用作衡量大小。</p><p>p年代t一个r数据集给我们一组观测数据点或资本股票,分别可以解释为一个未知的概率密度函数的样本好几年了。分析某些特征的密度,确定未知的密度。例如,如果密度函数改变了从单峰双峰,它可以被视为暗示中间大小类稀薄,支持上述理论观点。曲线图在图<一个href="//www.newsama.com/journals/aor/2011/269239/fig5/" target="_blank">5</一个>事实上似乎支持假设随着时间的推移,有一个沉重的尾巴上大小类出现,中间大小类得到减少。</p><gydF4y2Badiv class="floats-partial-section partial-carousel-wrapper" data-section="fig5"> <div class="floats-partial-content fig-content-fig5"> <div class="partial-carousel--single-image"> <img alt="" name="269239.fig.005" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.005.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图5</年代p一个n><一个一个ria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/aor/2011/269239/fig5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> (归一化)的PDF netcap从1960年到1991年。规范化是netcap平均每年一个。对不同年的数据绘制在不同的色调和潇洒的传奇。</t一个ble> </div> </div> </div> <p>为了更多量化的方式讨论这个问题,我们首先符合对数正态分布的概率密度函数(pdf)分布。</p><p>gydF4y2Ba图<一个href="//www.newsama.com/journals/aor/2011/269239/fig6/" target="_blank">6</一个>给出了一些阴谋与相应的位序-规模分布符合对数正态分布(更确切,累积分布<年代vg height="14.8625" id="M169" style="vertical-align:-3.34572pt;width:36.525002px;" version="1.1" viewbox="0 0 36.525002 14.8625" width="36.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.52,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ></t年代p一个n></text> <text transform="matrix(1,0,0,-1,-58.03,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n></text> </g> </g> </svg>中定义的(<一个href="#EEq10">. 1</一个>)获得的对数正态分布<年代vg height="13.45" id="M170" style="vertical-align:-2.21957pt;width:28.4125px;" version="1.1" viewbox="0 0 28.4125 13.45" width="28.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.4267821" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.590281" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.46693" y="0"> )</t年代p一个n></text> </g> </g> </svg>)。整个协议好虽然很小但截然不同的差异。这种差异在图绘制同样的年<一个href="//www.newsama.com/journals/aor/2011/269239/fig7/" target="_blank">7</一个>,很明显,他们有一个共同特征。</p><gydF4y2Badiv class="floats-partial-section partial-carousel-wrapper" data-section="fig6"> <div class="floats-partial-content fig-content-fig6"> <div class="partial-carousel--single-image"> <img alt="" name="269239.fig.006a" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.006a.jpg"> <br> <strong></strong> </div> <div class="partial-carousel--single-image"> <img alt="" name="269239.fig.006b" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.006b.jpg"> <br> <strong></strong> </div> <div class="partial-carousel--single-image"> <img alt="" name="269239.fig.006c" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.006c.jpg"> <br> <strong></strong> </div> <div class="partial-carousel--single-image"> <img alt="" name="269239.fig.006d" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.006d.jpg"> <br> <strong></strong> </div> <div class="partial-carousel--single-image"> <img alt="" name="269239.fig.006e" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.006e.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig6"> <button class="partial-carousel-dot" aria-label=""><img alt="" name="269239.fig.006a" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.006a.jpg"><br><strong></strong></button> <button class="partial-carousel-dot" aria-label=""><img alt="" name="269239.fig.006b" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.006b.jpg"><br><strong></strong></button> <button class="partial-carousel-dot" aria-label=""><img alt="" name="269239.fig.006c" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.006c.jpg"><br><strong></strong></button> <button class="partial-carousel-dot" aria-label=""><img alt="" name="269239.fig.006d" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.006d.jpg"><br><strong></strong></button> <button class="partial-carousel-dot" aria-label=""><img alt="" name="269239.fig.006e" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.006e.jpg"><br><strong></strong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig6"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图6</年代p一个n><一个一个ria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/aor/2011/269239/fig6/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 位序-规模情节的对数正态分布符合1970年,1975年,1980年、1985年和1990年在对数的规模。在所有的情况下,整体配合的很好,除了小系统的差异,这是一个减少的迹象。</t一个ble> </div> </div> </div> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig7"> <div class="floats-partial-content fig-content-fig7"> <div class="partial-carousel--single-image"> <img alt="" name="269239.fig.007a" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.007a.jpg"> <br> <strong></strong> </div> <div class="partial-carousel--single-image"> <img alt="" name="269239.fig.007b" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.007b.jpg"> <br> <strong></strong> </div> <div class="partial-carousel--single-image"> <img alt="" name="269239.fig.007c" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.007c.jpg"> <br> <strong></strong> </div> <div class="partial-carousel--single-image"> <img alt="" name="269239.fig.007d" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.007d.jpg"> <br> <strong></strong> </div> <div class="partial-carousel--single-image"> <img alt="" name="269239.fig.007e" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.007e.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig7"> <button class="partial-carousel-dot" aria-label=""><img alt="" name="269239.fig.007a" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.007a.jpg"><br><strong></strong></button> <button class="partial-carousel-dot" aria-label=""><img alt="" name="269239.fig.007b" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.007b.jpg"><br><strong></strong></button> <button class="partial-carousel-dot" aria-label=""><img alt="" name="269239.fig.007c" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.007c.jpg"><br><strong></strong></button> <button class="partial-carousel-dot" aria-label=""><img alt="" name="269239.fig.007d" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.007d.jpg"><br><strong></strong></button> <button class="partial-carousel-dot" aria-label=""><img alt="" name="269239.fig.007e" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.007e.jpg"><br><strong></strong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig7"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图7</年代p一个n><一个一个ria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/aor/2011/269239/fig7/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <a href="//www.newsama.com/journals/aor/2011/269239/fig6/">6</一个><年代vg height="13.3125" id="M171" style="vertical-align:-1.95624pt" version="1.1" viewbox="0 0 94.8125 13.3125" width="94.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.3125)"> <g transform="translate(72,-61.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.339981" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.380369" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.543869" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.108425" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.359924" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.485676" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.737175" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.950924" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.202423" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.328178" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.579674" y="0"> ]</t年代p一个n></text> </g> </g> </svg> <svg height="7.1624999" id="M172" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg> <svg height="14.2" id="M173" style="vertical-align:-2.73372pt" version="1.1" viewbox="0 0 89.375 14.2" width="89.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2)"> <g transform="translate(72,-60.64)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> o</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.890833" y="0"> g</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.38133" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.544828" y="0"> n</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.796329" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.247639" y="0"> t</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.723473" y="0"> c</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.274803" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.826134" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.077637" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="67.241135" y="0"> )</t年代p一个n></text> </g> </g> </svg> <svg height="13.9625" id="M174" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 101.2375 13.9625" width="101.2375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9625)"> <g transform="translate(72,-60.83)"> <text transform="matrix(1,0,0,-1,-71.95,63.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2765059" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.11,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-52.71,63.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.666498" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.829998" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.606625" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.258942" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.599159" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.476292" y="0"> )</t年代p一个n></text> </g> </g> </svg> <svg height="12.7625" id="M175" style="vertical-align:-1.76814pt" version="1.1" viewbox="0 0 22.950001 12.7625" width="22.950001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.7625)"> <g transform="translate(72,-61.79)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2765059" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.477754" y="0"> </t年代p一个n></text> </g> </g> </svg> <svg height="7.1374998" id="M176" style="vertical-align:-0.10033pt" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg> <table> 不同等级规模和对数正态分布适合年一样在图gydF4y2Ba。黑色的曲线是适合的范围,gydF4y2Ba在那里gydF4y2Ba横向协调吗,ggydF4y2BaydF4y2Ba与,ggydF4y2BaydF4y2Ba作为自由参数。</t一个ble> </div> </div> </div> <p>这意味着他们不是在对数正态分布随机波动。最显著的特征是,他们倾向−1和0之间,这意味着由于累积概率的导数是负的pdf,对数正态分布的实际pdf pdf加上一个双峰值pdf的第一峰值在−1和第二高峰略小于1。twin-peak的强度可以通过拟合这些差异测量等功能<年代vg height="13.9625" id="M177" style="vertical-align:-2.21957pt;width:101.2375px;" version="1.1" viewbox="0 0 101.2375 13.9625" width="101.2375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9625)"> <g transform="translate(72,-60.83)"> <text transform="matrix(1,0,0,-1,-71.95,63.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2765059" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.11,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-52.71,63.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.666498" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.829998" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.606625" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.258942" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.599159" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.476292" y="0"> )</t年代p一个n></text> </g> </g> </svg>(与<年代vg height="7.1624999" id="M178" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>被“振幅”的水平坐标)和测量<年代vg height="7.1750002" id="M179" style="vertical-align:-0.1254pt;width:7.9749999px;" version="1.1" viewbox="0 0 7.9749999 7.1750002" width="7.9749999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.175)"> <g transform="translate(72,-66.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。我们选择这样做的<年代vg height="13.3125" id="M180" style="vertical-align:-1.95624pt;width:94.8125px;" version="1.1" viewbox="0 0 94.8125 13.3125" width="94.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.3125)"> <g transform="translate(72,-61.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.339981" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.380369" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.543869" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.108425" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.359924" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.485676" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.737175" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.950924" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.202423" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.328178" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.579674" y="0"> ]</t年代p一个n></text> </g> </g> </svg>为了避免大的波动大<年代vg height="7.1624999" id="M181" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和由此产生的曲线绘制在坚实的黑色曲线。我们发现协议与实际的差别是在合理的范围内。</p><p>gydF4y2Ba由此产生的振幅<年代vg height="7.1750002" id="M182" style="vertical-align:-0.1254pt;width:7.9749999px;" version="1.1" viewbox="0 0 7.9749999 7.1750002" width="7.9749999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.175)"> <g transform="translate(72,-66.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>绘制在图<一个href="//www.newsama.com/journals/aor/2011/269239/fig8/" target="_blank">8</一个>连同一个线性。系统的趋势<年代vg height="7.1750002" id="M183" style="vertical-align:-0.1254pt;width:7.9749999px;" version="1.1" viewbox="0 0 7.9749999 7.1750002" width="7.9749999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.175)"> <g transform="translate(72,-66.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>增加确认实际上中间变薄。此前的估计1970年窦曲线的变化,1975年,1980年、1985年和1990年在图表示<一个href="//www.newsama.com/journals/aor/2011/269239/fig8/" target="_blank">8</一个>它是可见的,振幅随时间上升,表明公司的分布变得集中在上下端。(另一种方法来估计公司规模的双峰分布数据是使用内核估计和Markow链方式;看到加藤et al。<一个href="#B17">15</一个>]。)</p><gydF4y2Badiv class="floats-partial-section partial-carousel-wrapper" data-section="fig8"> <div class="floats-partial-content fig-content-fig8"> <div class="partial-carousel--single-image"> <img alt="" name="269239.fig.008" src="https://static-02.hindawi.com/articles/aor/volume-2011/269239/figures/269239.fig.008.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图8</年代p一个n><一个一个ria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/aor/2011/269239/fig8/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="7.1750002" id="M184" style="vertical-align:-0.1254pt" version="1.1" viewbox="0 0 7.9749999 7.1750002" width="7.9749999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.175)"> <g transform="translate(72,-66.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg> <svg height="11.1" id="M185" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 131.75 11.1" width="131.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1)"> <g transform="translate(72,-63.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.7398367" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.780226" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.031727" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.157476" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.408978" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.660477" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.911976" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.163475" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.815788" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="77.156013" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="83.407516" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="86.533264" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="92.78476" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="99.036263" y="0"> 0</t年代p一个n></text> </g> </g> </svg> <svg height="7.1750002" id="M186" style="vertical-align:-0.1254pt" version="1.1" viewbox="0 0 7.9749999 7.1750002" width="7.9749999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.175)"> <g transform="translate(72,-66.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg> <table> “振幅”的情节1970gydF4y2Ba年- 1991年。虚线为最适合gydF4y2Ba。稳定增长的,gydF4y2Ba这是一个减少的迹象,是明显的。</t一个ble> </div> </div> </div> <h4 id="conclusions">5。结论</gydF4y2Bah4> <p>在本文中,我们首先研究了两个扩展法律、帕累托定律和Gibrat定律。似乎适用于大型企业。细致平衡的法律下的关系也进行了研究。讨论了纯运动学上地,独立于任何模型提出。然而,这种研究有助于隔离动力特性,这还有待解释。这是力量和这种分析的力量。结果,我们现在有一个特定的形状增长率pdf Gibrat框架的定律,这应该是现代分析的目标公司规模的动态。分析公司的尾巴上下大小分布通过帕累托法则和Gibrat 'law经验统计研究的补充在中间会发生什么。我们的研究经验解决问题的“稀释”中间和公司规模的双峰分布的问题。</p><p>为了理论激励这样一个范围更大的研究,即公司类的双峰大小分布的研究从长远来看,我们引入了动态模型的公司行为,公司可能会暴露在本地增加回报,非线性调整资本成本,信用蔓延,由风险溢价和信贷约束。使用动态编程,我们计算的动力公司大小和他们的长期大小分布。双峰分布预测。经验,这意味着随着时间的推移,有一个“薄”公司大小的类在中间。我们的统计分析支持理论模型的预测。</p><p>gydF4y2Ba最后,我们要注意,当然,公司在行业大小分布的进化可能是更复杂的比上面的特征是我们的统计和分析研究。许多实证研究的动力公司大小分布在一个行业的生命周期记录力量影响的大小分布的复杂性等公司整体需求的增长,行业需求,成本和技术冲击,融资实践,和行业监管。(调查的各种力量的增长在某些行业的生命周期阶段,看到Mazzucato Semmler [<一个href="#B21">23</一个>]。)然而,我们想强调,我们的论文可能会给出一个理论基本原理和一些经验证据,有助于突出一些主要机制可能导致双峰分布和公司规模的波动从长远来看。</p><gydF4y2Bah4 id="appendices">附录</gydF4y2Bah4> <h4 id="a.-scaling-laws">a .缩放法律</gydF4y2Bah4> <p>在这里,我们给出一个分析帕累托法则和Gibrat定律,通常观察到的数据。我们提出一个理论讨论这两个法律之间的关系。又被称为比例法。</p><p><年代p一个ncl作为年代="statement" id="head1"><span class="statement-title"><i class="statement-title">帕累托法则和Gibrat定律(下面的更多细节和实证验证使用大型欧盟数据集,看到藤原et al。<一个href="#B11">4</一个>]。)</我></年代p一个n><br>累积概率分布函数<年代vg height="14.8625" id="M187" style="vertical-align:-3.34572pt;width:36.525002px;" version="1.1" viewbox="0 0 36.525002 14.8625" width="36.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.52,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ></t年代p一个n></text> <text transform="matrix(1,0,0,-1,-58.03,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n></text> </g> </g> </svg>可以定义如下的pdf吗<年代vg height="13.45" id="M188" style="vertical-align:-2.21957pt;width:28.4125px;" version="1.1" viewbox="0 0 28.4125 13.45" width="28.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.4267821" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.590281" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.46693" y="0"> )</t年代p一个n></text> </g> </g> </svg>:<年代p一个ncl作为年代=”equation" id="EEq10"> <svg height="36.837502" id="M189" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 36.837502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,36.8375)"> <g transform="translate(72,-42.53)"> <text transform="matrix(1,0,0,-1,148.35,54.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,155.77,51.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ></t年代p一个n></text> <text transform="matrix(1,0,0,-1,164.35,54.16)"> <tspan style="font-size: 12.50px; " x="30.719999" y="7.6999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.666979" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,202.07,68.19)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-1.25" y="25.530001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,212.75,54.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.39" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.24" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,236.87,59.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,240.34,51.65)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9400001" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.591596" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,261.81,59.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,265.28,54.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="196.75" y="0.02"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="200.9135" y="0.02"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="209.89066" y="0.02"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="213.0164" y="0.02"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="219.2679" y="0.02"> )</t年代p一个n></text> </g> </g> </svg></span>分布<年代vg height="14.8625" id="M190" style="vertical-align:-3.34572pt;width:36.525002px;" version="1.1" viewbox="0 0 36.525002 14.8625" width="36.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.52,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ></t年代p一个n></text> <text transform="matrix(1,0,0,-1,-58.03,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n></text> </g> </g> </svg>因此<年代vg height="13.45" id="M191" style="vertical-align:-2.21957pt;width:28.4125px;" version="1.1" viewbox="0 0 28.4125 13.45" width="28.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.4267821" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.590281" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.46693" y="0"> )</t年代p一个n></text> </g> </g> </svg>服从幂律为大<年代vg height="7.1624999" id="M192" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>如果<年代p一个ncl作为年代=”equation" id="EEq11"> <svg height="18.4625" id="M193" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.4625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.4625)"> <g transform="translate(72,-57.23)"> <text transform="matrix(1,0,0,-1,171.23,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.37773" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.541229" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.417879" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.057213" y="0"> ∝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.085098" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,220.2,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="11.325088" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="17.320208" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,242.4,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="219.63" y="-0.46000001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="223.7935" y="-0.46000001"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="232.77066" y="-0.46000001"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="235.89641" y="-0.46000001"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="242.1479" y="-0.46000001"> )</t年代p一个n></text> </g> </g> </svg></span>这是著名的Pareto-Zipf定律(“帕累托法则”以后)。(见帕累托(<一个href="#B23">24</一个>]。)此外,帕累托指数<年代vg height="9.6750002" id="M194" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>通常波动在1公司大小和变化在2个人收入(<一个href="#B11">4</一个>]。一个奇怪的事实是,除了中央值1和2之间的区别,后者的变化范围通常是更广泛的比前。<gydF4y2Babr>增长率<年代vg height="10.325" id="M195" style="vertical-align:-0.0pt;width:11.6875px;" version="1.1" viewbox="0 0 11.6875 10.325" width="11.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>被定义为<年代vg height="14.6" id="M196" style="vertical-align:-3.13504pt;width:64.800003px;" version="1.1" viewbox="0 0 64.800003 14.6" width="64.800003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.715551" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.755939" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-40.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.44,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-25.08,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>,在那里<年代vg height="10.925" id="M197" style="vertical-align:-3.13504pt;width:14.8125px;" version="1.1" viewbox="0 0 14.8125 10.925" width="14.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>是公司第一年的日志大小和<年代vg height="10.925" id="M198" style="vertical-align:-3.13504pt;width:14.8125px;" version="1.1" viewbox="0 0 14.8125 10.925" width="14.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>明年的。我们可以观察到不同本pdf (<年代vg height="7.1374998" id="M199" style="vertical-align:-0.10033pt;width:7.8874998px;" version="1.1" viewbox="0 0 7.8874998 7.1374998" width="7.8874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>)<年代vg height="10.925" id="M200" style="vertical-align:-3.13504pt;width:14.8125px;" version="1.1" viewbox="0 0 14.8125 10.925" width="14.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>经常相互重叠,Gibrat定律。这个法律表达的条件概率<年代vg height="14.8125" id="M201" style="vertical-align:-3.13504pt;width:61.837502px;" version="1.1" viewbox="0 0 61.837502 14.8125" width="61.837502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8125)"> <g transform="translate(72,-60.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.764843" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.928342" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.643892" y="0"> ∣</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.445526" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-31.62,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-26.75,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg>的增长率固定<年代vg height="10.925" id="M202" style="vertical-align:-3.13504pt;width:14.8125px;" version="1.1" viewbox="0 0 14.8125 10.925" width="14.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>作为<年代p一个ncl作为年代=”equation" id="EEq12"> <svg height="19.35" id="M203" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.35" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.35)"> <g transform="translate(72,-56.52)"> <text transform="matrix(1,0,0,-1,153.8,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.85" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.700001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.428055" y="0"> ∣</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.217182" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,197.91,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,202.78,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.49" y="-2.51"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.517885" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.380001" y="-2.52"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.543499" y="-2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.795719" y="-2.52"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.034718" y="-2.52"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="259.25" y="-2.51"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="263.41351" y="-2.51"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="272.39066" y="-2.51"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="275.51639" y="-2.51"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="281.76791" y="-2.51"> )</t年代p一个n></text> </g> </g> </svg></span><br>在下面,我们将讨论这两个法律之间的关系。</年代p一个n></p><p><span class="statement" id="head2"><span class="statement-title"><i class="statement-title">这两个法律关系</我></年代p一个n><br>上面提到的所有数据满足细致平衡的法律在某种程度上。同时pdf<年代vg height="14.6" id="M204" style="vertical-align:-3.13504pt;width:67.275002px;" version="1.1" viewbox="0 0 67.275002 14.6" width="67.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.52,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.27,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-44.23,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-39.36,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-27.27,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-22.4,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg>写,如下:<年代p一个ncl作为年代=”equation" id="EEq13"> <svg height="19.35" id="M205" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.35" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.35)"> <g transform="translate(72,-56.52)"> <text transform="matrix(1,0,0,-1,138.84,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,146.27,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,157.6,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,170.33,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,175.2,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,187.29,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,192.16,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3299999" y="-2.51"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.357885" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,220.95,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,232.29,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,245.02,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,249.89,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,261.98,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,266.85,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9400001" y="-2.51"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="195.17999" y="-2.51"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="199.34351" y="-2.51"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="208.32065" y="-2.51"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="211.4464" y="-2.51"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="217.69791" y="-2.51"> )</t年代p一个n></text> </g> </g> </svg></span>的准确性(<一个href="#EEq13">各</一个>)可以用二维Kolmogorov-Smirnov检查测试。<gydF4y2Babr>下面的可以证明的法律下细致平衡(<一个href="#B10">2</一个>]。<年代p一个ncl作为年代=”l我年代t”><年代pan class="list-item"><span class="list-label">(1)</年代p一个n><年代p一个ncl作为年代="list-content">如果Gibrat定律成立,帕累托法则是满意的。</年代p一个n></年代p一个n><span class="list-item"><span class="list-label">(2)</年代p一个n><年代p一个ncl作为年代="list-content">与上面相同的条件下,“反射法,”<年代p一个ncl作为年代=”equation" id="EEq14"> <svg height="19.475" id="M206" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.475" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.475)"> <g transform="translate(72,-56.42)"> <text transform="matrix(1,0,0,-1,145.74,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.840341" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.003839" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.25606" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.895393" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.935783" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,199.93,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="11.325088" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="17.320208" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,222.13,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.85" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.700001" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,249.08,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,259.95,58.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9299998" y="-2.51"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="202.08" y="-2.5599999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="206.2435" y="-2.5599999"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="215.22066" y="-2.5599999"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="218.34641" y="-2.5599999"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="224.5979" y="-2.5599999"> )</t年代p一个n></text> </g> </g> </svg></span>是满意的。</年代p一个n></年代p一个n></span><br>证明如下:我们表示联合pdf<年代vg height="10.925" id="M207" style="vertical-align:-3.13504pt;width:14.8125px;" version="1.1" viewbox="0 0 14.8125 10.925" width="14.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>和增长率<年代vg height="14.6" id="M208" style="vertical-align:-3.13504pt;width:64.800003px;" version="1.1" viewbox="0 0 64.800003 14.6" width="64.800003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.715551" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.755939" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-40.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.44,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-25.08,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>用<年代vg height="14.6" id="M209" style="vertical-align:-3.13504pt;width:66.775002px;" version="1.1" viewbox="0 0 66.775002 14.6" width="66.775002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.52,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-53.17,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-42.13,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-37.26,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.453468" y="0"> )</t年代p一个n></text> </g> </g> </svg>。自<年代vg height="14.6" id="M210" style="vertical-align:-3.13504pt;width:242.2px;" version="1.1" viewbox="0 0 242.2 14.6" width="242.2" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.52,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.27,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-44.23,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-39.36,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-27.27,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-22.4,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.815095" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-4.71,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,0.17,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,13.7,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,22.04,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,41.51,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,52.86,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,63.9,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,68.77,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.453468" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.616966" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.268562" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,100.93,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,105.8,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代p一个n></text> </g> </g> </svg>在变量的变化<年代vg height="14.6" id="M211" style="vertical-align:-3.13504pt;width:46.424999px;" version="1.1" viewbox="0 0 46.424999 14.6" width="46.424999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.91,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.04,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-43.95,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-39.08,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg>来<年代vg height="14.6" id="M212" style="vertical-align:-3.13504pt;width:43.299999px;" version="1.1" viewbox="0 0 43.299999 14.6" width="43.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.91,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.04,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.465971" y="0"> )</t年代p一个n></text> </g> </g> </svg>,这两个pdf的相关如下:<年代p一个ncl作为年代=”equation" id="EEq15"> <svg height="38.575001" id="M213" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.575001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,38.575)"> <g transform="translate(72,-41.14)"> <text transform="matrix(1,0,0,-1,127.19,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,134.62,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,148.05,46.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3800001" y="-7.3299999"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,164.31,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,169.18,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.4099998" y="-9.1400003"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,182.46,59.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <g> <path d="m 175.59,56.57 11.75,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,175.59,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,182.46,41.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,188.53,46.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.85" y="-7.3299999"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.890388" y="-7.3299999"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,220.3,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,225.17,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,232.6,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,243.93,50.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8600001" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,256.66,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,261.54,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,273.62,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,278.5,50.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9299998" y="-2.52"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="183.53" y="-2.52"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="187.6935" y="-2.52"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="196.67065" y="-2.52"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="199.7964" y="-2.52"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="206.0479" y="-2.52"> )</t年代p一个n></text> </g> </g> </svg></span><br>我们定义了条件概率<年代vg height="14.8125" id="M214" style="vertical-align:-3.13504pt;width:61.837502px;" version="1.1" viewbox="0 0 61.837502 14.8125" width="61.837502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8125)"> <g transform="translate(72,-60.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.764843" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.928342" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.643892" y="0"> ∣</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.445526" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-31.62,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-26.75,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg>如下:<年代p一个ncl作为年代=”equation" id="EEq16"> <svg height="49.775002" id="M215" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 49.775002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,49.775)"> <g transform="translate(72,-32.18)"> <text transform="matrix(1,0,0,-1,123.52,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,130.95,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,144.38,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,157.11,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,161.98,61.13)"> <tspan style="font-size: 12.50px; " x="14.47" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.790001" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.817886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,205.24,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,212.19,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,224.92,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,229.8,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9299998" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.780001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.629999" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.345551" y="-2.51"> ∣</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.147182" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,281.83,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,286.71,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="175.32001" y="-2.51"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="179.48351" y="-2.51"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="188.46065" y="-2.51"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="191.58641" y="-2.51"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="197.83791" y="-2.51"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-100.94" y="21.83"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-88.912117" y="21.83"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,205.24,33.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,214.29,36.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.75" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.599998" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1700001" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.42222" y="0.0099999998"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.661217" y="0.0099999998"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,257.77,33.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,266.12,36.79)"> <tspan style="font-size: 12.50px; " x="16.049999" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ∣</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.7891288" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.99" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="195.91" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="200.0735" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="209.05066" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="212.17641" y="0"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="218.4279" y="0"> )</t年代p一个n></text> </g> </g> </svg></span>这两个<年代vg height="14.6" id="M217" style="vertical-align:-3.13504pt;width:40.599998px;" version="1.1" viewbox="0 0 40.599998 14.6" width="40.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.52,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.65,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-48.61,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-43.73,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg>和<年代vg height="14.6" id="M218" style="vertical-align:-3.13504pt;width:40.099998px;" version="1.1" viewbox="0 0 40.099998 14.6" width="40.099998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.52,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.55,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.415719" y="0"> )</t年代p一个n></text> </g> </g> </svg>是边际<年代p一个ncl作为年代=”equation" id="EEq18"> <svg height="86.537498" id="M219" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 86.537498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,86.5375)"> <g transform="translate(72,-2.77)"> <text transform="matrix(1,0,0,-1,67.8,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,75.23,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,82.18,50.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,94.91,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,99.79,50.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3199997" y="-2.52"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.360001" y="5.1799998"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,128.15,67.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-1.25" y="25.52"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,138.84,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,146.26,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,159.7,50.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,172.43,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,177.3,53.45)"> <tspan style="font-size: 12.50px; " x="14.46" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.380001" y="7.3299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.759998" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.799999" y="7.6999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.4" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.051596" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,246.1,67.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-1.25" y="25.52"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,256.79,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,264.22,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,275.55,50.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,288.28,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,293.15,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,305.24,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,310.11,50.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9400001" y="-2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.591596" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,331.58,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,336.45,46.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-201.86" y="31.690001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.46" y="-7.3299999"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="125.58" y="-7.3299999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="129.7435" y="-7.3299999"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="138.72066" y="-7.3299999"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="141.84641" y="-7.3299999"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="148.0979" y="-7.3299999"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,142.02,11.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,151.08,14.44)"> <tspan style="font-size: 12.50px; " x="33.09" y="7.6999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.415719" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.042549" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,191.17,28.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-1.25" y="25.52"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,201.85,14.43)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,209.28,11.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,222.72,11.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,235.44,11.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,240.32,14.43)"> <tspan style="font-size: 12.50px; " x="14.46" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.4" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.051596" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,276.24,11.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,281.12,14.43)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="174.66" y="0.039999999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="178.8235" y="0.039999999"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="187.80066" y="0.039999999"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="190.92641" y="0.039999999"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="197.1779" y="0.039999999"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="203.4294" y="0.039999999"> )</t年代p一个n></text> </g> </g> </svg></span><br>相对应的经验事实是观察到藤原et al。<一个href="#B11">4</一个>]。他们可以被描述的这些pdf的如下。<年代p一个ncl作为年代=”年代t一个te米ent" id="head3"><span class="statement-title"><i class="statement-title">(一)详细的平衡</我></年代p一个n><br>联合pdf<年代vg height="14.6" id="M221" style="vertical-align:-3.13504pt;width:67.275002px;" version="1.1" viewbox="0 0 67.275002 14.6" width="67.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.52,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.27,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-44.23,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-39.36,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-27.27,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-22.4,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg>是一个对称函数<年代p一个ncl作为年代=”equation" id="EEq20"> <svg height="19.35" id="M222" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.35" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.35)"> <g transform="translate(72,-56.52)"> <text transform="matrix(1,0,0,-1,138.84,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,146.27,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,157.6,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,170.33,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,175.2,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,187.29,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,192.16,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3299999" y="-2.51"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.357885" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,220.95,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,232.29,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,245.02,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,249.89,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,261.98,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,266.85,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9400001" y="-2.51"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="188.92999" y="-2.51"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="193.09351" y="-2.51"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="202.07065" y="-2.51"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="205.1964" y="-2.51"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="211.44791" y="-2.51"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="217.6994" y="-2.51"> )</t年代p一个n></text> </g> </g> </svg></span></span><span class="statement" id="head4"><span class="statement-title"><i class="statement-title">(B)帕累托定律</我></年代p一个n><br>pdf<年代vg height="14.6" id="M223" style="vertical-align:-3.13504pt;width:34.5px;" version="1.1" viewbox="0 0 34.5 14.6" width="34.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.52,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.65,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n></text> </g> </g> </svg>遵循幂律为大<年代vg height="7.1624999" id="M224" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg><span class="equation" id="EEq21"> <svg height="18.4625" id="M225" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.4625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.4625)"> <g transform="translate(72,-57.23)"> <text transform="matrix(1,0,0,-1,169.73,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,177.15,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,184.11,61.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.666979" y="0"> ∝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.707369" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,221.7,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="11.325088" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="17.320208" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,243.9,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="211.88" y="-0.46000001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="216.0435" y="-0.46000001"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="225.02066" y="-0.46000001"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="228.14641" y="-0.46000001"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="234.3979" y="-0.46000001"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="240.6494" y="-0.46000001"> )</t年代p一个n></text> </g> </g> </svg></span>为<年代vg height="7.2624998" id="M226" style="vertical-align:-0.11285pt;width:51.5625px;" version="1.1" viewbox="0 0 51.5625 7.2624998" width="51.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.2625)"> <g transform="translate(72,-66.19)"> <text transform="matrix(1,0,0,-1,-71.95,66.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.427982" y="0"> →</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.557093" y="0"> ∞</t年代p一个n></text> </g> </g> </svg>与<年代vg height="13.55" id="M227" style="vertical-align:-2.29482pt;width:36.849998px;" version="1.1" viewbox="0 0 36.849998 13.55" width="36.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.077658" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.118048" y="0"> 0</t年代p一个n></text> </g> </g> </svg>。</年代p一个n><年代p一个ncl作为年代="statement" id="head5"><span class="statement-title"><i class="statement-title">(C) Gibrat定律</我></年代p一个n><br>的条件概率<年代vg height="13.8625" id="M228" style="vertical-align:-2.37006pt;width:55.737499px;" version="1.1" viewbox="0 0 55.737499 13.8625" width="55.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.8625)"> <g transform="translate(72,-60.91)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.764843" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.928342" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.643892" y="0"> ∣</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.445526" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.322174" y="0"> )</t年代p一个n></text> </g> </g> </svg>是独立于<年代vg height="7.1624999" id="M229" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg><span class="equation" id="EEq22"> <svg height="16.5375" id="M230" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 16.5375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5375)"> <g transform="translate(72,-58.77)"> <text transform="matrix(1,0,0,-1,160.01,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.840341" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.003839" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.731894" y="0"> ∣</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.533527" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.410175" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.049507" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.089897" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="73.930237" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.093735" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="87.345955" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="93.597458" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="295.76999" y="0.63"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="299.9335" y="0.63"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="308.91064" y="0.63"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="312.03641" y="0.63"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="318.2879" y="0.63"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="324.5394" y="0.63"> )</t年代p一个n></text> </g> </g> </svg></span>让我们先把详细的平衡条件(一)而言<年代vg height="14.6" id="M231" style="vertical-align:-3.13504pt;width:66.775002px;" version="1.1" viewbox="0 0 66.775002 14.6" width="66.775002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.52,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-53.17,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-42.13,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-37.26,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.453468" y="0"> )</t年代p一个n></text> </g> </g> </svg><span class="equation" id="EEq23"> <svg height="124.7125" id="M232" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 124.7125" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,124.7125)"> <g transform="translate(72,27.77)"> <text transform="matrix(1,0,0,-1,123.74,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,131.17,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,144.6,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8600001" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,157.33,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,162.21,61.13)"> <tspan style="font-size: 12.50px; " x="14.46" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.780001" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.820389" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,204.91,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,209.78,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,217.21,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,228.54,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,241.27,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,246.14,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,258.23,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,263.11,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-77.120003" y="21.83"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-65.079613" y="21.83"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,204.91,33.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,209.78,36.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,217.21,33.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,228.54,34.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,241.27,33.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,246.14,36.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,258.23,33.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,263.11,34.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-77.120003" y="25.67"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-63.880001" y="16.530001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,206.1,14.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <g> <path d="m 199.23,11.73 11.75,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,199.23,-0.15)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,206.1,-3.27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,212.17,8.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,219.05,5.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,223.92,8.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,231.35,5.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,242.68,6.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8600001" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,255.41,5.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,260.29,8.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,272.37,5.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,277.25,6.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-91.260002" y="29.25"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-79.219612" y="29.25"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,207.28,-18.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,218.15,-23.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,225.58,-26.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,239.01,-25.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8600001" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,251.74,-26.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,256.62,-23.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,271.08,-18.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,281.95,-25.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9299998" y="-2.51"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="173.83" y="-44.66"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="177.9935" y="-44.66"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="186.97066" y="-44.66"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="190.09641" y="-44.66"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="196.3479" y="-44.66"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="202.5994" y="-44.66"> )</t年代p一个n></text> </g> </g> </svg></span>(在哪里<一个href="#EEq20">A.11</一个>)是用于第二行和(<一个href="#EEq15">要求寄出</一个>)是用于第一和第三行。上面的关系可以改写如下使用条件概率<年代vg height="14.8125" id="M233" style="vertical-align:-3.13504pt;width:61.837502px;" version="1.1" viewbox="0 0 61.837502 14.8125" width="61.837502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8125)"> <g transform="translate(72,-60.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.764843" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.928342" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.643892" y="0"> ∣</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.445526" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-31.62,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-26.75,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg>在(<一个href="#EEq16">A.7</一个>):<gydF4y2Ba年代p一个ncl作为年代=”equation" id="EEq24"> <svg height="45.924999" id="M234" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 45.924999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,45.925)"> <g transform="translate(72,-35.26)"> <text transform="matrix(1,0,0,-1,141.47,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.85" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.700001" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,168.42,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,182.76,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.8016319" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,196.44,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,201.31,58.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m 141.47,53.58 65.69,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,146.9,39.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.85" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.700001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.428055" y="0"> ∣</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.217182" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,191,36.75)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,195.88,37.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.439999" y="-23.67"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.95" y="-13.09"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.990389" y="-13.09"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,241.75,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,248.7,58.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8600001" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,261.43,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,266.31,58.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m 234.32,53.58 37.84,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,234.32,39.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,241.75,36.75)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,248.7,37.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8600001" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,261.43,36.75)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,266.31,37.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.04" y="-13.09"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="189.47" y="-13.15"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="193.6335" y="-13.15"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="202.61066" y="-13.15"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="205.7364" y="-13.15"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="211.9879" y="-13.15"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="218.23941" y="-13.15"> )</t年代p一个n></text> </g> </g> </svg></span></span><br>在传递,需要注意的是,(<一个href="#EEq23">A.14</一个>)会导致以下:<年代p一个ncl作为年代=”equation" id="EEq25"> <svg height="163.3875" id="M235" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 163.3875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,163.3875)"> <g transform="translate(72,58.71)"> <text transform="matrix(1,0,0,-1,119.62,54.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,127.04,51.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,136.1,54.16)"> <tspan style="font-size: 12.50px; " x="33.09" y="7.6999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.415719" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.042549" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,176.19,68.19)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-1.25" y="25.530001"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,186.88,54.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,194.31,51.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,207.74,51.65)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,220.47,51.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,225.34,54.16)"> <tspan style="font-size: 12.50px; " x="14.47" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.4" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.051596" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,261.27,51.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,157.15,15.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.04" y="7.6900001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,176.19,29.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-1.25" y="25.530001"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,186.88,15.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,196.13,20.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,207,15.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,214.43,12.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,227.86,13.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,240.59,12.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,245.47,15.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,259.93,20.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,270.8,13.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9299998" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.581596" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,292.26,12.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,157.15,-22.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.04" y="7.6900001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,176.19,-8.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-1.25" y="25.52"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,186.88,-22.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,196.13,-17.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,207,-22.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,214.43,-25.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,227.86,-25.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,240.59,-25.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,245.47,-22.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,259.93,-17.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,270.8,-25.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9299998" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.581596" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,292.26,-25.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,157.15,-54.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,178.44,-49.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,189.31,-54.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,196.74,-57.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,205.8,-56.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,220.9,-49.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,231.77,-56.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9400001" y="-2.51"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="224.00999" y="-60.130001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="228.17349" y="-60.130001"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="237.15065" y="-60.130001"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="240.2764" y="-60.130001"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="246.52791" y="-60.130001"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="252.7794" y="-60.130001"> )</t年代p一个n></text> </g> </g> </svg></span>(在哪里<一个href="#EEq23">A.14</一个>)是用于第二行和第三行只是一个集成变量的变化。这个pdf边际增长率之间的关系<年代vg height="14.6" id="M236" style="vertical-align:-3.13504pt;width:40.099998px;" version="1.1" viewbox="0 0 40.099998 14.6" width="40.099998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.52,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.55,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.415719" y="0"> )</t年代p一个n></text> </g> </g> </svg>正增长(<年代vg height="11.0625" id="M237" style="vertical-align:-0.30096pt;width:38.887501px;" version="1.1" viewbox="0 0 38.887501 11.0625" width="38.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.715551" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.755939" y="0"> 1</t年代p一个n></text> </g> </g> </svg>)和负增长(<年代vg height="11.0625" id="M238" style="vertical-align:-0.30096pt;width:38.887501px;" version="1.1" viewbox="0 0 38.887501 11.0625" width="38.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.715551" y="0"> <</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.755939" y="0"> 1</t年代p一个n></text> </g> </g> </svg>)会导致下面的关系,它应该:<年代p一个ncl作为年代=”equation" id="EEq26"> <svg height="39.575001" id="M239" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 39.575001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,39.575)"> <g transform="translate(72,-40.34)"> <text transform="matrix(1,0,0,-1,131.18,44.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,138.18,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-1.25" y="25.52"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,148.87,52.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,156.3,48.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,165.35,52.01)"> <tspan style="font-size: 12.50px; " x="51.080002" y="7.6999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.415719" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.318815" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.034367" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,223.43,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-1.25" y="25.52"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,230.39,52.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,237.82,48.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,246.88,52.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.415719" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.654716" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.306313" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.558533" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="208.89999" y="-1.03"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="213.06349" y="-1.03"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="222.04065" y="-1.03"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="225.1664" y="-1.03"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="231.41791" y="-1.03"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="237.6694" y="-1.03"> )</t年代p一个n></text> </g> </g> </svg></span><br>让我们证明了属性(A)和(C) (B)。用Gibrat定律(<一个href="#EEq22">A.13</一个>)(<gydF4y2Ba一个href="#EEq24">所以</一个>),我们发现以下几点:<年代p一个ncl作为年代=”equation" id="EEq27"> <svg height="45.924999" id="M240" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 45.924999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,45.925)"> <g transform="translate(72,-35.26)"> <text transform="matrix(1,0,0,-1,151.28,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,158.71,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,165.67,58.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,178.4,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,183.27,58.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m 151.28,53.58 37.84,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,151.28,39.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,158.71,36.75)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,165.67,37.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,178.4,36.75)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,183.27,37.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.52" y="-13.09"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.26" y="-20.35"> 1</t年代p一个n></text> <g> <path d="m 207.02,53.58 9.26,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,207.02,41.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.65" y="-19.33"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.5" y="-16.82"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.35" y="-19.33"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,245.62,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,256.49,58.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m 218.67,53.58 43.67,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,225.79,41.7)"> <tspan style="font-size: 12.50px; " x="37.75" y="-8.75"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.840341" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.003839" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.25606" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="229.99001" y="-8.8100004"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="234.1535" y="-8.8100004"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="243.13065" y="-8.8100004"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="246.25641" y="-8.8100004"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="252.5079" y="-8.8100004"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="258.7594" y="-8.8100004"> )</t年代p一个n></text> </g> </g> </svg></span>这个关系可以满足只有一个幂律函数(<一个href="#EEq21">A.12</一个>)。<gydF4y2Babr><span class="statement" id="proof1"><span class="statement-title"><i class="statement-title">证明。</我></年代p一个n>让我们重写(<一个href="#EEq27">A.18</一个>)如下:<年代p一个ncl作为年代=”equation" id="EEq28"> <svg height="16.5375" id="M241" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 16.5375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5375)"> <g transform="translate(72,-58.77)"> <text transform="matrix(1,0,0,-1,148.21,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,155.64,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,162.6,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.666979" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.707369" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.22263" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.386131" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.638351" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.877346" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,231.91,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,238.87,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.415719" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.29237" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.531366" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="216.91" y="0.63"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="221.0735" y="0.63"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="230.05066" y="0.63"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="233.17641" y="0.63"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="239.4279" y="0.63"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="245.6794" y="0.63"> )</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代vg height="7.1624999" id="M242" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>表示<年代vg height="10.925" id="M243" style="vertical-align:-3.13504pt;width:14.8125px;" version="1.1" viewbox="0 0 14.8125 10.925" width="14.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.45" id="M244" style="vertical-align:-2.21957pt;width:33.575001px;" version="1.1" viewbox="0 0 33.575001 13.45" width="33.575001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.1772022" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.340701" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.59292" y="0"> )</t年代p一个n></text> </g> </g> </svg>表示的右边(<一个href="#EEq27">A.18</一个>);也就是说,<年代p一个ncl作为年代=”equation" id="EEq29"> <svg height="40.6875" id="M245" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 40.6875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,40.6875)"> <g transform="translate(72,-39.45)"> <text transform="matrix(1,0,0,-1,155.66,50.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.299999" y="-7.2600002"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.51" y="-0.0099999998"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.673499" y="-0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.925718" y="-0.0099999998"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.552547" y="-0.0099999998"> ≡</t年代p一个n></text> <g> <path d="m 201.46,53.58 9.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,201.46,41.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.64" y="-19.33"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.49" y="-16.82"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.34" y="-19.33"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,240.05,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,250.92,58.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m 213.1,53.58 43.67,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,220.22,41.7)"> <tspan style="font-size: 12.50px; " x="37.75" y="-8.75"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.840341" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.003839" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.25606" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="235.56" y="-10.9"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="239.7235" y="-10.9"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="248.70065" y="-10.9"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="251.8264" y="-10.9"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="258.07791" y="-10.9"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="264.32941" y="-10.9"> )</t年代p一个n></text> </g> </g> </svg></span>我们扩大这个方程<年代vg height="10.6875" id="M246" style="vertical-align:-0.0pt;width:38.887501px;" version="1.1" viewbox="0 0 38.887501 10.6875" width="38.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.715551" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.755939" y="0"> 1</t年代p一个n></text> </g> </g> </svg>通过表示<年代vg height="11.325" id="M247" style="vertical-align:-0.51414pt;width:63.887501px;" version="1.1" viewbox="0 0 63.887501 11.325" width="63.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.325)"> <g transform="translate(72,-62.94)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.715551" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.755939" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.783108" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.123325" y="0"> </t年代p一个n></text> </g> </g> </svg>与<年代vg height="11.1" id="M248" style="vertical-align:-0.32603pt;width:38.549999px;" version="1.1" viewbox="0 0 38.549999 11.1" width="38.549999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1)"> <g transform="translate(72,-63.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3397408" y="0"> ≪</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.480873" y="0"> 1</t年代p一个n></text> </g> </g> </svg>作为<年代p一个ncl作为年代=”equation" id="EEq30"> <svg height="76.75" id="M249" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 76.75" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,76.75)"> <g transform="translate(72,-10.6)"> <text transform="matrix(1,0,0,-1,71.35,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,78.78,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,85.74,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.666979" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.707369" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.22263" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.386131" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.413296" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.753517" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="72.629929" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.881424" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,172.05,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,179.01,63.2)"> <tspan style="font-size: 12.50px; " x="-74.589996" y="23.530001"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-62.560001" y="26.049999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3269978" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.354164" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.694386" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.570793" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.822296" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.698944" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-56.700001" y="23.530001"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-47.685337" y="23.530001"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-36.332615" y="23.530001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,152.11,44.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,157.66,39.67)"> <tspan style="font-size: 12.50px; " x="64.110001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.414999" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.653996" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.318575" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.658794" y="0"> ⋯</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.330002" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.256901" y="2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,229.2,36.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,236.16,39.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.979315" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.319534" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,274.79,44.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-1.88" y="9.2200003"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,280.34,39.67)"> <tspan style="font-size: 12.50px; " x="57.830002" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.279146" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.155556" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.820374" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.160595" y="0"> ⋯</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-175.92" y="24.450001"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-163.89212" y="24.450001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,123.88,12.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,130.84,15.22)"> <tspan style="font-size: 12.50px; " x="37.279999" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.139999" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.979315" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.319534" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,183.4,20.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,188.96,15.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.414999" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.653996" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,213.05,12.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,220.01,15.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.979315" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.319534" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.196186" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,265.51,20.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-1.87" y="9.2200003"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,271.07,15.22)"> <tspan style="font-size: 12.50px; " x="15.2" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.66" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.52" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.83" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.170219" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,329.46,20.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,334.34,12.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9299998" y="-2.52"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="121.44" y="-25.48"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="125.6035" y="-25.48"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="134.58066" y="-25.48"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="137.70641" y="-25.48"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="143.9579" y="-25.48"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="150.2094" y="-25.48"> )</t年代p一个n></text> </g> </g> </svg></span>我们使用这一事实在哪里<年代vg height="13.45" id="M250" style="vertical-align:-2.21957pt;width:57.025002px;" version="1.1" viewbox="0 0 57.025002 13.45" width="57.025002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.1772022" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.340701" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.592201" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.21903" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.259418" y="0"> 1</t年代p一个n></text> </g> </g> </svg>。我们也认为衍生品<年代vg height="15.4125" id="M251" style="vertical-align:-2.21957pt;width:34.474998px;" version="1.1" viewbox="0 0 34.474998 15.4125" width="34.474998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.4125)"> <g transform="translate(72,-59.67)"> <text transform="matrix(1,0,0,-1,-71.95,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.52,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.05,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.414999" y="0"> )</t年代p一个n></text> </g> </g> </svg>和<年代vg height="17.825001" id="M252" style="vertical-align:-4.22832pt;width:35.099998px;" version="1.1" viewbox="0 0 35.099998 17.825001" width="35.099998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.825)"> <g transform="translate(72,-57.74)"> <text transform="matrix(1,0,0,-1,-71.95,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.65,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-1.87" y="9.2200003"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.17,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n></text> </g> </g> </svg>存在于上述的有效性应检查结果。从上面,我们发现以下应满足:<年代p一个ncl作为年代=”equation" id="EEq31"> <svg height="17.9125" id="M253" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 17.9125" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.9125)"> <g transform="translate(72,-57.67)"> <text transform="matrix(1,0,0,-1,139.78,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,149.21,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,154.77,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.414999" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.653996" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,178.86,58.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,185.81,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.979315" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.319534" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.196186" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,231.32,66.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-1.88" y="9.2200003"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,236.88,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.666979" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.707369" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.958866" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="218.89999" y="0.23"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="223.06349" y="0.23"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="232.04065" y="0.23"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="235.1664" y="0.23"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="241.41791" y="0.23"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="247.6694" y="0.23"> )</t年代p一个n></text> </g> </g> </svg></span>给出的解决方案是谁的<年代p一个ncl作为年代=”equation" id="EEq32"> <svg height="20.737499" id="M254" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 20.737499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.7375)"> <g transform="translate(72,-55.41)"> <text transform="matrix(1,0,0,-1,163.83,59.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,171.26,56.08)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,178.21,59.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.679482" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.707369" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.096882" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,224.19,64.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,236.79,67.71)"> <tspan style="font-size: 6.25px; " x="0" y="0"> ′</t年代p一个n></text> <text transform="matrix(1,0,0,-1,239.09,64.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,249.8,59.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="205.98" y="-1.37"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="210.14349" y="-1.37"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="219.12065" y="-1.37"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="222.2464" y="-1.37"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="228.49791" y="-1.37"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="234.7494" y="-1.37"> )</t年代p一个n></text> </g> </g> </svg></span>这是期望的结果,帕累托法则,与之前的假设是一致的<年代vg height="17.825001" id="M255" style="vertical-align:-4.22832pt;width:35.099998px;" version="1.1" viewbox="0 0 35.099998 17.825001" width="35.099998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.825)"> <g transform="translate(72,-57.74)"> <text transform="matrix(1,0,0,-1,-71.95,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.65,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-1.87" y="9.2200003"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.17,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n></text> </g> </g> </svg>的存在。用结果(<一个href="#EEq32">A.23</一个>)(<gydF4y2Ba一个href="#EEq29">A.20</一个>)和(<一个href="#EEq27">A.18</一个>),我们发现<年代p一个ncl作为年代=”equation" id="EEq33"> <svg height="20.737499" id="M256" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 20.737499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.7375)"> <g transform="translate(72,-55.41)"> <text transform="matrix(1,0,0,-1,170.08,59.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.50276" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.666259" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.91848" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.557812" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.598202" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,223.94,64.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,230.54,67.71)"> <tspan style="font-size: 6.25px; " x="0" y="0"> ′</t年代p一个n></text> <text transform="matrix(1,0,0,-1,232.84,64.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.9144161" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,243.54,59.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="212.24001" y="-1.37"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="216.4035" y="-1.37"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="225.38065" y="-1.37"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="228.50641" y="-1.37"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="234.7579" y="-1.37"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="241.0094" y="-1.37"> )</t年代p一个n></text> </g> </g> </svg></span>这与假设是一致的吗<年代vg height="15.4125" id="M257" style="vertical-align:-2.21957pt;width:34.474998px;" version="1.1" viewbox="0 0 34.474998 15.4125" width="34.474998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.4125)"> <g transform="translate(72,-59.67)"> <text transform="matrix(1,0,0,-1,-71.95,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.52,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.05,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.414999" y="0"> )</t年代p一个n></text> </g> </g> </svg>的存在。</年代p一个n><br>从(<一个href="#EEq29">A.20</一个>)和(<一个href="#EEq33">A.24</一个>),我们发现以下关系:<年代p一个ncl作为年代=”equation" id="EEq34"> <svg height="19.475" id="M258" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.475" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.475)"> <g transform="translate(72,-56.42)"> <text transform="matrix(1,0,0,-1,145.74,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.840341" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.003839" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.25606" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.895393" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.935783" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,199.93,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="11.325088" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="17.320208" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,222.13,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.85" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.700001" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,249.08,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,259.95,58.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9299998" y="-2.51"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="195.83" y="-2.5599999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="199.9935" y="-2.5599999"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="208.97066" y="-2.5599999"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="212.09641" y="-2.5599999"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="218.3479" y="-2.5599999"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="224.5994" y="-2.5599999"> )</t年代p一个n></text> </g> </g> </svg></span>应与此形成鲜明对比的是(<一个href="#EEq25">A.16</一个>)。如果Gibrat定律(<一个href="#EEq22">A.13</一个>适用于所有<年代vg height="13.125" id="M259" style="vertical-align:-1.95624pt;width:67.3125px;" version="1.1" viewbox="0 0 67.3125 13.125" width="67.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.125)"> <g transform="translate(72,-61.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.339981" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.380369" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.543869" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.795368" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.009121" y="0"> ∞</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.586899" y="0"> ]</t年代p一个n></text> </g> </g> </svg>,然后<年代vg height="14.6" id="M260" style="vertical-align:-3.13504pt;width:93.675003px;" version="1.1" viewbox="0 0 93.675003 14.6" width="93.675003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.52,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.55,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.415719" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.042549" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.082939" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.847782" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.01128" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.2635" y="0"> )</t年代p一个n></text> </g> </g> </svg>从(<一个href="#EEq18">A.10</一个>)。如果是这样,(<一个href="#EEq34">A.25</一个>)与(<一个href="#EEq25">A.16</一个>),因为<年代vg height="13.55" id="M261" style="vertical-align:-2.29482pt;width:36.849998px;" version="1.1" viewbox="0 0 36.849998 13.55" width="36.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.077658" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.118048" y="0"> 0</t年代p一个n></text> </g> </g> </svg>。此外,帕累托法则我们来自Gibrat定律不是normalizable如果它适用于任何<年代vg height="7.1624999" id="M262" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。因此,Gibrat定律应该只在有限的范围<年代vg height="7.1624999" id="M263" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。<gydF4y2Babr>结果(<一个href="#EEq34">A.25</一个>)表明,该函数<年代vg height="13.45" id="M264" style="vertical-align:-2.21957pt;width:34.299999px;" version="1.1" viewbox="0 0 34.299999 13.45" width="34.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.764843" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.928342" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.180561" y="0"> )</t年代p一个n></text> </g> </g> </svg>是连续的<年代vg height="10.6875" id="M265" style="vertical-align:-0.0pt;width:38.887501px;" version="1.1" viewbox="0 0 38.887501 10.6875" width="38.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.715551" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.755939" y="0"> 1</t年代p一个n></text> </g> </g> </svg>,很容易被取代<年代vg height="11.325" id="M266" style="vertical-align:-0.51414pt;width:63.887501px;" version="1.1" viewbox="0 0 63.887501 11.325" width="63.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.325)"> <g transform="translate(72,-62.94)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.715551" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.755939" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.783108" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.123325" y="0"> </t年代p一个n></text> </g> </g> </svg>与<年代vg height="11.0625" id="M267" style="vertical-align:-0.30096pt;width:34.674999px;" version="1.1" viewbox="0 0 34.674999 11.0625" width="34.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3397408" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.380131" y="0"> 0</t年代p一个n></text> </g> </g> </svg>右手边和限制<年代vg height="11.325" id="M268" style="vertical-align:-0.51414pt;width:54.349998px;" version="1.1" viewbox="0 0 54.349998 11.325" width="54.349998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.325)"> <g transform="translate(72,-62.94)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.427742" y="0"> →</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.556852" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.121407" y="0"> 0</t年代p一个n></text> </g> </g> </svg>。</年代p一个n></p><h4 id="b.-the-hjb-equation">b的HJB方程</gydF4y2Bah4> <p>在一般情况下(<一个href="#EEq1">2。1</一个>)- (<一个href="#EEq1">2。3</一个>)与内源性信贷成本和融资溢价所(<一个href="#EEq9">3.1</一个>),我们有以下HJB方程:<年代p一个ncl作为年代=”equation" id="EEq35"> <svg height="38.575001" id="M269" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.575001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,38.575)"> <g transform="translate(72,-41.14)"> <text transform="matrix(1,0,0,-1,76.88,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.12" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.969999" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.746626" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.960377" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,118.04,58.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,125.2,53.45)"> <tspan style="font-size: 12.50px; " x="15.11" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.940125" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.43" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.457886" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.185219" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.736553" y="0"> x</t年代p一个n></text> <text transform="matrix(1,0,0,-1,171.51,45.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,187.37,46.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.3499999" y="-7.3299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.865023" y="-7.3299999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.028522" y="-7.3299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.805147" y="-7.3299999"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.018898" y="-7.3299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.632748" y="-7.3299999"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.571911" y="-7.3299999"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.119999" y="-15.55"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.771599" y="-15.55"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,261.34,66.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,268.5,61.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.940125" y="0"> )</t年代p一个n></text> <g> <path d="m 245.49,56.57 38.11,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,257.83,44.69)"> <tspan style="font-size: 12.50px; " x="70.480003" y="-1.4299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.049999" y="-8.7600002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.213497" y="-8.7600002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.852833" y="-8.7600002"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.193054" y="-8.7600002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.532314" y="-8.7600002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.308937" y="-8.7600002"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.919998" y="-8.7600002"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="204.83" y="-8.7600002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="208.9935" y="-8.7600002"> B</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="217.33299" y="-8.7600002"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="220.45876" y="-8.7600002"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="226.71025" y="-8.7600002"> )</t年代p一个n></text> </g> </g> </svg></span></p> <p>注意,在极限情况下,没有借贷和<年代vg height="10.7375" id="M270" style="vertical-align:-0.13794pt;width:41.287498px;" version="1.1" viewbox="0 0 41.287498 10.7375" width="41.287498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.103384" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.143772" y="0"> </t年代p一个n></text> </g> </g> </svg>,因此不断的折现率<年代vg height="10.7375" id="M271" style="vertical-align:-0.13794pt;width:8.3125px;" version="1.1" viewbox="0 0 8.3125 10.7375" width="8.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>拥有时,我们获得HJB方程<年代p一个ncl作为年代=”equation" id="EEq36"> <svg height="38.575001" id="M272" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.575001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,38.575)"> <g transform="translate(72,-41.14)"> <text transform="matrix(1,0,0,-1,100.06,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.077898" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.241398" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.018023" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.657356" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.697746" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.425079" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.97641" y="0"> x</t年代p一个n></text> <text transform="matrix(1,0,0,-1,152.6,45.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,168.46,46.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.3499999" y="-7.3299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.865023" y="-7.3299999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.028522" y="-7.3299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.805147" y="-7.3299999"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.018898" y="-7.3299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.632748" y="-7.3299999"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.571911" y="-7.3299999"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.119999" y="-15.55"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.771599" y="-15.55"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="76.849495" y="-15.55"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="81.012993" y="-15.55"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="87.789619" y="-15.55"> )</t年代p一个n></text> <g> <path d="m 226.58,56.57 33.84,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,236.79,44.69)"> <tspan style="font-size: 12.50px; " x="68.339996" y="-1.4299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.91" y="-8.7600002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.0735" y="-8.7600002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.712833" y="-8.7600002"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.053055" y="-8.7600002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.392315" y="-8.7600002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.168938" y="-8.7600002"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="76.769997" y="-8.7600002"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="225.87" y="-8.7600002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="230.03349" y="-8.7600002"> B</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="238.373" y="-8.7600002"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="241.49875" y="-8.7600002"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="247.75024" y="-8.7600002"> )</t年代p一个n></text> </g> </g> </svg></span></p> <p>在这种情况下,<年代vg height="13.45" id="M273" style="vertical-align:-2.21957pt;width:27.987499px;" version="1.1" viewbox="0 0 27.987499 13.45" width="27.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1892252" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.129351" y="0"> )</t年代p一个n></text> </g> </g> </svg>是信誉;换句话说,该公司最高贷款额等于资产价格<年代vg height="13.45" id="M274" style="vertical-align:-2.21957pt;width:27.987499px;" version="1.1" viewbox="0 0 27.987499 13.45" width="27.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1892252" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.129351" y="0"> )</t年代p一个n></text> </g> </g> </svg>。</p><p>gydF4y2Bahjb方程(<一个href="#EEq35">责任</一个>)可以写成<年代p一个ncl作为年代=”equation" id="EEq37"> <svg height="38.575001" id="M275" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.575001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,38.575)"> <g transform="translate(72,-41.14)"> <text transform="matrix(1,0,0,-1,83.29,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,92.49,58.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,99.65,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.940125" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.566956" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.607344" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.334679" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.886009" y="0"> x</t年代p一个n></text> <text transform="matrix(1,0,0,-1,140.11,45.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,155.96,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,168,58.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,180.96,46.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.3499999" y="-7.3299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.865023" y="-7.3299999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.028522" y="-7.3299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.805147" y="-7.3299999"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.018898" y="-7.3299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.632748" y="-7.3299999"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.571911" y="-7.3299999"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.119999" y="-15.55"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.771599" y="-15.55"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,254.93,66.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,262.09,61.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.940125" y="0"> )</t年代p一个n></text> <g> <path d="m 239.08,56.57 38.11,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,251.42,44.69)"> <tspan style="font-size: 12.50px; " x="70.480003" y="-1.4299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.049999" y="-8.7600002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.213497" y="-8.7600002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.852833" y="-8.7600002"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.193054" y="-8.7600002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.532314" y="-8.7600002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.308937" y="-8.7600002"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.919998" y="-8.7600002"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="211.24001" y="-8.7600002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="215.4035" y="-8.7600002"> B</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="223.743" y="-8.7600002"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="226.86874" y="-8.7600002"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="233.12025" y="-8.7600002"> )</t年代p一个n></text> </g> </g> </svg></span>这是一个标准的动态形式的HJB方程。接下来,为目的的一个例子,让我们指定<年代vg height="13.9625" id="M276" style="vertical-align:-2.21957pt;width:96.237503px;" version="1.1" viewbox="0 0 96.237503 13.9625" width="96.237503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9625)"> <g transform="translate(72,-60.83)"> <text transform="matrix(1,0,0,-1,-71.95,63.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.915119" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.078618" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.855244" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.056492" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.758579" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.397915" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.438301" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.989876" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-0.75,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>在那里,<年代vg height="11.0625" id="M277" style="vertical-align:-0.30096pt;width:36.612499px;" version="1.1" viewbox="0 0 36.612499 11.0625" width="36.612499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.890113" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.930502" y="0"> 1</t年代p一个n></text> </g> </g> </svg>利息支付是完全凸<年代vg height="10.325" id="M278" style="vertical-align:-0.0pt;width:11.625px;" version="1.1" viewbox="0 0 11.625 10.325" width="11.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。然后,我们有<年代p一个ncl作为年代=”equation" id="EEq38"> <svg height="41.862499" id="M279" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 41.862499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,41.8625)"> <g transform="translate(72,-38.51)"> <text transform="matrix(1,0,0,-1,87.68,50.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,96.89,55.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,104.05,50.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.940125" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.566956" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.607344" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.334679" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.886009" y="0"> x</t年代p一个n></text> <text transform="matrix(1,0,0,-1,144.5,43.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,158.27,43.48)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.3600001" y="-7.3299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.875023" y="-7.3299999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.038523" y="-7.3299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.815147" y="-7.3299999"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.0289" y="-7.3299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.642746" y="-7.3299999"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.581909" y="-7.3299999"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.119999" y="-14.58"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.771599" y="-14.58"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,232.25,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <g> <path d="m 216.39,53.94 20.93,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,220.14,42.06)"> <tspan style="font-size: 12.50px; " x="61.889999" y="-1.42"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.459999" y="-8.7600002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.623499" y="-8.7600002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.262833" y="-8.7600002"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.603054" y="-8.7600002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.942314" y="-8.7600002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.718941" y="-8.7600002"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,288.38,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.8090558" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,300.89,50.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,307.44,55.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.37112" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="12.804176" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,325.94,50.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="136.72" y="-1.3200001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="140.8835" y="-1.3200001"> B</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="149.22301" y="-1.3200001"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="152.34875" y="-1.3200001"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="158.60025" y="-1.3200001"> )</t年代p一个n></text> </g> </g> </svg></span></p> <p>平衡的HJB方程(<一个href="#EEq38">B.4</一个>),<gydF4y2Ba年代vg height="11.0625" id="M280" style="vertical-align:-0.30096pt;width:36.612499px;" version="1.1" viewbox="0 0 36.612499 11.0625" width="36.612499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.890113" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.930502" y="0"> 1</t年代p一个n></text> </g> </g> </svg>,如下所示。的算法研究更一般的问题(<一个href="#EEq37">B.3</一个>)或(<一个href="#EEq38">B.4</一个>)总结了Grune et al。<一个href="#B15">18</一个>]。注意,如果<年代vg height="10.6875" id="M281" style="vertical-align:-0.0pt;width:36.612499px;" version="1.1" viewbox="0 0 36.612499 10.6875" width="36.612499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.890113" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.930502" y="0"> 1</t年代p一个n></text> </g> </g> </svg>,我们有一个HJB方程的标准形式。</p><p>gydF4y2Ba如果HJB方程(<一个href="#EEq38">B.4</一个>)持有<年代vg height="13.9625" id="M282" style="vertical-align:-2.21957pt;width:81.262497px;" version="1.1" viewbox="0 0 81.262497 13.9625" width="81.262497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9625)"> <g transform="translate(72,-60.83)"> <text transform="matrix(1,0,0,-1,-71.95,63.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.915119" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.078618" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.780706" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.407536" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.447926" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.999496" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-12.74,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,金融溢价取决于公司的债务。这个扩展提出了Grune et al。<一个href="#B15">18</一个>]。为<年代vg height="13.9625" id="M283" style="vertical-align:-2.21957pt;width:81.262497px;" version="1.1" viewbox="0 0 81.262497 13.9625" width="81.262497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9625)"> <g transform="translate(72,-60.83)"> <text transform="matrix(1,0,0,-1,-71.95,63.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.915119" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.078618" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.780706" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.407536" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.447926" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.999496" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-12.74,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>为<年代vg height="12.3" id="M284" style="vertical-align:-1.29163pt;width:36.612499px;" version="1.1" viewbox="0 0 36.612499 12.3" width="36.612499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.3)"> <g transform="translate(72,-62.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.890113" y="0"> ≥</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.930502" y="0"> 1</t年代p一个n></text> </g> </g> </svg>为候选人,它会导致以下方程平衡稳定状态:<年代p一个ncl作为年代=”equation" id="EEq39"> <svg height="46.724998" id="M285" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 46.724998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,46.725)"> <g transform="translate(72,-34.62)"> <text transform="matrix(1,0,0,-1,101.22,52.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0146627" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.367388" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.618887" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.482553" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,139.48,57.68)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,153.89,52.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.91" y="-8.3500004"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.949188" y="-8.3500004"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,183.63,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.9273758" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.922496" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,202.21,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.455149" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.795368" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,242.36,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,249.31,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.190665" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.530886" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.88241" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.133911" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,293.23,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.37112" y="0"> </t年代p一个n></text> <g> <path d="m 167.13,55.74 144.08,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,167.13,39.23)"> <tspan style="font-size: 12.50px; " x="13.98" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.83" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.5390692" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,193.73,44.3)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,201.95,39.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.327718" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.666979" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.231773" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.571995" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,248.87,42.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,253.74,39.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,260.52,44.3)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.37112" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,275.83,36.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,281.68,46.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.1131039" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="14.108224" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="18.484224" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="21.39864" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="23.831696" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,312.41,52.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="150.25" y="2.4300001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="154.4135" y="2.4300001"> B</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="162.75301" y="2.4300001"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="165.87875" y="2.4300001"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="172.13025" y="2.4300001"> )</t年代p一个n></text> </g> </g> </svg></span></p> <p>在这里,再一次,<年代vg height="10.6875" id="M286" style="vertical-align:-0.0pt;width:36.612499px;" version="1.1" viewbox="0 0 36.612499 10.6875" width="36.612499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.890113" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.930502" y="0"> 1</t年代p一个n></text> </g> </g> </svg>稳态候选人,抛开消费,为标准的HJB方程是一样的,也就是说,当<年代vg height="13.45" id="M287" style="vertical-align:-2.21957pt;width:108px;" version="1.1" viewbox="0 0 108 13.45" width="108" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.915119" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.078618" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.855244" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.056492" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.758579" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.922077" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.698704" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.862206" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.501537" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="70.541924" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="77.093498" y="0"> </t年代p一个n></text> </g> </g> </svg>,因此在(<一个href="#EEq37">B.3</一个>)和(<一个href="#EEq38">B.4</一个>),<gydF4y2Ba年代vg height="10.6875" id="M288" style="vertical-align:-0.0pt;width:36.612499px;" version="1.1" viewbox="0 0 36.612499 10.6875" width="36.612499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.890113" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.930502" y="0"> 1</t年代p一个n></text> </g> </g> </svg>成立。解决问题的方法的细节(<一个href="#EEq1">2。1</一个>)- (<一个href="#EEq1">2。3</一个>),看到Grune et al。<一个href="#B15">18</一个>,为进一步的应用算法,看到Grune Semmler [<一个href="#B14">21</一个>]。</p><gydF4y2Bah4 id="acknowledgments">确认</gydF4y2Bah4> <p>作者要感谢博士Masanao青木,毛罗·Gallegati博士Corrado Di Guilmi博士和大成建设Kaizouji合作作品在不同阶段的研究。他们要感谢两个裁判杂志的广泛评论。</p></gydF4y2Badiv> <div class="xml-content"> <h4 class="references" id="references">引用</gydF4y2Bah4> <ol> <li id="B13">r . 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Semmler&publication_year=1999" target="_blank">谷歌学术搜索</一个></年代p一个n></li> <li id="B23">诉帕累托,<我>课堂上d 'Economie政治</我>,麦克米伦,伦敦,英国,1897年。<年代p一个ncl作为年代=”reflinks"></span></li> </ol> </div> <div class="xml-content"> <h4 class="copyright" id="copyright">版权</gydF4y2Bah4> <p>版权©2011 Hideaki青山等。这是一个开放的分布式下文章<一个rel="license" href="http://creativecommons.org/licenses/by/3.0/">知识共享归属许可</一个>,它允许无限制的使用、分配和复制在任何媒介,提供最初的工作是正确引用。</p></gydF4y2Badiv> </div> </article> </div> </div> </div> <div class="biblio__StyledBibblio-sc-17w4z31-0 fSkSUQ"> <div id="takeover" class="biblio__TakeoverWrapper-sc-17w4z31-2 kqVUJv"> <div id="bib--hide-takeover-element-mobile"> <div id="bib--takeover-element-mobile"> <h4 class="biblio__H4-sc-17w4z31-4 esVMqk">相关文章</gydF4y2Bah4> <div id="bib--rcm-takeover-element-mobile"> 对本文没有相关内容可用。</gydF4y2Badiv> </div> </div> </div> </div> <div class="biblio__StyledBibblio-sc-17w4z31-0 fSkSUQ"> <div class="biblio__FooterWrapper-sc-17w4z31-3 iGPSPq mobile-widget" 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pdf_desktop button__group" href="//www.newsama.com/downloads/journals/aor/2011/269239.pdf" aria-label="" target="_blank" id="toolbar__dcNavSmall"><span><img alt="" class="sc-EHOje jOLhQl sc-kTUwUJ eujois" title="" role="presentation" src="https://static-02.hindawi.com/next_assets/QTXPp35dHcz81F9E4L5m3/_next/static/node_modules/hindawi-ui/src/icon/svg/pdf.svg" height="24"><span class="text">PDF</年代p一个n></年代p一个n><span class="sc-htoDjs bqeMOy sc-dqBHgY cQgXqt fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> <a class="sc-htpNat bUhGXt link sc-jtRfpW dUABlg sc-cBdUnI bQvNmJ ref_desktop" href="//www.newsama.com/journals/aor/2011/269239.ris" aria-label="" target="" id="toolbar__dcNavLarge"><span><img alt="" class="sc-EHOje jOLhQl sc-kTUwUJ eujois" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"><span class="text">下载引用</年代p一个n></年代p一个n><span class="sc-htoDjs bqeMOy sc-dqBHgY cQgXqt fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> <a class="sc-htpNat bUhGXt link sc-jtRfpW dUABlg sc-exkUMo ikaeWC ref_desktop" href="//www.newsama.com/journals/aor/2011/269239.ris" aria-label="" target="" id="toolbar__dcNavSmall"><span><img alt="" class="sc-EHOje jOLhQl sc-kTUwUJ eujois" title="" role="presentation" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHhtbG5zOnhsaW5rPSJodHRwOi8vd3d3LnczLm9yZy8xOTk5L3hsaW5rIiB3aWR0aD0iMTgiIGhlaWdodD0iMjIiIHZpZXdCb3g9IjAgMCAxOCAyMiI+PGRlZnM+PGNsaXBQYXRoIGlkPSJhIj48cGF0aCBkPSJNMywyMmEzLDMsMCwwLDEtMy0zVjNBMywzLDAsMCwxLDMsMGg4YS45OTEuOTkxLDAsMCwxLC41NzMuMTgxbDAsMCwuMDA4LjAwNmEuOTU1Ljk1NSwwLDAsMSwuMTIyLjFsNiw2YTEuMDI1LDEuMDI1LDAsMCwxLC4xLjEyMmwuMDA2LjAxLDAsMEExLDEsMCwwLDEsMTgsNi45NzVWMTlhMywzLDAsMCwxLTMsM1pNMiwzVjE5YTEsMSwwLDAsMCwxLDFIMTVhMSwxLDAsMCwwLDEtMVY4SDExYTEsMSwwLDAsMS0xLTFWMkgzQTEsMSwwLDAsMCwyLDNaTTEyLDZoMi41ODdMMTIsMy40MTRaTTUsMTdhMSwxLDAsMSwxLDAtMmg4YTEsMSwwLDEsMSwwLDJabTAtNGExLDEsMCwxLDEsMC0yaDhhMSwxLDAsMSwxLDAsMlpNNSw5QTEsMSwwLDEsMSw1LDdIN0ExLDEsMCwwLDEsNyw5WiIgdHJhbnNmb3JtPSJ0cmFuc2xhdGUoMyAxKSIvPjwvY2xpcFBhdGg+PC9kZWZzPjxnIHRyYW5zZm9ybT0idHJhbnNsYXRlKC0zIC0xKSI+PHBhdGggZD0iTTMsMjJhMywzLDAsMCwxLTMtM1YzQTMsMywwLDAsMSwzLDBoOGEuOTkxLjk5MSwwLDAsMSwuNTczLjE4MWwwLDAsLjAwOC4wMDZhLjk1NS45NTUsMCwwLDEsLjEyMi4xbDYsNmExLjAyNSwxLjAyNSwwLDAsMSwuMS4xMjJsLjAwNi4wMSwwLDBBMSwxLDAsMCwxLDE4LDYuOTc1VjE5YTMsMywwLDAsMS0zLDNaTTIsM1YxOWExLDEsMCwwLDAsMSwxSDE1YTEsMSwwLDAsMCwxLTFWOEgxMWExLDEsMCwwLDEtMS0xVjJIM0ExLDEsMCwwLDAsMiwzWk0xMiw2aDIuNTg3TDEyLDMuNDE0Wk01LDE3YTEsMSwwLDEsMSwwLTJoOGExLDEsMCwxLDEsMCwyWm0wLTRhMSwxLDAsMSwxLDAtMmg4YTEsMSwwLDEsMSwwLDJaTTUsOUExLDEsMCwxLDEsNSw3SDdBMSwxLDAsMCwxLDcsOVoiIHRyYW5zZm9ybT0idHJhbnNsYXRlKDMgMSkiLz48ZyBjbGlwLXBhdGg9InVybCgjYSkiPjxyZWN0IHdpZHRoPSIyNCIgaGVpZ2h0PSIyNCIgZmlsbD0icmdiYSgwLDAsMCwwKSIvPjxyZWN0IHdpZHRoPSIyNCIgaGVpZ2h0PSIyNCIvPjwvZz48L2c+PC9zdmc+" height="24"><span class="text">引用</年代p一个n></年代p一个n><span class="sc-htoDjs bqeMOy sc-dqBHgY cQgXqt fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> </div> </div> <div class="journal_article__ArticleStickyBottomToolbar-sc-t08z80-1 biDsJe article_sticky_bottom_toolbar"> <div class="sc-iYUSvU xdFeU article_bottom_toolbar"> <div class="sc-cHSUfg hlwZCh accordion" property="background-color" color="#D8D8D8" id="toolbar__dofNav"> <span><img alt="" class="sc-EHOje jOLhQl sc-iNhVCk fhBqDd" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"><span class="sc-bfYoXt jLRaNL">下载其他格式</年代p一个n><年代p一个ncl作为年代="sc-gbOuXE kvCIiS">更多的</年代p一个n></年代p一个n> <span class="sc-htoDjs bMdQcY sc-eAKXzc bmKKdh icon-colored _1CwL9R82TPl2HxDleeYGDR icon-themeable" title="" font-size="11"></span> </div> <div class="sc-cTjmhe fEoWte"> <a class="sc-htpNat bUhGXt link sc-cugefK irOfVO open_panel" href="//www.newsama.com/downloads/journals/aor/2011/269239.epub" aria-label="ePub" property="background-color" color="#D8D8D8"> <div class="sc-fnwBNb gUqhXf"> ePub</gydF4y2Badiv><img alt="" class="sc-EHOje jOLhQl sc-iNhVCk fhBqDd" title="" role="presentation" 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height="24"><span class="sc-bfYoXt jLRaNL">订单打印副本</年代p一个n><年代p一个ncl作为年代="sc-gbOuXE kvCIiS">订单</年代p一个n></年代p一个n><span class="sc-htoDjs kNoiZu sc-eAKXzc bmKKdh right__icon icon-colored _32KP5uexH-Bgs7Kj8Gk1Tz icon-themeable" title="" font-size="16"></span></a> <div class="sc-bFADNz dxRcBT"> <div class="sc-cqpYsc bTgkQB"> <div> 的观点<年代p一个n>1368年年</年代p一个n></div> <div> 下载<年代p一个n>1143年年</年代p一个n></div> </div> <div> <div class="sc-hBbWxd exhBez"> <span class="__dimensions_badge_embed__" data-doi="10.1155/2011/269239" data-style="small_circle"></span>引用</gydF4y2Badiv> </div> </div> <nav class="sc-bRBYWo fXBKFa sc-dRFtgE evqjui" id="toolbar__iconNav"> <h3 class="sc-Rmtcm hNPrIr">分享文章</gydF4y2Bah3> <ul class="sc-hzDkRC bnbfTS"> <li class="iconBorder"><a class="sc-htpNat bUhGXt link" href="https://twitter.com/share?url=https://doi.org/10.1155/2011/269239&via=Hindawi" aria-label="Sharing on Twitter" rel="noopener noreferrer" target="_blank"><img alt="" class="sc-EHOje jOLhQl socialTwitter" title="" 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