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class="vector-toc-numb">2</span> <span>Coste marginal a largo plazo</span> </div> </a> <ul id="toc-Coste_marginal_a_largo_plazo-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relación_entre_el_coste_marginal_y_el_coste_total_medio" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Relación_entre_el_coste_marginal_y_el_coste_total_medio"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Relación entre el coste marginal y el coste total medio</span> </div> </a> <ul id="toc-Relación_entre_el_coste_marginal_y_el_coste_total_medio-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Maximización_del_beneficio" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Maximización_del_beneficio"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Maximización del beneficio</span> </div> </a> <ul id="toc-Maximización_del_beneficio-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Véase_también" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Véase_también"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Véase también</span> </div> </a> <ul id="toc-Véase_también-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referencias" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referencias"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Referencias</span> </div> </a> <ul id="toc-Referencias-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografía" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografía"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Bibliografía</span> </div> </a> <ul id="toc-Bibliografía-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="Contenidos" 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="Cambiar a la tabla de contenidos" > <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">Cambiar a la tabla de contenidos</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">Coste 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 a un artículo en otro idioma. Disponible en 37 idiomas" > <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 idiomas</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 (azerbaiyano)" lang="az" hreflang="az" data-title="Marjinal xərclər" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaiyano" 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 (catalán)" lang="ca" hreflang="ca" data-title="Cost marginal" data-language-autonym="Català" data-language-local-name="catalán" 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 (alemán)" lang="de" hreflang="de" data-title="Grenzkosten" data-language-autonym="Deutsch" data-language-local-name="alemán" 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 (inglés)" lang="en" hreflang="en" data-title="Marginal cost" data-language-autonym="English" data-language-local-name="inglés" 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-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Kostu_marjinal" title="Kostu marjinal (euskera)" lang="eu" hreflang="eu" data-title="Kostu marjinal" data-language-autonym="Euskara" data-language-local-name="euskera" 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 (finés)" lang="fi" hreflang="fi" data-title="Rajakustannus" data-language-autonym="Suomi" data-language-local-name="finés" 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 (francés)" lang="fr" hreflang="fr" data-title="Coût marginal" data-language-autonym="Français" data-language-local-name="francés" 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 (gallego)" lang="gl" hreflang="gl" data-title="Custo marxinal" data-language-autonym="Galego" data-language-local-name="gallego" 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 (hebreo)" lang="he" hreflang="he" data-title="עלות שולית" data-language-autonym="עברית" data-language-local-name="hebreo" 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 (indonesio)" lang="id" hreflang="id" data-title="Biaya marginal" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesio" 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 (islandés)" lang="is" hreflang="is" data-title="Jaðarkostnaður" data-language-autonym="Íslenska" data-language-local-name="islandés" 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 (japonés)" lang="ja" hreflang="ja" data-title="限界費用" data-language-autonym="日本語" data-language-local-name="japonés" 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 (canarés)" lang="kn" hreflang="kn" data-title="ಕನಿಷ್ಠ ವೆಚ್ಚ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="canarés" 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 (macedonio)" lang="mk" hreflang="mk" data-title="Маргинален трошок" data-language-autonym="Македонски" data-language-local-name="macedonio" 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 (neerlandés)" lang="nl" hreflang="nl" data-title="Marginale kosten" data-language-autonym="Nederlands" data-language-local-name="neerlandés" 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 (noruego bokmal)" lang="nb" hreflang="nb" data-title="Grensekostnad" data-language-autonym="Norsk bokmål" data-language-local-name="noruego bokmal" 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 (pastún)" lang="ps" hreflang="ps" data-title="لمن لگښت" data-language-autonym="پښتو" data-language-local-name="pastún" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Custo_marginal" title="Custo marginal (portugués)" lang="pt" hreflang="pt" data-title="Custo marginal" data-language-autonym="Português" data-language-local-name="portugués" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Cost_marginal" title="Cost marginal (rumano)" lang="ro" hreflang="ro" data-title="Cost marginal" data-language-autonym="Română" data-language-local-name="rumano" 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 (ruso)" lang="ru" hreflang="ru" data-title="Предельные издержки" data-language-autonym="Русский" data-language-local-name="ruso" 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 (cingalés)" lang="si" hreflang="si" data-title="ආන්තික පිරිවැය" data-language-autonym="සිංහල" data-language-local-name="cingalés" 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 (serbio)" lang="sr" hreflang="sr" data-title="Маргинални трошак" data-language-autonym="Српски / srpski" data-language-local-name="serbio" 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 (tailandés)" lang="th" hreflang="th" data-title="ต้นทุนส่วนเพิ่ม" data-language-autonym="ไทย" data-language-local-name="tailandés" 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 (chino)" lang="zh" hreflang="zh" data-title="边际成本" data-language-autonym="中文" data-language-local-name="chino" 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" title="Editar 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id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="es" dir="ltr"><p>En <a href="/wiki/Econom%C3%ADa_(ciencia_econ%C3%B3mica)" class="mw-redirect" title="Economía (ciencia económica)">economía</a>, el <b>coste marginal</b> es el cambio en el <a href="/wiki/Coste_total" title="Coste total">coste total</a> que se produce cuando se incrementa la cantidad producida, el <a href="/wiki/Coste" title="Coste">coste</a> de producir una cantidad adicional.<sup id="cite_ref-1" class="reference separada"><a href="#cite_note-1"><span class="corchete-llamada">[</span>1<span class="corchete-llamada">]</span></a></sup> En algunos contextos, se refiere al incremento de una unidad de producción y, en otros, a la tasa de variación del coste total al aumentar la producción en una cantidad infinitesimal. Como muestra la Figura 1, el coste marginal se mide en dólares por unidad, mientras que el coste total se expresa en dólares, y el coste marginal es la pendiente del coste total, es decir, la velocidad a la que aumenta con la producción. El coste marginal es distinto del <a href="/wiki/Coste_medio" title="Coste medio">coste medio</a>, que es el coste total dividido por el número de unidades producidas. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Archivo:Marginal_and_Total_Cost.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/9/95/Marginal_and_Total_Cost.png" decoding="async" width="213" height="262" class="mw-file-element" data-file-width="213" data-file-height="262" /></a><figcaption>Figura 1: Costes de producción marginal y total.</figcaption></figure> <p>En cada nivel de producción y periodo de tiempo considerado, el coste marginal incluye todos los costes que varían con el nivel de producción, mientras que los costes que no varían con la producción son fijos. Por ejemplo, el coste marginal de producir un automóvil incluirá los costes de mano de obra y piezas necesarias para el automóvil adicional, pero no el coste fijo del edificio de la fábrica que no varían con la producción. El coste marginal puede ser a corto o a largo plazo, según los costes que varíen con la producción, ya que a largo plazo incluso el tamaño de la nave se elige en función de la producción deseada. </p><p>Si la función de costes <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}"></span> es <a href="/wiki/Funci%C3%B3n_continua" title="Función continua">continua</a> y <a href="/wiki/Funci%C3%B3n_diferenciable" title="Función diferenciable">diferenciable</a>, el coste 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 MC}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle MC}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c34f200ee412708546670f54ce4db2e53b8e15f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.209ex; height:2.176ex;" alt="{\displaystyle MC}"></span> es la primera derivada de la función de costes con respecto a la cantidad de producción <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>:<sup id="cite_ref-2" class="reference separada"><a href="#cite_note-2"><span class="corchete-llamada">[</span>2<span class="corchete-llamada">]</span></a></sup> </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 MC(Q)={\frac {\ dC}{\ dQ}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mi>C</mi> <mo stretchy="false">(</mo> <mi>Q</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mtext> </mtext> <mi>d</mi> <mi>C</mi> </mrow> <mrow> <mtext> </mtext> <mi>d</mi> <mi>Q</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle MC(Q)={\frac {\ dC}{\ dQ}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d96ad88e7df8d679794eebc313e67b62eae0b107" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.072ex; height:5.843ex;" alt="{\displaystyle MC(Q)={\frac {\ dC}{\ dQ}}.}"></span> </p><p>Si la función de costes no es diferenciable, el coste marginal puede expresarse de la siguiente manera: </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 MC={\frac {\Delta C}{\Delta Q}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mi>C</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>C</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>Q</mi> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle MC={\frac {\Delta C}{\Delta Q}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55c6904b33b04eb9ea4f7aead956686616b3ade3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.564ex; height:5.843ex;" alt="{\displaystyle MC={\frac {\Delta C}{\Delta Q}},}"></span> </p><p>donde <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 \Delta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32769037c408874e1890f77554c65f39c523ebe2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.936ex; height:2.176ex;" alt="{\displaystyle \Delta }"></span> denota un cambio incremental de una unidad. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Coste_marginal_a_corto_plazo">Coste marginal a corto plazo</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Coste_marginal&action=edit&section=1" title="Editar sección: Coste marginal a corto plazo"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="https://en.wikipedia.org/wiki/File:Short_run_marginal_cost.png"><img resource="/wiki/Archivo:Short_run_marginal_cost.png" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Short_run_marginal_cost.png/220px-Short_run_marginal_cost.png" decoding="async" width="220" height="157" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Short_run_marginal_cost.png/330px-Short_run_marginal_cost.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Short_run_marginal_cost.png/440px-Short_run_marginal_cost.png 2x" data-file-width="594" data-file-height="425" /></a><figcaption>Gráfico del coste marginal a corto plazo.</figcaption></figure> <p>El coste marginal a corto plazo es la variación del coste total cuando se produce un producto adicional a corto plazo y algunos costes son fijos. En el gráfico adjunto, el coste marginal a corto plazo <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 SMC}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mi>M</mi> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle SMC}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed1e4b16a3bfdd45ffa9f42343554f8edb26cc98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.708ex; height:2.176ex;" alt="{\displaystyle SMC}"></span> tiene forma de U, con la cantidad en el eje de abscisas y el coste por unidad en el eje de ordenadas. </p><p>A corto plazo, la empresa tiene algunos costes que son fijos independientemente de la cantidad de producción (por ejemplo, edificios, maquinaria). Otros costes, como la mano de obra y los materiales, varían con la producción y, por tanto, aparecen en el coste marginal. El coste marginal puede descender primero, como en el diagrama, si el coste adicional por unidad es elevado si la empresa opera con un nivel de producción demasiado bajo, o puede empezar plano o subir inmediatamente. En un momento dado, el coste marginal aumenta a medida que el aumento de los insumos variables, como la mano de obra, ejerce una presión creciente sobre los activos fijos, como el tamaño del edificio. A largo plazo, la empresa aumentaría sus activos fijos para corresponder a la producción deseada; el corto plazo se define como el periodo en el que esos activos no pueden modificarse. </p> <div class="mw-heading mw-heading2"><h2 id="Coste_marginal_a_largo_plazo">Coste marginal a largo plazo</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Coste_marginal&action=edit&section=2" title="Editar sección: Coste marginal a largo plazo"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="https://en.wikipedia.org/wiki/File:Long_run_marginal_cost.png"><img resource="/wiki/Archivo:Long_run_marginal_cost.png" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Long_run_marginal_cost.png/220px-Long_run_marginal_cost.png" decoding="async" width="220" height="148" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Long_run_marginal_cost.png/330px-Long_run_marginal_cost.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Long_run_marginal_cost.png/440px-Long_run_marginal_cost.png 2x" data-file-width="466" data-file-height="313" /></a><figcaption>Gráfico del coste marginal a largo plazo.</figcaption></figure> <p>El largo plazo se define como el periodo de tiempo en el que ningún insumo es fijo. Todo, incluido el tamaño del edificio y la maquinaria, puede elegirse de forma óptima para la cantidad de producción deseada. Por consiguiente, aunque el coste marginal a corto plazo aumente debido a las limitaciones de capacidad, el coste marginal a largo plazo <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 LMC}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mi>M</mi> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle LMC}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8030712358c69156c5aabc44469cd9e0f225cd9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.791ex; height:2.176ex;" alt="{\displaystyle LMC}"></span> puede ser constante. O puede haber <a href="/wiki/Rendimientos_de_escala" title="Rendimientos de escala">rendimientos crecientes o decrecientes a escala</a> si la productividad tecnológica o de gestión cambia con la cantidad. O pueden darse ambos casos, como en el diagrama de la derecha, en el que el coste marginal primero disminuye (rendimientos crecientes a escala) y luego aumenta (rendimientos decrecientes a escala).<sup id="cite_ref-3" class="reference separada"><a href="#cite_note-3"><span class="corchete-llamada">[</span>3<span class="corchete-llamada">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Relación_entre_el_coste_marginal_y_el_coste_total_medio"><span id="Relaci.C3.B3n_entre_el_coste_marginal_y_el_coste_total_medio"></span>Relación entre el coste marginal y el coste total medio</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Coste_marginal&action=edit&section=3" title="Editar sección: Relación entre el coste marginal y el coste total medio"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>El coste marginal se cruza con el coste total medio y el coste variable medio en su punto más bajo. Tome como representación gráfica la Figura 2: </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="https://en.wikipedia.org/wiki/File:Avc_atc_mc.png"><img resource="/wiki/Archivo:Avc_atc_mc.png" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Avc_atc_mc.png/220px-Avc_atc_mc.png" decoding="async" width="220" height="173" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Avc_atc_mc.png/330px-Avc_atc_mc.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/52/Avc_atc_mc.png/440px-Avc_atc_mc.png 2x" data-file-width="477" data-file-height="376" /></a><figcaption>Figura 2: Relación entre el coste marginal y el coste total medio</figcaption></figure> <p>Supongamos que el punto de partida del nivel de producción es <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>. El coste marginal es la variación del coste total de una producción adicional ((<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 n+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a135e65a42f2d73cccbfc4569523996ca0036f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.398ex; height:2.343ex;" alt="{\displaystyle n+1}"></span>)ª unidad). Por lo tanto: (consulte la Figura 3; en donde <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 ACn}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mi>C</mi> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ACn}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebe94f6211378cb287f9621c9ec0b8769d8b8214" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.904ex; height:2.176ex;" alt="{\displaystyle ACn}"></span> es el costo medio(<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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>), <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 TCn}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mi>C</mi> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle TCn}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e117229e4ed43536004b2391d79b29fb55942951" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.797ex; height:2.176ex;" alt="{\displaystyle TCn}"></span> es el costo total(<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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>), <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 Qn}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Qn}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a1578e750b50fb4a6992755e73d24dff136e1f34" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.233ex; height:2.509ex;" alt="{\displaystyle Qn}"></span> es el nivel de producción(<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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>), <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 MC}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle MC}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c34f200ee412708546670f54ce4db2e53b8e15f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.209ex; height:2.176ex;" alt="{\displaystyle MC}"></span> es el costo marginal). </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="https://en.wikipedia.org/wiki/File:Average_cost,_total_cost_and_marginal_cost.png"><img resource="/wiki/Archivo:Average_cost,_total_cost_and_marginal_cost.png" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Average_cost%2C_total_cost_and_marginal_cost.png/220px-Average_cost%2C_total_cost_and_marginal_cost.png" decoding="async" width="220" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Average_cost%2C_total_cost_and_marginal_cost.png/330px-Average_cost%2C_total_cost_and_marginal_cost.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Average_cost%2C_total_cost_and_marginal_cost.png/440px-Average_cost%2C_total_cost_and_marginal_cost.png 2x" data-file-width="554" data-file-height="363" /></a><figcaption>Figura 3: Costo medio.</figcaption></figure> <p>En este caso, cuando el coste marginal de la (<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 n+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a135e65a42f2d73cccbfc4569523996ca0036f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.398ex; height:2.343ex;" alt="{\displaystyle n+1}"></span>)ª unidad es inferior al coste medio(<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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>), el coste medio(<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 n+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a135e65a42f2d73cccbfc4569523996ca0036f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.398ex; height:2.343ex;" alt="{\displaystyle n+1}"></span>) tendrá un valor inferior al coste medio(<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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>). Ocurre lo contrario cuando el coste marginal de la (<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 n+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a135e65a42f2d73cccbfc4569523996ca0036f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.398ex; height:2.343ex;" alt="{\displaystyle n+1}"></span>)ª unidad es superior al coste medio(<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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>). En este caso, el coste medio(<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 n+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a135e65a42f2d73cccbfc4569523996ca0036f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.398ex; height:2.343ex;" alt="{\displaystyle n+1}"></span>) será mayor que el coste medio(<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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>). Si la curva de coste 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 SMC}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mi>M</mi> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle SMC}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed1e4b16a3bfdd45ffa9f42343554f8edb26cc98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.708ex; height:2.176ex;" alt="{\displaystyle SMC}"></span> se encuentra por debajo de la curva de coste total medio <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 SAC}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mi>A</mi> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle SAC}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51415462f6a8bbdd48e383dc26a62b85a178b6c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.009ex; height:2.176ex;" alt="{\displaystyle SAC}"></span>, ésta se inclinará hacia abajo, y si el coste marginal se encuentra por encima de la curva de coste medio, ésta se inclinará hacia arriba. En la Figura 2, se puede observar que antes de que la curva de coste 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 SMC}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mi>M</mi> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle SMC}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed1e4b16a3bfdd45ffa9f42343554f8edb26cc98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.708ex; height:2.176ex;" alt="{\displaystyle SMC}"></span> y la curva de coste total medio <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 SAC}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mi>A</mi> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle SAC}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51415462f6a8bbdd48e383dc26a62b85a178b6c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.009ex; height:2.176ex;" alt="{\displaystyle SAC}"></span> se crucen, la curva de coste medio tiene una pendiente descendente, mientras que después de la intersección, la curva de coste medio tiene una pendiente ascendente. El gráfico en forma de U refleja la ley de los rendimientos decrecientes. Una empresa solo puede producir hasta cierto punto, pero después de que la producción del (<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 n+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a135e65a42f2d73cccbfc4569523996ca0036f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.398ex; height:2.343ex;" alt="{\displaystyle n+1}"></span>)ª producto alcance un coste mínimo, la producción posterior solo aumentará el coste total medio <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 SAC}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mi>A</mi> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle SAC}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51415462f6a8bbdd48e383dc26a62b85a178b6c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.009ex; height:2.176ex;" alt="{\displaystyle SAC}"></span>.<sup id="cite_ref-FOOTNOTENwoyokeIlechuwku2018_4-0" class="reference separada"><a href="#cite_note-FOOTNOTENwoyokeIlechuwku2018-4"><span class="corchete-llamada">[</span>4<span class="corchete-llamada">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Maximización_del_beneficio"><span id="Maximizaci.C3.B3n_del_beneficio"></span>Maximización del beneficio</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Coste_marginal&action=edit&section=4" title="Editar sección: Maximización del beneficio"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="https://en.wikipedia.org/wiki/File:Profit_maximizing_graph.png"><img resource="/wiki/Archivo:Profit_maximizing_graph.png" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Profit_maximizing_graph.png/220px-Profit_maximizing_graph.png" decoding="async" width="220" height="227" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Profit_maximizing_graph.png/330px-Profit_maximizing_graph.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Profit_maximizing_graph.png/440px-Profit_maximizing_graph.png 2x" data-file-width="873" data-file-height="900" /></a><figcaption>Gráfico de maximización del beneficio.</figcaption></figure> <p>El gráfico adjunto de maximización de beneficios representa la cantidad óptima de producción cuando se interceptan tanto la línea del coste marginal como la del beneficio marginal. La línea negra representa la intersección en la que los beneficios son mayores (ingreso marginal=coste 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 MR=MC}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mi>R</mi> <mo>=</mo> <mi>M</mi> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle MR=MC}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab0ed05039c1d2be42fa549a9ec1c1948f62b2f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.513ex; height:2.176ex;" alt="{\displaystyle MR=MC}"></span>). La parte izquierda de la línea vertical negra marcada como «cantidad máxima de beneficio» es donde el ingreso marginal es mayor que el coste marginal. Si una empresa fija su producción en el lado izquierdo del gráfico y decide aumentar la producción, el ingreso adicional por producción obtenida superará el coste adicional por producción. A partir del «gráfico de maximización de beneficios», podríamos observar que los ingresos cubren tanto la barra <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 A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> como la <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 B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span>, mientras que el coste sólo cubre la <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 B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span>. Por supuesto, <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 A+B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>+</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A+B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4279cdbd3cb8ec4c3423065d9a7d83a82cfc89e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.348ex; height:2.343ex;" alt="{\displaystyle A+B}"></span> le reportan un beneficio, pero el aumento de la producción hasta el punto de <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 MR=MC}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mi>R</mi> <mo>=</mo> <mi>M</mi> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle MR=MC}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab0ed05039c1d2be42fa549a9ec1c1948f62b2f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.513ex; height:2.176ex;" alt="{\displaystyle MR=MC}"></span> arroja un beneficio adicional que puede cubrir los ingresos por la <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 A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> que falta. </p><p>Por otro lado, el lado derecho de la línea negra (ingreso marginal = coste marginal), muestra que el coste marginal es mayor que el ingreso marginal. Supongamos que una empresa fija su producción en este lado, si reduce la producción, el coste disminuirá de <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}"></span> y <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 D}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}"></span>, lo que supera la disminución de los ingresos que es <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 D}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}"></span>. Por lo tanto, la disminución de la producción hasta el punto de (ingreso marginal=coste marginal) dará lugar a un aumento de los beneficios.<sup id="cite_ref-FOOTNOTECooperJohn2012_5-0" class="reference separada"><a href="#cite_note-FOOTNOTECooperJohn2012-5"><span class="corchete-llamada">[</span>5<span class="corchete-llamada">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Véase_también"><span id="V.C3.A9ase_tambi.C3.A9n"></span>Véase también</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Coste_marginal&action=edit&section=5" title="Editar sección: Véase también"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Tipo_marginal" title="Tipo marginal">Tipo marginal</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Referencias">Referencias</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Coste_marginal&action=edit&section=6" title="Editar sección: Referencias"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="listaref" style="list-style-type: decimal;"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><span id="CITAREFO'SullivanSheffrin2003" class="citation libro">O'Sullivan, Arthur; Sheffrin, Steven M. (2003). <a rel="nofollow" class="external text" href="https://archive.org/details/economicsprincip00osul"><i>Economics: Principles in Action</i></a> <span style="color:var(--color-subtle, #555 );">(en inglés)</span>. Upper Saddle River, NJ: Pearson Prentice Hall. p. <a rel="nofollow" class="external text" href="https://archive.org/details/economicsprincip00osul/page/n127">111</a>. <small><a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Especial:FuentesDeLibros/0-13-063085-3" title="Especial:FuentesDeLibros/0-13-063085-3">0-13-063085-3</a></small>.</span><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fes.wikipedia.org%3ACoste+marginal&rft.au=O%27Sullivan%2C+Arthur&rft.au=Sheffrin%2C+Steven+M.&rft.aufirst=Arthur&rft.aulast=O%27Sullivan&rft.btitle=Economics%3A+Principles+in+Action&rft.date=2003&rft.genre=book&rft.isbn=0-13-063085-3&rft.pages=111&rft.place=Upper+Saddle+River%2C+NJ&rft.pub=Pearson+Prentice+Hall&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Feconomicsprincip00osul&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><span id="CITAREFSimonBlume1994" class="citation libro">Simon, Carl; Blume, Lawrence (1994). <a rel="nofollow" class="external text" href="https://archive.org/details/mathematicsforec0000simo"><i>Mathematics for Economists</i></a> <span style="color:var(--color-subtle, #555 );">(en inglés)</span>. W. W. Norton & Company. <small><a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Especial:FuentesDeLibros/0393957330" title="Especial:FuentesDeLibros/0393957330">0393957330</a></small>.</span><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fes.wikipedia.org%3ACoste+marginal&rft.au=Blume%2C+Lawrence&rft.au=Simon%2C+Carl&rft.aufirst=Carl&rft.aulast=Simon&rft.btitle=Mathematics+for+Economists&rft.date=1994&rft.genre=book&rft.isbn=0393957330&rft.pub=W.+W.+Norton+%26+Company&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmathematicsforec0000simo&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">The classic reference is Jakob Viner, "Cost Curves and Supply Curve," <i>Zeitschrift fur Nationalokonomie,</i> 3:23-46 (1932).</span> </li> <li id="cite_note-FOOTNOTENwoyokeIlechuwku2018-4"><span class="mw-cite-backlink"><a href="#cite_ref-FOOTNOTENwoyokeIlechuwku2018_4-0">↑</a></span> <span class="reference-text"><a href="#CITAREFNwoyokeIlechuwku2018">Nwoyoke y Ilechuwku, 2018</a>.</span> </li> <li id="cite_note-FOOTNOTECooperJohn2012-5"><span class="mw-cite-backlink"><a href="#cite_ref-FOOTNOTECooperJohn2012_5-0">↑</a></span> <span class="reference-text"><a href="#CITAREFCooperJohn2012">Cooper y John, 2012</a>.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografía"><span id="Bibliograf.C3.ADa"></span>Bibliografía</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Coste_marginal&action=edit&section=7" title="Editar sección: Bibliografía"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span id="CITAREFBio2021-05-19" class="citation web">Bio, Full (19 de mayo de 2021). <a rel="nofollow" class="external text" href="https://www.investopedia.com/terms/m/marginalcostofproduction.asp">«Marginal Cost Of Production Definition»</a>. <i><a href="/wiki/Investopedia" title="Investopedia">Investopedia</a></i> <span style="color:var(--color-subtle, #555 );">(en inglés)</span>.</span><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fes.wikipedia.org%3ACoste+marginal&rft.atitle=Marginal+Cost+Of+Production+Definition&rft.au=Bio%2C+Full&rft.aufirst=Full&rft.aulast=Bio&rft.date=2021-05-19&rft.genre=article&rft.jtitle=Investopedia&rft_id=https%3A%2F%2Fwww.investopedia.com%2Fterms%2Fm%2Fmarginalcostofproduction.asp&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></li> <li><span id="CITAREFNwokoyeIlechukwu2018" class="citation libro">Nwokoye, Ebele Stella; Ilechukwu, Nneamaka (2018). <a rel="nofollow" class="external text" href="https://www.researchgate.net/publication/326841533">«CHAPTER FIVE THEORY OF COSTS»</a>. <i>ResearchGate</i> <span style="color:var(--color-subtle, #555 );">(en inglés)</span>.</span><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fes.wikipedia.org%3ACoste+marginal&rft.atitle=CHAPTER+FIVE+THEORY+OF+COSTS&rft.au=Ilechukwu%2C+Nneamaka&rft.au=Nwokoye%2C+Ebele+Stella&rft.aufirst=Ebele+Stella&rft.aulast=Nwokoye&rft.date=2018&rft.genre=article&rft.jtitle=ResearchGate&rft_id=https%3A%2F%2Fwww.researchgate.net%2Fpublication%2F326841533&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></li> <li><span id="CITAREF2012_Book_Archive2012" class="citation libro">Cooper, Russell; John, Andrew (2012). <a rel="nofollow" class="external text" href="https://2012books.lardbucket.org/books/theory-and-applications-of-microeconomics/">«Theory and Applications of Microeconomics - Table of Contents»</a>. <i>2012 Book Archive</i> <span style="color:var(--color-subtle, #555 );">(en inglés)</span>.</span><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fes.wikipedia.org%3ACoste+marginal&rft.atitle=Theory+and+Applications+of+Microeconomics+-+Table+of+Contents&rft.au=Cooper%2C+Russell&rft.au=John%2C+Andrew&rft.aufirst=Russell&rft.aulast=Cooper&rft.date=2012&rft.genre=article&rft.jtitle=2012+Book+Archive&rft_id=https%3A%2F%2F2012books.lardbucket.org%2Fbooks%2Ftheory-and-applications-of-microeconomics%2F&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></li></ul> <style data-mw-deduplicate="TemplateStyles:r161257576">.mw-parser-output .mw-authority-control{margin-top:1.5em}.mw-parser-output .mw-authority-control .navbox table{margin:0}.mw-parser-output .mw-authority-control .navbox hr:last-child{display:none}.mw-parser-output .mw-authority-control .navbox+.mw-mf-linked-projects{display:none}.mw-parser-output .mw-authority-control .mw-mf-linked-projects{display:flex;padding:0.5em;border:1px solid var(--border-color-base,#a2a9b1);background-color:var(--background-color-neutral,#eaecf0);color:var(--color-base,#202122)}.mw-parser-output .mw-authority-control .mw-mf-linked-projects ul li{margin-bottom:0}.mw-parser-output .mw-authority-control .navbox{border:1px solid var(--border-color-base,#a2a9b1);background-color:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .mw-authority-control .navbox-list{border-color:#f8f9fa}.mw-parser-output .mw-authority-control .navbox th{background-color:#eeeeff}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .mw-mf-linked-projects{border:1px solid var(--border-color-base,#72777d);background-color:var(--background-color-neutral,#27292d);color:var(--color-base,#eaecf0)}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .navbox{border:1px solid var(--border-color-base,#72777d)!important;background-color:var(--background-color-neutral-subtle,#202122)!important}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .navbox-list{border-color:#202122!important}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .navbox th{background-color:#27292d!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .mw-mf-linked-projects{border:1px solid var(--border-color-base,#72777d)!important;background-color:var(--background-color-neutral,#27292d)!important;color:var(--color-base,#eaecf0)!important}html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .navbox{border:1px solid var(--border-color-base,#72777d)!important;background-color:var(--background-color-neutral-subtle,#202122)!important}html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .navbox-list{border-color:#202122!important}html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .navbox th{background-color:#27292d!important}}</style><div class="mw-authority-control"><div role="navigation" class="navbox" aria-label="Navbox" style="width: inherit;padding:3px"><table class="hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width: 12%; 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