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id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Início</div> </a> </li> <li id="toc-Custo_marginal_e_o_custo_médio" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Custo_marginal_e_o_custo_médio"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Custo marginal e o custo médio</span> </div> </a> <button aria-controls="toc-Custo_marginal_e_o_custo_médio-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Alternar a subsecção Custo marginal e o custo médio</span> </button> <ul id="toc-Custo_marginal_e_o_custo_médio-sublist" class="vector-toc-list"> <li id="toc-Exemplo" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Exemplo"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Exemplo</span> </div> </a> <ul id="toc-Exemplo-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Ver_também" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ver_também"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Ver também</span> </div> </a> <ul id="toc-Ver_também-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referências" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referências"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Referências</span> </div> </a> <ul id="toc-Referências-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografia"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Bibliografia</span> </div> </a> <ul id="toc-Bibliografia-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Conteúdo" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Alternar o índice" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Alternar o índice</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Custo marginal</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Ir para um artigo noutra língua. Disponível em 37 línguas" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-37" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">37 línguas</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D9%83%D9%84%D9%81%D8%A9_%D8%AD%D8%AF%D9%8A%D8%A9" title="تكلفة حدية — árabe" lang="ar" hreflang="ar" data-title="تكلفة حدية" data-language-autonym="العربية" data-language-local-name="árabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Marjinal_x%C9%99rcl%C9%99r" title="Marjinal xərclər — azerbaijano" lang="az" hreflang="az" data-title="Marjinal xərclər" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaijano" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Cost_marginal" title="Cost marginal — catalão" lang="ca" hreflang="ca" data-title="Cost marginal" data-language-autonym="Català" data-language-local-name="catalão" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Mezn%C3%AD_n%C3%A1klady" title="Mezní náklady — checo" lang="cs" hreflang="cs" data-title="Mezní náklady" data-language-autonym="Čeština" data-language-local-name="checo" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Grenzkosten" title="Grenzkosten — alemão" lang="de" hreflang="de" data-title="Grenzkosten" data-language-autonym="Deutsch" data-language-local-name="alemão" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Marginal_cost" title="Marginal cost — inglês" lang="en" hreflang="en" data-title="Marginal cost" data-language-autonym="English" data-language-local-name="inglês" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Mar%C4%9Denaj_kostoj" title="Marĝenaj kostoj — esperanto" lang="eo" hreflang="eo" data-title="Marĝenaj kostoj" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Coste_marginal" title="Coste marginal — espanhol" lang="es" hreflang="es" data-title="Coste marginal" data-language-autonym="Español" data-language-local-name="espanhol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Kostu_marjinal" title="Kostu marjinal — basco" lang="eu" hreflang="eu" data-title="Kostu marjinal" data-language-autonym="Euskara" data-language-local-name="basco" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%87%D8%B2%DB%8C%D9%86%D9%87_%D9%86%D9%87%D8%A7%DB%8C%DB%8C" title="هزینه نهایی — persa" lang="fa" hreflang="fa" data-title="هزینه نهایی" data-language-autonym="فارسی" data-language-local-name="persa" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Rajakustannus" title="Rajakustannus — finlandês" lang="fi" hreflang="fi" data-title="Rajakustannus" data-language-autonym="Suomi" data-language-local-name="finlandês" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Co%C3%BBt_marginal" title="Coût marginal — francês" lang="fr" hreflang="fr" data-title="Coût marginal" data-language-autonym="Français" data-language-local-name="francês" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Custo_marxinal" title="Custo marxinal — galego" lang="gl" hreflang="gl" data-title="Custo marxinal" data-language-autonym="Galego" data-language-local-name="galego" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A2%D7%9C%D7%95%D7%AA_%D7%A9%D7%95%D7%9C%D7%99%D7%AA" title="עלות שולית — hebraico" lang="he" hreflang="he" data-title="עלות שולית" data-language-autonym="עברית" data-language-local-name="hebraico" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Hat%C3%A1rk%C3%B6lts%C3%A9g" title="Határköltség — húngaro" lang="hu" hreflang="hu" data-title="Határköltség" data-language-autonym="Magyar" data-language-local-name="húngaro" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Biaya_marginal" title="Biaya marginal — indonésio" lang="id" hreflang="id" data-title="Biaya marginal" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonésio" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Ja%C3%B0arkostna%C3%B0ur" title="Jaðarkostnaður — islandês" lang="is" hreflang="is" data-title="Jaðarkostnaður" data-language-autonym="Íslenska" data-language-local-name="islandês" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Costo_marginale" title="Costo marginale — italiano" lang="it" hreflang="it" data-title="Costo marginale" data-language-autonym="Italiano" data-language-local-name="italiano" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%99%90%E7%95%8C%E8%B2%BB%E7%94%A8" title="限界費用 — japonês" lang="ja" hreflang="ja" data-title="限界費用" data-language-autonym="日本語" data-language-local-name="japonês" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%96%E1%83%A6%E1%83%95%E1%83%A0%E1%83%A3%E1%83%9A%E1%83%98_%E1%83%AE%E1%83%90%E1%83%A0%E1%83%AF%E1%83%94%E1%83%91%E1%83%98" title="ზღვრული ხარჯები — georgiano" lang="ka" hreflang="ka" data-title="ზღვრული ხარჯები" data-language-autonym="ქართული" data-language-local-name="georgiano" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%95%E0%B2%A8%E0%B2%BF%E0%B2%B7%E0%B3%8D%E0%B2%A0_%E0%B2%B5%E0%B3%86%E0%B2%9A%E0%B3%8D%E0%B2%9A" title="ಕನಿಷ್ಠ ವೆಚ್ಚ — canarim" lang="kn" hreflang="kn" data-title="ಕನಿಷ್ಠ ವೆಚ್ಚ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="canarim" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%95%9C%EA%B3%84_%EB%B9%84%EC%9A%A9" title="한계 비용 — coreano" lang="ko" hreflang="ko" data-title="한계 비용" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Ribin%C4%97s_s%C4%85naudos" title="Ribinės sąnaudos — lituano" lang="lt" hreflang="lt" data-title="Ribinės sąnaudos" data-language-autonym="Lietuvių" data-language-local-name="lituano" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9C%D0%B0%D1%80%D0%B3%D0%B8%D0%BD%D0%B0%D0%BB%D0%B5%D0%BD_%D1%82%D1%80%D0%BE%D1%88%D0%BE%D0%BA" title="Маргинален трошок — macedónio" lang="mk" hreflang="mk" data-title="Маргинален трошок" data-language-autonym="Македонски" data-language-local-name="macedónio" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Marginale_kosten" title="Marginale kosten — neerlandês" lang="nl" hreflang="nl" data-title="Marginale kosten" data-language-autonym="Nederlands" data-language-local-name="neerlandês" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Grensekostnad" title="Grensekostnad — norueguês bokmål" lang="nb" hreflang="nb" data-title="Grensekostnad" data-language-autonym="Norsk bokmål" data-language-local-name="norueguês bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Koszt_kra%C5%84cowy" title="Koszt krańcowy — polaco" lang="pl" hreflang="pl" data-title="Koszt krańcowy" data-language-autonym="Polski" data-language-local-name="polaco" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D9%84%D9%85%D9%86_%D9%84%DA%AF%DA%9A%D8%AA" title="لمن لگښت — pastó" lang="ps" hreflang="ps" data-title="لمن لگښت" data-language-autonym="پښتو" data-language-local-name="pastó" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Cost_marginal" title="Cost marginal — romeno" lang="ro" hreflang="ro" data-title="Cost marginal" data-language-autonym="Română" data-language-local-name="romeno" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D1%8C%D0%BD%D1%8B%D0%B5_%D0%B8%D0%B7%D0%B4%D0%B5%D1%80%D0%B6%D0%BA%D0%B8" title="Предельные издержки — russo" lang="ru" hreflang="ru" data-title="Предельные издержки" data-language-autonym="Русский" data-language-local-name="russo" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%86%E0%B6%B1%E0%B7%8A%E0%B6%AD%E0%B7%92%E0%B6%9A_%E0%B6%B4%E0%B7%92%E0%B6%BB%E0%B7%92%E0%B7%80%E0%B7%90%E0%B6%BA" title="ආන්තික පිරිවැය — cingalês" lang="si" hreflang="si" data-title="ආන්තික පිරිවැය" data-language-autonym="සිංහල" data-language-local-name="cingalês" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9C%D0%B0%D1%80%D0%B3%D0%B8%D0%BD%D0%B0%D0%BB%D0%BD%D0%B8_%D1%82%D1%80%D0%BE%D1%88%D0%B0%D0%BA" title="Маргинални трошак — sérvio" lang="sr" hreflang="sr" data-title="Маргинални трошак" data-language-autonym="Српски / srpski" data-language-local-name="sérvio" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Marginalkostnad" title="Marginalkostnad — sueco" lang="sv" hreflang="sv" data-title="Marginalkostnad" data-language-autonym="Svenska" data-language-local-name="sueco" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%95%E0%B9%89%E0%B8%99%E0%B8%97%E0%B8%B8%E0%B8%99%E0%B8%AA%E0%B9%88%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%9E%E0%B8%B4%E0%B9%88%E0%B8%A1" title="ต้นทุนส่วนเพิ่ม — tailandês" lang="th" hreflang="th" data-title="ต้นทุนส่วนเพิ่ม" data-language-autonym="ไทย" data-language-local-name="tailandês" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%93%D1%80%D0%B0%D0%BD%D0%B8%D1%87%D0%BD%D1%96_%D0%B2%D0%B8%D1%82%D1%80%D0%B0%D1%82%D0%B8" title="Граничні витрати — ucraniano" lang="uk" hreflang="uk" data-title="Граничні витрати" data-language-autonym="Українська" data-language-local-name="ucraniano" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Chi_ph%C3%AD_bi%C3%AAn" title="Chi phí biên — vietnamita" lang="vi" hreflang="vi" data-title="Chi phí biên" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamita" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%BE%B9%E9%99%85%E6%88%90%E6%9C%AC" title="边际成本 — chinês" lang="zh" hreflang="zh" data-title="边际成本" data-language-autonym="中文" data-language-local-name="chinês" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q382444#sitelinks-wikipedia" 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typeof="mw:File/Thumb"><a href="/wiki/Ficheiro:Marginalcost.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Marginalcost.gif/220px-Marginalcost.gif" decoding="async" width="220" height="167" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Marginalcost.gif/330px-Marginalcost.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Marginalcost.gif/440px-Marginalcost.gif 2x" data-file-width="520" data-file-height="394" /></a><figcaption>Representação gráfica do custo marginal</figcaption></figure> <p>Em <a href="/wiki/Economia" title="Economia">economia</a> e <a href="/wiki/Finan%C3%A7as" title="Finanças">finanças</a>, <b>custo marginal</b> é a mudança no custo total de produção advinda da variação em uma unidade da quantidade produzida. Por outras palavras, podemos ainda dizer que o <b>custo marginal</b> representa o acréscimo do custo total pela produção de mais uma unidade, podendo ainda dizer-se que é o corresponde ao custo da última unidade produzida.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span>[</span>1<span>]</span></a></sup> </p><p>Matematicamente, a função de custo marginal (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathop {Cmg} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-OP"> <mi>C</mi> <mi>m</mi> <mi>g</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathop {Cmg} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b83c26479839a778a77f169785e96fed84812cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.923ex; height:2.509ex;" alt="{\displaystyle \mathop {Cmg} }"></span>) é expressa como a <a href="/wiki/Derivada" title="Derivada">derivada</a> da função do <a href="/wiki/Teoria_da_firma#Custo_total" title="Teoria da firma">custo total</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle CT}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle CT}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c93c9e52522e57c941a6c41a609e28aef8ff4f7f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.403ex; height:2.176ex;" alt="{\displaystyle CT}"></span>) em termos da <a href="/wiki/Quantidade" title="Quantidade">quantidade</a> total produzida (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span>), como se segue: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathop {Cmg} ={\frac {dCT}{dQ}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-OP"> <mi>C</mi> <mi>m</mi> <mi>g</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>C</mi> <mi>T</mi> </mrow> <mrow> <mi>d</mi> <mi>Q</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathop {Cmg} ={\frac {dCT}{dQ}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/277b06711cd5290d696c4e9cc846956ded825a48" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.476ex; height:5.843ex;" alt="{\displaystyle \mathop {Cmg} ={\frac {dCT}{dQ}}}"></span> </p><p>Em um gráfico, a curva que representa a evolução do custo marginal é uma parábola côncava, devido à <a href="/wiki/Lei_dos_rendimentos_decrescentes" title="Lei dos rendimentos decrescentes">Lei dos rendimentos decrescentes</a>. No ponto mínimo de curva, se encontra o número de bens que devem ser produzidos para que o custo marginal seja mínimo. O custo marginal começa por ser decrescente, tem um valor mínimo, passando depois a ser representado por uma curva crescente. Este andamento, do custo marginal, é explicado por dois fatores: numa primeira fase, o custo marginal cai porque os custos fixos são progressivamente diluídos por mais unidades. A partir de determinado ponto impera a já referida <a href="/wiki/Lei_dos_rendimentos_decrescentes" title="Lei dos rendimentos decrescentes">Lei dos rendimentos decrescentes</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Custo_marginal_e_o_custo_médio"><span id="Custo_marginal_e_o_custo_m.C3.A9dio"></span>Custo marginal e o custo médio</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Custo_marginal&veaction=edit&section=1" title="Editar secção: Custo marginal e o custo médio" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Custo_marginal&action=edit&section=1" title="Editar código-fonte da secção: Custo marginal e o custo médio"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Relação entre o custo marginal, o <a href="/wiki/Custo_m%C3%A9dio" title="Custo médio">custo médio</a> e o custo variável médio (em <a href="/wiki/Concorr%C3%AAncia_perfeita" title="Concorrência perfeita">concorrência perfeita</a>). Enquanto o custo marginal for inferior ao <a href="/wiki/Custo_m%C3%A9dio" title="Custo médio">custo médio</a>, o primeiro faz baixar o valor do segundo. Quando o custo marginal (custo de cada produto adicional) for exatamente igual ao <a href="/wiki/Custo_m%C3%A9dio" title="Custo médio">custo médio</a> (custo de cada produto produzido), este não está nem a aumentar nem a diminuir, e situa-se exatamente onde o custo médio é mínimo. A partir do ponto, onde o custo marginal se situa acima do custo médio, aquele começa a puxar este para cima. Deste modo, a curva de custo médio é uma curva em U, sendo o respectivo ponto mínimo aquele em que o custo marginal iguala o custo médio e, sendo consequentemente, coincidente com o custo mínimo. O ponto de intersecção do custo marginal (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle CMg}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mi>M</mi> <mi>g</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle CMg}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74a52cffc757b0563c77755b1a4e94ea10677171" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.325ex; height:2.509ex;" alt="{\displaystyle CMg}"></span>) com o <a href="/wiki/Custo_m%C3%A9dio" title="Custo médio">custo médio</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle CMe}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mi>M</mi> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle CMe}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/096ed10e9287483b47ad1fae789cc2e1ddb37d1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.292ex; height:2.176ex;" alt="{\displaystyle CMe}"></span>), no seu ponto mínimo, é denominado por <b>limiar de rentabilidade</b>. Neste ponto, a <a href="/wiki/Teoria_da_firma#Receita_total" title="Teoria da firma">receita total</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle RT}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle RT}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb170acd8d7f68f4b37aa1f3a822717b9a3f470b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.4ex; height:2.176ex;" alt="{\displaystyle RT}"></span>)é exatamente igual ao <a href="/wiki/Teoria_da_firma#Custo_total" title="Teoria da firma">custo total</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle CT}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle CT}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c93c9e52522e57c941a6c41a609e28aef8ff4f7f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.403ex; height:2.176ex;" alt="{\displaystyle CT}"></span>), pelo que o <a href="/wiki/Lucro" title="Lucro">lucro</a> é zero (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle LT=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mi>T</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle LT=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d85206f5923b87c35efa6a513e9fe63d554bf89d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.48ex; height:2.176ex;" alt="{\displaystyle LT=0}"></span>).<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span>[</span>2<span>]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span>[</span>3<span>]</span></a></sup> </p><p><b>Condições do limiar de rentabilidade</b> Para <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle LT=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mi>T</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle LT=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d85206f5923b87c35efa6a513e9fe63d554bf89d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.48ex; height:2.176ex;" alt="{\displaystyle LT=0}"></span> Termos, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle LT=RT-CT}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mi>T</mi> <mo>=</mo> <mi>R</mi> <mi>T</mi> <mo>−</mo> <mi>C</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle LT=RT-CT}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6591a11edb30a59ce34f52f8d0ed45d9e1434149" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:15.961ex; height:2.343ex;" alt="{\displaystyle LT=RT-CT}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle CT=RT}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mi>T</mi> <mo>=</mo> <mi>R</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle CT=RT}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c144269870de4b940f532d87c36293ee77d628d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.901ex; height:2.176ex;" alt="{\displaystyle CT=RT}"></span>, logo</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P=CMe=CMg}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mi>C</mi> <mi>M</mi> <mi>e</mi> <mo>=</mo> <mi>C</mi> <mi>M</mi> <mi>g</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P=CMe=CMg}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ff96786474e780fae20a52b25b772e207afbb78" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.559ex; height:2.509ex;" alt="{\displaystyle P=CMe=CMg}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Exemplo">Exemplo</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Custo_marginal&veaction=edit&section=2" title="Editar secção: Exemplo" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Custo_marginal&action=edit&section=2" title="Editar código-fonte da secção: Exemplo"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Em uma empresa, o custo, em reais, para produzir q unidades de televisores é dado por <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C(q)=0,02q^{3}-6q^{2}+900q+1000}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>02</mn> <msup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>−</mo> <mn>6</mn> <msup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>900</mn> <mi>q</mi> <mo>+</mo> <mn>1000</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C(q)=0,02q^{3}-6q^{2}+900q+1000}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f70c7637e0a24e0b615ced08d02f8369673b06f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:35.423ex; height:3.176ex;" alt="{\displaystyle C(q)=0,02q^{3}-6q^{2}+900q+1000}"></span>. O custo marginal é dado pela derivada da função. <sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span>[</span>4<span>]</span></a></sup> </p><p><br /> Assim, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Cmg={\frac {dC}{dq}}=0,06q^{2}-12q+900}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mi>m</mi> <mi>g</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>C</mi> </mrow> <mrow> <mi>d</mi> <mi>q</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>06</mn> <msup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>12</mn> <mi>q</mi> <mo>+</mo> <mn>900</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Cmg={\frac {dC}{dq}}=0,06q^{2}-12q+900}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/015538ee28da5fde941b1aae3249ab1d4c54520c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:34.156ex; height:5.843ex;" alt="{\displaystyle Cmg={\frac {dC}{dq}}=0,06q^{2}-12q+900}"></span>. </p> <div class="mw-heading mw-heading2"><h2 id="Ver_também"><span id="Ver_tamb.C3.A9m"></span>Ver também</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Custo_marginal&veaction=edit&section=3" title="Editar secção: Ver também" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Custo_marginal&action=edit&section=3" title="Editar código-fonte da secção: Ver também"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Custo" title="Custo">Custo</a></li></ul> <h2 id="Referências" style="cursor: help;" title="Esta seção foi configurada para não ser editável diretamente. Edite a página toda ou a seção anterior em vez disso."><span id="Refer.C3.AAncias"></span>Referências</h2> <div class="reflist" style="list-style-type: decimal;"><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.knoow.net/cienceconempr/economia/customarginal.htm">Conceito de Custo Marginal</a></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20140813175144/http://learnthings.co.za/content/secondary/portuguese/Home/portugues/businesss/grade10/operation/theproduc/economicf/analisedo/default.htm">«Análise do limiar de rentabilidade»</a><span class="reference-accessdate">. Consultado em 13 de agosto de 2014</span>. Arquivado do <a rel="nofollow" class="external text" href="http://learnthings.co.za/content/secondary/portuguese/Home/portugues/businesss/grade10/operation/theproduc/economicf/analisedo/default.htm">original</a> em 13 de agosto de 2014</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fpt.wikipedia.org%3ACusto+marginal&rft.btitle=An%C3%A1lise+do+limiar+de+rentabilidade&rft.genre=unknown&rft_id=http%3A%2F%2Flearnthings.co.za%2Fcontent%2Fsecondary%2Fportuguese%2FHome%2Fportugues%2Fbusinesss%2Fgrade10%2Foperation%2Ftheproduc%2Feconomicf%2Fanalisedo%2Fdefault.htm&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.fep.up.pt/docentes/joao/material/micro2/micro2_concperfeita.pdf">MICROECONOMIA II</a></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="https://educacionalplenus.com.br/aplicacoes-em-economia-e-administracao-custo-marginal-exercicio-1/">«Exemplo de Custo Marginal»</a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fpt.wikipedia.org%3ACusto+marginal&rft.btitle=Exemplo+de+Custo+Marginal&rft.genre=unknown&rft_id=https%3A%2F%2Feducacionalplenus.com.br%2Faplicacoes-em-economia-e-administracao-custo-marginal-exercicio-1%2F&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografia">Bibliografia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Custo_marginal&veaction=edit&section=4" title="Editar secção: Bibliografia" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Custo_marginal&action=edit&section=4" title="Editar código-fonte da secção: Bibliografia"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>de Sousa, Maria Fialho, Gomes, Orlando - "Análise Económica" - Edições Sílabo.</li></ul> <table class="noprint" style="border-top:none; border-bottom:none; background:transparent; color: inherit"><tbody><tr> <td style="text-align: center;"><span typeof="mw:File"><a href="/wiki/Ficheiro:P_economie_blue.svg" class="mw-file-description"><img alt="Ícone de esboço" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/P_economie_blue.svg/30px-P_economie_blue.svg.png" decoding="async" width="30" height="31" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/P_economie_blue.svg/45px-P_economie_blue.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/02/P_economie_blue.svg/60px-P_economie_blue.svg.png 2x" data-file-width="361" data-file-height="371" /></a></span></td> <td><i>Este artigo sobre <a href="/wiki/Economia" title="Economia">economia</a> é um <a href="/wiki/Wikip%C3%A9dia:Esbo%C3%A7o" title="Wikipédia:Esboço">esboço</a>. Você pode ajudar a Wikipédia <b><span class="plainlinks"><a class="external text" href="https://pt.wikipedia.org/w/index.php?title=Custo_marginal&action=edit">expandindo-o</a></span></b>.</i><div class="plainlinks hlist navbar mini" style="position:absolute; right:15px; font-size:smaller; display:none;"><ul><li class="nv-ver"><a href="/wiki/Predefini%C3%A7%C3%A3o:Esbo%C3%A7o-economia" title="Predefinição:Esboço-economia"><abbr title="Ver esta predefinição">v</abbr></a></li><li class="nv-discutir"><a href="/wiki/Predefini%C3%A7%C3%A3o_Discuss%C3%A3o:Esbo%C3%A7o-economia" title="Predefinição Discussão:Esboço-economia"><abbr title="Discutir esta predefinição">d</abbr></a></li><li class="nv-editar"><a class="external text" href="https://pt.wikipedia.org/w/index.php?title=Predefini%C3%A7%C3%A3o:Esbo%C3%A7o-economia&action=edit"><abbr title="Editar esta predefinição">e</abbr></a></li></ul></div></td> </tr></tbody></table> <div role="navigation" class="navbox" aria-labelledby="Microeconomia" 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