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data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li 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">(Top)</div> </a> </li> <li id="toc-Utility_function" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Utility_function"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Utility function</span> </div> </a> <ul id="toc-Utility_function-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Applications</span> </div> </a> <ul id="toc-Applications-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Preference" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Preference"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Preference</span> </div> </a> <button aria-controls="toc-Preference-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>Toggle Preference subsection</span> </button> <ul id="toc-Preference-sublist" class="vector-toc-list"> <li id="toc-Revealed_preference" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Revealed_preference"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Revealed preference</span> </div> </a> <ul id="toc-Revealed_preference-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Functions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Functions"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span><span><span>Functions</span></span></span> </div> </a> <button aria-controls="toc-Functions-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>Toggle <span><span>Functions</span></span> subsection</span> </button> <ul id="toc-Functions-sublist" class="vector-toc-list"> <li id="toc-Cardinal" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cardinal"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Cardinal</span> </div> </a> <ul id="toc-Cardinal-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ordinal" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ordinal"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Ordinal</span> </div> </a> <ul id="toc-Ordinal-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Examples" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Examples"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Examples</span> </div> </a> <ul id="toc-Examples-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Marginal_utility" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Marginal_utility"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Marginal utility</span> </div> </a> <button aria-controls="toc-Marginal_utility-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>Toggle Marginal utility subsection</span> </button> <ul id="toc-Marginal_utility-sublist" class="vector-toc-list"> <li id="toc-Law_of_diminishing_marginal_utility" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Law_of_diminishing_marginal_utility"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Law of diminishing marginal utility</span> </div> </a> <ul id="toc-Law_of_diminishing_marginal_utility-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Marginal_rate_of_substitution_(MRS)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Marginal_rate_of_substitution_(MRS)"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Marginal rate of substitution (MRS)</span> </div> </a> <ul id="toc-Marginal_rate_of_substitution_(MRS)-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Expected_utility" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Expected_utility"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Expected utility</span> </div> </a> <button aria-controls="toc-Expected_utility-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>Toggle Expected utility subsection</span> </button> <ul id="toc-Expected_utility-sublist" class="vector-toc-list"> <li id="toc-Von_Neumann–Morgenstern" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Von_Neumann–Morgenstern"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Von Neumann–Morgenstern</span> </div> </a> <ul id="toc-Von_Neumann–Morgenstern-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Indirect_utility" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Indirect_utility"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Indirect utility</span> </div> </a> <button aria-controls="toc-Indirect_utility-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>Toggle Indirect utility subsection</span> </button> <ul id="toc-Indirect_utility-sublist" class="vector-toc-list"> <li id="toc-Money" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Money"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Money</span> </div> </a> <ul id="toc-Money-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Budget_constraints" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Budget_constraints"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Budget constraints</span> </div> </a> <button aria-controls="toc-Budget_constraints-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>Toggle Budget constraints subsection</span> </button> <ul id="toc-Budget_constraints-sublist" class="vector-toc-list"> <li id="toc-Constrained_utility_optimisation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Constrained_utility_optimisation"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Constrained utility optimisation</span> </div> </a> <ul id="toc-Constrained_utility_optimisation-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Discussion_and_criticism" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Discussion_and_criticism"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Discussion and criticism</span> </div> </a> <ul id="toc-Discussion_and_criticism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Measuring_utility_functions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Measuring_utility_functions"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Measuring utility functions</span> </div> </a> <ul id="toc-Measuring_utility_functions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">14</span> <span>External links</span> </div> </a> <ul id="toc-External_links-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="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <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="Toggle the table of contents" > <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">Toggle the table of contents</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">Utility</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="Go to an article in another language. Available in 46 languages" > <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-46" 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">46 languages</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/%D9%85%D9%86%D9%81%D8%B9%D8%A9" title="منفعة – Arabic" lang="ar" hreflang="ar" data-title="منفعة" data-language-autonym="العربية" data-language-local-name="Arabic" 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/Faydal%C4%B1l%C4%B1q" title="Faydalılıq – Azerbaijani" lang="az" hreflang="az" data-title="Faydalılıq" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%89%E0%A6%AA%E0%A6%AF%E0%A7%8B%E0%A6%97" title="উপযোগ – Bangla" lang="bn" hreflang="bn" data-title="উপযোগ" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D0%BE%D0%BB%D0%B5%D0%B7%D0%BD%D0%BE%D1%81%D1%82" title="Полезност – Bulgarian" lang="bg" hreflang="bg" data-title="Полезност" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A3%D1%81%C4%83%D0%BB%D0%BB%C4%83%D0%BB%C4%83%D1%85" title="Усăллăлăх – Chuvash" lang="cv" hreflang="cv" data-title="Усăллăлăх" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/U%C5%BEitek_(ekonomie)" title="Užitek (ekonomie) – Czech" lang="cs" hreflang="cs" data-title="Užitek (ekonomie)" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Nytte" title="Nytte – Danish" lang="da" hreflang="da" data-title="Nytte" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Nutzen_(Wirtschaft)" title="Nutzen (Wirtschaft) – German" lang="de" hreflang="de" data-title="Nutzen (Wirtschaft)" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Utilidad_(econom%C3%ADa)" title="Utilidad (economía) – Spanish" lang="es" hreflang="es" data-title="Utilidad (economía)" data-language-autonym="Español" data-language-local-name="Spanish" 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/Baliagarritasun_(ekonomia)" title="Baliagarritasun (ekonomia) – Basque" lang="eu" hreflang="eu" data-title="Baliagarritasun (ekonomia)" data-language-autonym="Euskara" data-language-local-name="Basque" 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%85%D8%B7%D9%84%D9%88%D8%A8%DB%8C%D8%AA" title="مطلوبیت – Persian" lang="fa" hreflang="fa" data-title="مطلوبیت" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Utilit%C3%A9_(%C3%A9conomie)" title="Utilité (économie) – French" lang="fr" hreflang="fr" data-title="Utilité (économie)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%9A%A8%EC%9A%A9" title="효용 – Korean" lang="ko" hreflang="ko" data-title="효용" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%89%E0%A4%AA%E0%A4%AF%E0%A5%8B%E0%A4%97%E0%A4%BF%E0%A4%A4%E0%A4%BE" title="उपयोगिता – Hindi" lang="hi" hreflang="hi" data-title="उपयोगिता" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Korisnost_(ekonomska_znanost)" title="Korisnost (ekonomska znanost) – Croatian" lang="hr" hreflang="hr" data-title="Korisnost (ekonomska znanost)" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Daya_guna" title="Daya guna – Indonesian" lang="id" hreflang="id" data-title="Daya guna" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Utilit%C3%A0_(economia)" title="Utilità (economia) – Italian" lang="it" hreflang="it" data-title="Utilità (economia)" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%89%E0%B2%AA%E0%B2%AF%E0%B3%81%E0%B2%95%E0%B3%8D%E0%B2%A4%E0%B2%A4%E0%B3%86" title="ಉಪಯುಕ್ತತೆ – Kannada" lang="kn" hreflang="kn" data-title="ಉಪಯುಕ್ತತೆ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9F%D0%B0%D0%B9%D0%B4%D0%B0%D0%BB%D1%8B%D0%BB%D1%8B%D2%9B" title="Пайдалылық – Kazakh" lang="kk" hreflang="kk" data-title="Пайдалылық" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Hasznoss%C3%A1gi_f%C3%BCggv%C3%A9ny" title="Hasznossági függvény – Hungarian" lang="hu" hreflang="hu" data-title="Hasznossági függvény" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D0%BE%D1%80%D0%B8%D1%81%D1%82_(%D0%95%D0%BA%D0%BE%D0%BD%D0%BE%D0%BC%D0%B8%D1%98%D0%B0)" title="Корист (Економија) – Macedonian" lang="mk" hreflang="mk" data-title="Корист (Економија)" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%89%E0%B4%AA%E0%B4%AF%E0%B5%81%E0%B4%95%E0%B5%8D%E0%B4%A4%E0%B4%A4" title="ഉപയുക്തത – Malayalam" lang="ml" hreflang="ml" data-title="ഉപയുക്തത" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Utiliti" title="Utiliti – Malay" lang="ms" hreflang="ms" data-title="Utiliti" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Nut_(economie)" title="Nut (economie) – Dutch" lang="nl" hreflang="nl" data-title="Nut (economie)" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%8A%B9%E7%94%A8" title="効用 – Japanese" lang="ja" hreflang="ja" data-title="効用" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Nyttefunksjon" title="Nyttefunksjon – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Nyttefunksjon" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Naflilik" title="Naflilik – Uzbek" lang="uz" hreflang="uz" data-title="Naflilik" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/U%C5%BCyteczno%C5%9B%C4%87_(ekonomia)" title="Użyteczność (ekonomia) – Polish" lang="pl" hreflang="pl" data-title="Użyteczność (ekonomia)" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Utilidade_(economia)" title="Utilidade (economia) – Portuguese" lang="pt" hreflang="pt" data-title="Utilidade (economia)" data-language-autonym="Português" data-language-local-name="Portuguese" 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/Utilitate" title="Utilitate – Romanian" lang="ro" hreflang="ro" data-title="Utilitate" data-language-autonym="Română" data-language-local-name="Romanian" 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%D0%BE%D0%BB%D0%B5%D0%B7%D0%BD%D0%BE%D1%81%D1%82%D1%8C" title="Полезность – Russian" lang="ru" hreflang="ru" data-title="Полезность" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%A2%D1%83%D2%BB%D0%B0" title="Туһа – Yakut" lang="sah" hreflang="sah" data-title="Туһа" data-language-autonym="Саха тыла" data-language-local-name="Yakut" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Utility" title="Utility – Simple English" lang="en-simple" hreflang="en-simple" data-title="Utility" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/%C3%9A%C5%BEitok_(ekon%C3%B3mia)" title="Úžitok (ekonómia) – Slovak" lang="sk" hreflang="sk" data-title="Úžitok (ekonómia)" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%BE%D1%80%D0%B8%D1%81%D0%BD%D0%BE%D1%81%D1%82" title="Корисност – Serbian" lang="sr" hreflang="sr" data-title="Корисност" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Hy%C3%B6ty" title="Hyöty – Finnish" lang="fi" hreflang="fi" data-title="Hyöty" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Nytta" title="Nytta – Swedish" lang="sv" hreflang="sv" data-title="Nytta" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AE%AF%E0%AE%A9%E0%AF%8D%E0%AE%AA%E0%AE%BE%E0%AE%9F%E0%AF%81" title="பயன்பாடு – Tamil" lang="ta" hreflang="ta" data-title="பயன்பாடு" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a 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فۇنكىسيەسى" data-language-autonym="ئۇيغۇرچە / Uyghurche" data-language-local-name="Uyghur" class="interlanguage-link-target"><span>ئۇيغۇرچە / Uyghurche</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Uti%C5%82it%C3%A0_(economia)" title="Utiłità (economia) – Venetian" lang="vec" hreflang="vec" data-title="Utiłità (economia)" data-language-autonym="Vèneto" data-language-local-name="Venetian" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Th%E1%BB%8Fa_d%E1%BB%A5ng" title="Thỏa dụng – Vietnamese" lang="vi" hreflang="vi" data-title="Thỏa dụng" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E6%95%88%E7%94%A8" title="效用 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="效用" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%95%88%E7%94%A8" title="效用 – Cantonese" lang="yue" hreflang="yue" data-title="效用" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%95%88%E7%94%A8" title="效用 – Chinese" lang="zh" hreflang="zh" data-title="效用" data-language-autonym="中文" data-language-local-name="Chinese" 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/Q466707#sitelinks-wikipedia" 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data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about the economic concept. For other uses, see <a href="/wiki/Utility_(disambiguation)" class="mw-disambig" title="Utility (disambiguation)">Utility (disambiguation)</a>.</div> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output 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/><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409" /><table class="sidebar sidebar-collapse nomobile nowraplinks" style="width:18.0em;"><tbody><tr><td class="sidebar-pretitle">Part of <a href="/wiki/Category:Utilitarianism" title="Category:Utilitarianism">a series</a> on</td></tr><tr><th class="sidebar-title-with-pretitle" style="font-size:180%;font-weight:normal;"><a href="/wiki/Utilitarianism" title="Utilitarianism">Utilitarianism</a></th></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:left;padding-left:0.3em;;color: var(--color-base)">Predecessors</div><div class="sidebar-list-content mw-collapsible-content"><div class="plainlist"> <ul><li><a href="/wiki/Mozi" title="Mozi">Mozi</a></li> <li><a href="/wiki/Shantideva" title="Shantideva">Shantideva</a></li> <li><a href="/wiki/David_Hume" title="David Hume">David Hume</a></li> <li><a href="/wiki/Claude_Adrien_Helv%C3%A9tius" title="Claude Adrien Helvétius">Claude Adrien Helvétius</a></li> <li><a href="/wiki/Cesare_Beccaria" title="Cesare Beccaria">Cesare Beccaria</a></li> <li><a href="/wiki/William_Godwin" title="William Godwin">William Godwin</a></li> <li><a href="/wiki/Francis_Hutcheson_(philosopher)" title="Francis Hutcheson (philosopher)">Francis Hutcheson</a></li> <li><a href="/wiki/William_Paley" title="William Paley">William Paley</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:left;padding-left:0.3em;;color: var(--color-base)"><a href="/wiki/List_of_utilitarians" title="List of utilitarians">Key proponents</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="plainlist"> <ul><li><a href="/wiki/Jeremy_Bentham" title="Jeremy Bentham">Jeremy Bentham</a></li> <li><a href="/wiki/John_Stuart_Mill" title="John Stuart Mill">John Stuart Mill</a></li> <li><a href="/wiki/Henry_Sidgwick" title="Henry Sidgwick">Henry Sidgwick</a></li> <li><a href="/wiki/R._M._Hare" title="R. M. Hare">R. M. Hare</a></li> <li><a href="/wiki/Peter_Singer" title="Peter Singer">Peter Singer</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:left;padding-left:0.3em;;color: var(--color-base)">Types of utilitarianism</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Negative_utilitarianism" title="Negative utilitarianism">Negative</a></li> <li><a href="/wiki/Rule_utilitarianism" title="Rule utilitarianism">Rule</a></li> <li><a href="/wiki/Act_utilitarianism" title="Act utilitarianism">Act</a></li> <li><a href="/wiki/Two-level_utilitarianism" title="Two-level utilitarianism">Two-level</a></li> <li><a href="/wiki/Total_utilitarianism" class="mw-redirect" title="Total utilitarianism">Total</a></li> <li><a href="/wiki/Average_utilitarianism" class="mw-redirect" title="Average utilitarianism">Average</a></li> <li><a href="/wiki/Preference_utilitarianism" title="Preference utilitarianism">Preference</a></li> <li><a href="/wiki/Utilitarianism#Classical_utilitarianism" title="Utilitarianism">Classical</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:left;padding-left:0.3em;;color: var(--color-base)">Key concepts</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Pain" title="Pain">Pain</a></li> <li><a href="/wiki/Suffering" title="Suffering">Suffering</a></li> <li><a href="/wiki/Pleasure" title="Pleasure">Pleasure</a></li> <li><a class="mw-selflink selflink">Utility</a></li> <li><a href="/wiki/Happiness" title="Happiness">Happiness</a></li> <li><a href="/wiki/Eudaimonia" title="Eudaimonia">Eudaimonia</a></li> <li><a href="/wiki/Consequentialism" title="Consequentialism">Consequentialism</a></li> <li><a href="/wiki/Equal_consideration_of_interests" title="Equal consideration of interests">Equal consideration</a></li> <li><a href="/wiki/Felicific_calculus" title="Felicific calculus">Felicific calculus</a></li> <li><a href="/wiki/Utilitarian_social_choice_rule" class="mw-redirect" title="Utilitarian social choice rule">Utilitarian social choice rule</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:left;padding-left:0.3em;;color: var(--color-base)">Problems</div><div class="sidebar-list-content mw-collapsible-content"><div class="plainlist"> <ul><li><a href="/wiki/Demandingness_objection" title="Demandingness objection">Demandingness objection</a></li> <li><a href="/wiki/Mere_addition_paradox" title="Mere addition paradox">Mere addition paradox</a></li> <li><a href="/wiki/Paradox_of_hedonism" title="Paradox of hedonism">Paradox of hedonism</a></li> <li><a href="/wiki/Replaceability_argument" title="Replaceability argument">Replaceability argument</a></li> <li><a href="/wiki/Utility_monster" title="Utility monster">Utility monster</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:left;padding-left:0.3em;;color: var(--color-base)">Works</div><div class="sidebar-list-content mw-collapsible-content"><div class="plainlist"> <ul><li><i><a href="/wiki/An_Introduction_to_the_Principles_of_Morals_and_Legislation" title="An Introduction to the Principles of Morals and Legislation">An Introduction to the Principles of Morals and Legislation</a></i> <span style="font-size:85%;">(1780)</span></li> <li><i><a href="/wiki/On_Liberty" title="On Liberty">On Liberty</a></i> <span style="font-size:85%;">(1859)</span></li> <li><i><a href="/wiki/Utilitarianism_(book)" title="Utilitarianism (book)">Utilitarianism</a></i> <span style="font-size:85%;">(1861)</span></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:left;padding-left:0.3em;;color: var(--color-base)">Related topics</div><div class="sidebar-list-content mw-collapsible-content"><div class="plainlist"> <ul><li><a href="/wiki/Rational_choice_theory" class="mw-redirect" title="Rational choice theory">Rational choice theory</a></li> <li><a href="/wiki/Game_theory" title="Game theory">Game theory</a></li> <li><a href="/wiki/Neoclassical_economics" title="Neoclassical economics">Neoclassical economics</a></li> <li><a href="/wiki/Population_ethics" title="Population ethics">Population ethics</a></li> <li><a href="/wiki/Effective_altruism" title="Effective altruism">Effective altruism</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-below"> <a href="/wiki/Portal:Philosophy" title="Portal:Philosophy">Philosophy portal</a></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Utilitarianism" title="Template:Utilitarianism"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Utilitarianism" title="Template talk:Utilitarianism"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Utilitarianism" title="Special:EditPage/Template:Utilitarianism"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>In <a href="/wiki/Economics" title="Economics">economics</a>, <b>utility</b> is a measure of a certain person's satisfaction from a certain state of the world. Over time, the term has been used with at least two meanings. </p> <ul><li>In a <a href="/wiki/Normative_economics" class="mw-redirect" title="Normative economics">normative</a> context, utility refers to a goal or objective that we wish to maximize, i.e., an <a href="/wiki/Objective_function" class="mw-redirect" title="Objective function">objective function</a>. This kind of utility bears a closer resemblance to the original <a href="/wiki/Utilitarianism" title="Utilitarianism">utilitarian</a> concept, developed by moral philosophers such as <a href="/wiki/Jeremy_Bentham" title="Jeremy Bentham">Jeremy Bentham</a> and <a href="/wiki/John_Stuart_Mill" title="John Stuart Mill">John Stuart Mill</a>.</li> <li>In a <a href="/wiki/Positive_economics" class="mw-redirect" title="Positive economics">descriptive</a> context, the term refers to an <i>apparent</i> objective function; such a function is <a href="/wiki/Revealed_preference" title="Revealed preference">revealed by a person's behavior</a>, and specifically by their preferences over <a href="/wiki/Lottery_(probability)" class="mw-redirect" title="Lottery (probability)">lotteries</a>.</li></ul> <p>The relationship between these two kinds of utility functions has been a source of controversy among both <a href="/wiki/Economics" title="Economics">economists</a> and <a href="/wiki/Ethics" title="Ethics">ethicists</a>, with most maintaining that the two are distinct but generally related. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Utility_function">Utility function</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=1" title="Edit section: Utility function"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Consider a set of alternatives among which a person has a preference ordering. A <b>utility function</b> represents that ordering if it is possible to assign a <a href="/wiki/Real_number" title="Real number">real number</a> to each alternative in such a manner that <i>alternative a</i> is assigned a number greater than <i>alternative b</i> if and only if the individual prefers <i>alternative a</i> to <i>alternative b</i>. In this situation, someone who selects the most preferred alternative must also choose one that maximizes the associated utility function. </p><p>Suppose James has utility function <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 U={\sqrt {xy}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>x</mi> <mi>y</mi> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U={\sqrt {xy}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7721d6e6ac1b15f7495086bbf7272726b533d71c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:9.302ex; height:3.009ex;" alt="{\displaystyle U={\sqrt {xy}}}" /></span> such that <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 x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}" /></span> is the number of apples and <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 y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}" /></span> is the number of chocolates. Alternative A has <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 x=9}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mn>9</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=9}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48e0f066e1ed9b842844915c490d57b8384c9969" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.591ex; height:2.176ex;" alt="{\displaystyle x=9}" /></span> apples and <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 y=16}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mn>16</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=16}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/80357e893b45c66d432146b2a5ce8cb22d00ecd4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.579ex; height:2.509ex;" alt="{\displaystyle y=16}" /></span> chocolates; alternative B has <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 x=13}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mn>13</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=13}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6fb285765caa4151c032e1555c72830a51809a36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.753ex; height:2.176ex;" alt="{\displaystyle x=13}" /></span> apples and <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 y=13}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mn>13</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=13}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd3880d60aa4abcbec4e619d95d3a09bef3dac97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.579ex; height:2.509ex;" alt="{\displaystyle y=13}" /></span> chocolates. Putting the values <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 x,y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>,</mo> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x,y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ea0abffd33a692ded22accc104515a032851dff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.519ex; height:2.009ex;" alt="{\displaystyle x,y}" /></span> into the utility function yields <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 {\sqrt {9\times 16}}=12}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>9</mn> <mo>×</mo> <mn>16</mn> </msqrt> </mrow> <mo>=</mo> <mn>12</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {9\times 16}}=12}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93c54a67cd895a7ed07276b6c5869b6356d52e91" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.687ex; height:2.843ex;" alt="{\displaystyle {\sqrt {9\times 16}}=12}" /></span> for alternative A and <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 {\sqrt {13\times 13}}=13}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>13</mn> <mo>×</mo> <mn>13</mn> </msqrt> </mrow> <mo>=</mo> <mn>13</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {13\times 13}}=13}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/343aa3d61fb72710ed2827e4454a2489df3fe9f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.849ex; height:2.843ex;" alt="{\displaystyle {\sqrt {13\times 13}}=13}" /></span> for B, so James prefers alternative B. In general economic terms, a utility function ranks preferences concerning a set of goods and services. </p><p><a href="/wiki/G%C3%A9rard_Debreu" title="Gérard Debreu">Gérard Debreu</a> derived the conditions required for a preference ordering to be representable by a utility function.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> For a finite set of alternatives, these require only that the preference ordering is complete (so the individual can determine which of any two alternatives is preferred or that they are indifferent), and that the preference order is <a href="/wiki/Transitive_relation" title="Transitive relation">transitive</a>. </p><p>Suppose the set of alternatives is not finite (for example, even if the number of goods is finite, the quantity chosen can be any real number on an interval). In that case, a continuous utility function exists representing a consumer's preferences if and only if the consumer's preferences are complete, transitive, and continuous.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=2" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Utility can be represented through sets of <a href="/wiki/Indifference_curve" title="Indifference curve">indifference curve</a>, which are <a href="/wiki/Level_curves" class="mw-redirect" title="Level curves">level curves</a> of the function itself and which plot the combination of commodities that an individual would accept to maintain a given level of satisfaction. Combining indifference curves with budget constraints allows for individual <a href="/wiki/Demand_function" class="mw-redirect" title="Demand function">demand curves</a> derivation. </p><p>A diagram of a general indifference curve is shown below (Figure 1). The vertical and horizontal axes represent an individual's consumption of commodity Y and X respectively. All the combinations of commodity X and Y along the same indifference curve are regarded indifferently by individuals, which means all the combinations along an indifference curve result in the same utility value. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:A_simple_diagram_of_Indifference_curve.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/A_simple_diagram_of_Indifference_curve.png/220px-A_simple_diagram_of_Indifference_curve.png" decoding="async" width="220" height="194" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/A_simple_diagram_of_Indifference_curve.png/330px-A_simple_diagram_of_Indifference_curve.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/28/A_simple_diagram_of_Indifference_curve.png/440px-A_simple_diagram_of_Indifference_curve.png 2x" data-file-width="964" data-file-height="848" /></a><figcaption>Figure 1</figcaption></figure> <p>Individual and social utility can be construed as the value of a utility function and a <a href="/wiki/Social_welfare_function" title="Social welfare function">social welfare function</a>, respectively. When coupled with production or commodity constraints, by some assumptions, these functions can be used to analyze <a href="/wiki/Pareto_efficiency" title="Pareto efficiency">Pareto efficiency</a>, such as illustrated by <a href="/wiki/Edgeworth_box" title="Edgeworth box">Edgeworth boxes</a> in <a href="/wiki/Contract_curve" title="Contract curve">contract curves</a>. Such efficiency is a major concept in <a href="/wiki/Welfare_economics" title="Welfare economics">welfare economics</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Preference">Preference</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=3" title="Edit section: Preference"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>While <a href="/wiki/Preference_(economics)" title="Preference (economics)">preferences</a> are the conventional foundation of choice theory in <a href="/wiki/Microeconomics" title="Microeconomics">microeconomics</a>, it is often convenient to represent preferences with a utility <a href="/wiki/Function_(mathematics)" title="Function (mathematics)">function</a>. Let <i>X</i> be the <b>consumption set</b>, the set of all mutually exclusive baskets the consumer could consume. The consumer's <b>utility function</b> <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 u\colon X\to \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo>:</mo> <mi>X</mi> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u\colon X\to \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eedc6d67e86e9bf65cf3cc825edad82c1ea32bbc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.636ex; height:2.176ex;" alt="{\displaystyle u\colon X\to \mathbb {R} }" /></span> ranks each possible outcome in the consumption set. If the consumer strictly prefers <i>x</i> to <i>y</i> or is indifferent between them, then <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 u(x)\geq u(y)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>≥</mo> <mi>u</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u(x)\geq u(y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49db011500396283895f5ac88f3f8dafca5ffbd6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.862ex; height:2.843ex;" alt="{\displaystyle u(x)\geq u(y)}" /></span>. </p><p>For example, suppose a consumer's consumption set is <i>X</i> = {nothing, 1 apple,1 orange, 1 apple and 1 orange, 2 apples, 2 oranges}, and his utility function is <i>u</i>(nothing) = 0, <i>u</i>(1 apple) = 1, <i>u</i>(1 orange) = 2, <i>u</i>(1 apple and 1 orange) = 5, <i>u</i>(2 apples) = 2 and <i>u</i>(2 oranges) = 4. Then this consumer prefers 1 orange to 1 apple but prefers one of each to 2 oranges. </p><p>In micro-economic models, there is usually a finite set of L commodities, and a consumer may consume an arbitrary amount of each commodity. This gives a consumption set of <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 \mathbb {R} _{+}^{L}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} _{+}^{L}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/821b9af9f3ab2926803d2870dab84b72818fd5f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.189ex; height:3.343ex;" alt="{\displaystyle \mathbb {R} _{+}^{L}}" /></span>, and each package <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 x\in \mathbb {R} _{+}^{L}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>∈</mo> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\in \mathbb {R} _{+}^{L}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/333ba67fdeec3f90f4a9c2dff8676e97edfc771d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.359ex; height:3.343ex;" alt="{\displaystyle x\in \mathbb {R} _{+}^{L}}" /></span> is a vector containing the amounts of each commodity. For the example, there are two commodities: apples and oranges. If we say apples are the first commodity, and oranges the second, then the consumption set is <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 X=\mathbb {R} _{+}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> <mo>=</mo> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X=\mathbb {R} _{+}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed7ba5b56d80380a8449ff436d9bc4ab0067ee7d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.267ex; height:3.343ex;" alt="{\displaystyle X=\mathbb {R} _{+}^{2}}" /></span> and <i>u</i>(0, 0) = 0, <i>u</i>(1, 0) = 1, <i>u</i>(0, 1) = 2, <i>u</i>(1, 1) = 5, <i>u</i>(2, 0) = 2, <i>u</i>(0, 2) = 4 as before. For <i>u</i> to be a utility function on <i>X</i>, however, it must be defined for every package in <i>X</i>, so now the function must be defined for fractional apples and oranges too. One function that would fit these numbers is <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 u(x_{\text{apples}},x_{\text{oranges}})=x_{\text{apples}}+2x_{\text{oranges}}+2x_{\text{apples}}x_{\text{oranges}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>apples</mtext> </mrow> </msub> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>oranges</mtext> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>apples</mtext> </mrow> </msub> <mo>+</mo> <mn>2</mn> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>oranges</mtext> </mrow> </msub> <mo>+</mo> <mn>2</mn> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>apples</mtext> </mrow> </msub> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>oranges</mtext> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u(x_{\text{apples}},x_{\text{oranges}})=x_{\text{apples}}+2x_{\text{oranges}}+2x_{\text{apples}}x_{\text{oranges}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1dc49a7160ef468f19f9b4122b6745658f2ee820" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:54.958ex; height:3.009ex;" alt="{\displaystyle u(x_{\text{apples}},x_{\text{oranges}})=x_{\text{apples}}+2x_{\text{oranges}}+2x_{\text{apples}}x_{\text{oranges}}.}" /></span> </p><p>Preferences have three main <b>properties</b>: </p> <ul><li><b>Completeness</b></li></ul> <p>Assume an individual has two choices, A and B. By ranking the two choices, one and only one of the following relationships is true: an individual strictly prefers A (A > B); an individual strictly prefers B (B>A); an individual is indifferent between A and B (A = B). Either <i>a</i> ≥ <i>b</i> OR <i>b</i> ≥ <i>a</i> (OR both) for all (<i>a</i>,<i>b</i>) </p> <ul><li><b>Transitivity</b></li></ul> <p>Individuals' preferences are consistent over bundles. If an individual prefers bundle A to bundle B and bundle B to bundle C, then it can be assumed that the individual prefers bundle A to bundle C. (If <i>a</i> ≥ <i>b</i> and <i>b</i> ≥ <i>c</i>, then <i>a</i> ≥ <i>c</i> for all (<i>a</i>,<i>b</i>,<i>c</i>)). </p> <ul><li><b>Non-satiation</b> or <b>monotonicity</b></li></ul> <p>If bundle A contains all the goods that a bundle B contains, but A also includes more of at least one good than B. The individual prefers A over B.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> If, for example, bundle A = {1 apple,2 oranges}, and bundle B = {1 apple,1 orange}, then A is preferred over B. </p> <div class="mw-heading mw-heading3"><h3 id="Revealed_preference">Revealed preference</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=4" title="Edit section: Revealed preference"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>It was recognized that utility could not be measured or observed directly, so instead economists devised a way to infer relative utilities from observed choice. These 'revealed preferences', as termed by <a href="/wiki/Paul_Samuelson" title="Paul Samuelson">Paul Samuelson</a>, were revealed e.g. in people's willingness to pay: </p> <blockquote><p> Utility is assumed to be correlative to Desire or Want. It has been argued already that desires cannot be measured directly, but only indirectly, by the outward phenomena which they cause: and that in those cases with which economics is mainly concerned the measure is found by the price which a person is willing to pay for the fulfillment or satisfaction of his desire.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 78">: 78 </span></sup></p></blockquote> <div class="mw-heading mw-heading2"><h2 id="Functions"><style data-mw-deduplicate="TemplateStyles:r1238216509">.mw-parser-output .vanchor>:target~.vanchor-text{background-color:#b1d2ff}@media screen{html.skin-theme-clientpref-night .mw-parser-output .vanchor>:target~.vanchor-text{background-color:#0f4dc9}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .vanchor>:target~.vanchor-text{background-color:#0f4dc9}}</style><span class="vanchor"><span id="Functions"></span><span id="Utility_functions"></span><span class="vanchor-text">Functions</span></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=5" title="Edit section: Functions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Utility functions</b>, expressing utility as a function of the amounts of the various goods consumed, are treated as either <i>cardinal</i> or <i>ordinal</i>, depending on whether they are or are not interpreted as providing more information than simply the rank ordering of preferences among bundles of goods, such as information concerning the strength of preferences. </p> <div class="mw-heading mw-heading3"><h3 id="Cardinal">Cardinal</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=6" title="Edit section: Cardinal"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Cardinal_utility" title="Cardinal utility">Cardinal utility</a></div> <p>Cardinal utility states that the utilities obtained from consumption can be measured and ranked objectively and are representable by numbers.<sup id="cite_ref-:0_5-0" class="reference"><a href="#cite_note-:0-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> There are fundamental assumptions of cardinal utility. Economic agents should be able to rank different bundles of goods based on their preferences or utilities and sort different transitions between two bundles of goods.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>A cardinal utility function can be transformed to another utility function by a positive linear transformation (multiplying by a positive number, and adding some other number); however, both utility functions represent the same preferences.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>When cardinal utility is assumed, the magnitude of utility differences is treated as an ethically or behaviorally significant quantity. For example, suppose a cup of orange juice has utility of 120 "utils", a cup of tea has a utility of 80 utils, and a cup of water has a utility of 40 utils. With cardinal utility, it can be concluded that the cup of orange juice is better than the cup of tea by the same amount by which the cup of tea is better than the cup of water. This means that if a person has a cup of tea, they would be willing to take any bet with a probability, p, greater than .5 of getting a cup of juice, with a risk of getting a cup of water equal to 1-p. One cannot conclude, however, that the cup of tea is two-thirds of the goodness of the cup of juice because this conclusion would depend not only on magnitudes of utility differences but also on the "zero" of utility. For example, if the "zero" of utility were located at -40, then a cup of orange juice would be 160 utils more than zero, a cup of tea 120 utils more than zero. Cardinal utility can be considered as the assumption that quantifiable characteristics, such as height, weight, temperature, etc can measure utility. </p><p><a href="/wiki/Neoclassical_economics" title="Neoclassical economics">Neoclassical economics</a> has largely retreated from using cardinal utility functions as the basis of economic behavior. A notable exception is in the context of analyzing choice with conditions of risk (see <a href="#Expected_utility">below</a>). </p><p>Sometimes cardinal utility is used to aggregate utilities across persons, to create a <a href="/wiki/Social_welfare_function" title="Social welfare function">social welfare function</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Ordinal">Ordinal</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=7" title="Edit section: Ordinal"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Ordinal_utility" title="Ordinal utility">Ordinal utility</a></div> <p>Instead of giving actual numbers over different bundles, ordinal utilities are only the rankings of utilities received from different bundles of goods or services.<sup id="cite_ref-:0_5-1" class="reference"><a href="#cite_note-:0-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> For example, ordinal utility could tell that having two ice creams provide a greater utility to individuals in comparison to one ice cream but could not tell exactly how much extra utility received by the individual. Ordinal utility, it does not require individuals to specify how much extra utility they received from the preferred bundle of goods or services in comparison to other bundles. They are only needed to tell which bundles they prefer. </p><p>When ordinal utilities are used, differences in utils (values assumed by the utility function) are treated as ethically or behaviorally meaningless: the utility index encodes a full behavioral ordering between members of a choice set, but tells nothing about the related <i>strength of preferences</i>. For the above example, it would only be possible to say that juice is preferred to tea to water. Thus, ordinal utility utilizes comparisons, such as "preferred to", "no more", "less than", etc. </p><p>If a function <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 u(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1e5ff65a28eed29d36ddae9c6ae3b596fd14370" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.469ex; height:2.843ex;" alt="{\displaystyle u(x)}" /></span> is ordinal and non-negative, it is equivalent to the function <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 u(x)^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo stretchy="false">(</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u(x)^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6d8fee5d555932383d2c7a95501e8dc05698938" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.523ex; height:3.176ex;" alt="{\displaystyle u(x)^{2}}" /></span>, because taking the square is an increasing <a href="/wiki/Monotonic_function#Monotonic_transformation" title="Monotonic function">monotone (or monotonic) transformation</a>. This means that the ordinal preference induced by these functions is the same (although they are two different functions). In contrast, if <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 u(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1e5ff65a28eed29d36ddae9c6ae3b596fd14370" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.469ex; height:2.843ex;" alt="{\displaystyle u(x)}" /></span> is cardinal, it is not equivalent to <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 u(x)^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo stretchy="false">(</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u(x)^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6d8fee5d555932383d2c7a95501e8dc05698938" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.523ex; height:3.176ex;" alt="{\displaystyle u(x)^{2}}" /></span>. </p> <div class="mw-heading mw-heading3"><h3 id="Examples">Examples</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=8" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In order to simplify calculations, various alternative assumptions have been made concerning details of human preferences, and these imply various alternative utility functions such as: </p> <ul><li><a href="/wiki/Constant_elasticity_of_substitution" title="Constant elasticity of substitution">CES</a> (<i>constant elasticity of substitution</i>).</li> <li><a href="/wiki/Isoelastic_utility" title="Isoelastic utility">Isoelastic utility</a></li> <li><a href="/wiki/Exponential_utility" title="Exponential utility">Exponential utility</a></li> <li><a href="/wiki/Quasilinear_utility" title="Quasilinear utility">Quasilinear utility</a></li> <li><a href="/wiki/Homothetic_preferences" title="Homothetic preferences">Homothetic preferences</a></li> <li><a href="/wiki/Stone%E2%80%93Geary_utility_function" title="Stone–Geary utility function">Stone–Geary utility function</a></li> <li><a href="/wiki/Gorman_polar_form" title="Gorman polar form">Gorman polar form</a> <ul><li><a href="/wiki/Greenwood%E2%80%93Hercowitz%E2%80%93Huffman_preferences" title="Greenwood–Hercowitz–Huffman preferences">Greenwood–Hercowitz–Huffman preferences</a></li> <li><a href="/wiki/King%E2%80%93Plosser%E2%80%93Rebelo_preferences" title="King–Plosser–Rebelo preferences">King–Plosser–Rebelo preferences</a></li></ul></li> <li><a href="/wiki/Hyperbolic_absolute_risk_aversion" title="Hyperbolic absolute risk aversion">Hyperbolic absolute risk aversion</a></li></ul> <p>Most utility functions used for modeling or theory are <b>well-behaved.</b> They are usually monotonic and quasi-concave. However, it is possible for rational preferences not to be representable by a utility function. An example is <a href="/wiki/Lexicographic_preferences" title="Lexicographic preferences">lexicographic preferences</a> which are not continuous and cannot be represented by a continuous utility function.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Marginal_utility">Marginal utility</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=9" title="Edit section: Marginal utility"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Economists distinguish between total utility and marginal utility. Total utility is the utility of an alternative, an entire consumption bundle or situation in life. The rate of change of utility from changing the quantity of one good consumed is termed the marginal utility of that good. Marginal utility therefore measures the slope of the utility function with respect to the changes of one good.<sup id="cite_ref-:1_9-0" class="reference"><a href="#cite_note-:1-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Marginal utility usually decreases with consumption of the good, the idea of "diminishing marginal utility". In calculus notation, the marginal utility of good X is <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 MU_{x}={\frac {\partial U}{\partial X}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>X</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle MU_{x}={\frac {\partial U}{\partial X}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49f676aaa63365a1072032b399ab4aa871df98f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:12.435ex; height:5.509ex;" alt="{\displaystyle MU_{x}={\frac {\partial U}{\partial X}}}" /></span>. When a good's marginal utility is positive, additional consumption of it increases utility; if zero, the consumer is satiated and indifferent about consuming more; if negative, the consumer would pay to reduce his consumption.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Law_of_diminishing_marginal_utility">Law of diminishing marginal utility</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=10" title="Edit section: Law of diminishing marginal utility"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Rational individuals only consume additional units of goods if it increases the marginal utility. However, the law of diminishing marginal utility means an additional unit consumed brings a lower marginal utility than that carried by the previous unit consumed. For example, drinking one bottle of water makes a thirsty person satisfied; as the consumption of water increases, he may feel begin to feel bad which causes the marginal utility to decrease to zero or even become negative. Furthermore, this is also used to analyze progressive taxes as the greater taxes can result in the loss of utility. </p> <div class="mw-heading mw-heading3"><h3 id="Marginal_rate_of_substitution_(MRS)"><span id="Marginal_rate_of_substitution_.28MRS.29"></span>Marginal rate of substitution (MRS)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=11" title="Edit section: Marginal rate of substitution (MRS)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Marginal rate of substitution is the slope of the indifference curve, which measures how much an individual is willing to switch from one good to another. Using a mathematic equation, <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 MRS=-\operatorname {d} \!x_{2}/\operatorname {d} \!x_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mi>R</mi> <mi>S</mi> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace"></mspace> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace"></mspace> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle MRS=-\operatorname {d} \!x_{2}/\operatorname {d} \!x_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2525ad1083dc813123769aadd156966a8facf89" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.902ex; height:2.843ex;" alt="{\displaystyle MRS=-\operatorname {d} \!x_{2}/\operatorname {d} \!x_{1}}" /></span>keeping <i>U</i>(<i>x</i><sub>1</sub>,<i>x</i><sub>2</sub>) constant. Thus, MRS is how much an individual is willing to pay for consuming a greater amount of <i>x</i><sub>1</sub>. </p><p>MRS is related to marginal utility. The relationship between marginal utility and MRS is:<sup id="cite_ref-:1_9-1" class="reference"><a href="#cite_note-:1-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </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 MRS={\frac {MU_{1}}{MU_{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mi>R</mi> <mi>S</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>M</mi> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi>M</mi> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle MRS={\frac {MU_{1}}{MU_{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29563942f56d46a71c48df5367c71301d18d47ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:14.724ex; height:5.509ex;" alt="{\displaystyle MRS={\frac {MU_{1}}{MU_{2}}}}" /></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Expected_utility">Expected utility</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=12" title="Edit section: Expected utility"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Expected_utility_hypothesis" title="Expected utility hypothesis">Expected utility hypothesis</a></div> <p>Expected utility theory deals with the analysis of choices among <b>risky</b> projects with multiple (possibly multidimensional) outcomes. </p><p>The <a href="/wiki/St._Petersburg_paradox" title="St. Petersburg paradox">St. Petersburg paradox</a> was first proposed by <a href="/wiki/Nicolaus_I_Bernoulli" title="Nicolaus I Bernoulli">Nicholas Bernoulli</a> in 1713 and solved by <a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Daniel Bernoulli</a> in 1738, although the Swiss mathematician <a href="/wiki/Gabriel_Cramer" title="Gabriel Cramer">Gabriel Cramer</a> proposed taking the expectation of a square-root utility function of money in an 1728 letter to N. Bernoulli. D. Bernoulli argued that the paradox could be resolved if decision-makers displayed <a href="/wiki/Risk_aversion" title="Risk aversion">risk aversion</a> and argued for a logarithmic cardinal utility function. (Analysis of international survey data during the 21st century has shown that insofar as utility represents happiness, as for <a href="/wiki/Utilitarianism" title="Utilitarianism">utilitarianism</a>, it is indeed proportional to log of income.) </p><p>The first important use of the expected utility theory was that of <a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a> and <a href="/wiki/Oskar_Morgenstern" title="Oskar Morgenstern">Oskar Morgenstern</a>, who used the assumption of expected utility maximization in their formulation of <a href="/wiki/Game_theory" title="Game theory">game theory</a>. </p><p>In finding the probability-weighted average of the utility from each possible outcome: </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 {\text{EU}}=\Pr(z)\cdot u({\text{Value}}(z))+\Pr(y)\cdot u({\text{Value}}(y))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>EU</mtext> </mrow> <mo>=</mo> <mo movablelimits="true" form="prefix">Pr</mo> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>u</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>Value</mtext> </mrow> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo>+</mo> <mo movablelimits="true" form="prefix">Pr</mo> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>u</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>Value</mtext> </mrow> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{EU}}=\Pr(z)\cdot u({\text{Value}}(z))+\Pr(y)\cdot u({\text{Value}}(y))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6cc90d6e2e6d4e6b923a04992156dc1698c0dfc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:47.369ex; height:2.843ex;" alt="{\displaystyle {\text{EU}}=\Pr(z)\cdot u({\text{Value}}(z))+\Pr(y)\cdot u({\text{Value}}(y))}" /></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Von_Neumann–Morgenstern"><span id="Von_Neumann.E2.80.93Morgenstern"></span>Von Neumann–Morgenstern</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=13" title="Edit section: Von Neumann–Morgenstern"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Von_Neumann%E2%80%93Morgenstern_utility_theorem" title="Von Neumann–Morgenstern utility theorem">Von Neumann–Morgenstern utility theorem</a></div> <p>Von Neumann and Morgenstern addressed situations in which the outcomes of choices are not known with certainty, but have probabilities associated with them. </p><p>A notation for a <i><a href="/wiki/Lottery_(probability)" class="mw-redirect" title="Lottery (probability)">lottery</a></i> is as follows: if options A and B have probability <i>p</i> and 1 − <i>p</i> in the lottery, we write it as a linear combination: </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 L=pA+(1-p)B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <mi>p</mi> <mi>A</mi> <mo>+</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L=pA+(1-p)B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92cdc7fee165b4f8af8579d523ff6226d3cf31a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.18ex; height:2.843ex;" alt="{\displaystyle L=pA+(1-p)B}" /></span></dd></dl> <p>More generally, for a lottery with many possible options: </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 L=\sum _{i}p_{i}A_{i},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L=\sum _{i}p_{i}A_{i},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c7287803c12c9b46b54b6ca6da2fe4f8ce74fab7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:13.582ex; height:5.509ex;" alt="{\displaystyle L=\sum _{i}p_{i}A_{i},}" /></span></dd></dl> <p>where <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 \sum _{i}p_{i}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{i}p_{i}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef0f56c2062ef0e4a44688eb34ce66820413ddc7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:9.972ex; height:5.509ex;" alt="{\displaystyle \sum _{i}p_{i}=1}" /></span>. </p><p>By making some reasonable assumptions about the way choices behave, von Neumann and Morgenstern showed that if an agent can choose between the lotteries, then this agent has a utility function such that the desirability of an arbitrary lottery can be computed as a linear combination of the utilities of its parts, with the weights being their probabilities of occurring. </p><p>This is termed the <i>expected utility theorem</i>. The required assumptions are four axioms about the properties of the agent's <a href="/wiki/Preference_(economics)" title="Preference (economics)">preference relation</a> over 'simple lotteries', which are lotteries with just two options. Writing <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\preceq A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo>⪯</mo> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B\preceq A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7630f81ffd3df39067ccda5c1c69dba497043a8e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.606ex; height:2.343ex;" alt="{\displaystyle B\preceq A}" /></span> to mean 'A is weakly preferred to B' ('A is preferred at least as much as B'), the axioms are: </p> <ol><li>completeness: For any two simple lotteries <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 L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}" /></span> and <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 M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}" /></span>, either <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 L\preceq M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>⪯</mo> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L\preceq M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3be7cacab54af1796add5f3fe053a61b77e4ab4c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.124ex; height:2.343ex;" alt="{\displaystyle L\preceq M}" /></span> or <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 M\preceq L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo>⪯</mo> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M\preceq L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d473a66d8dd5bfbcfe336066eedfcd9a85c5091" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.124ex; height:2.343ex;" alt="{\displaystyle M\preceq L}" /></span> (or both, in which case they are viewed as equally desirable).</li> <li>transitivity: for any three lotteries <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 L,M,N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>,</mo> <mi>M</mi> <mo>,</mo> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L,M,N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82ec8e5b50816fc40ef75e37a261c1209964cdd4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.157ex; height:2.509ex;" alt="{\displaystyle L,M,N}" /></span>, if <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 L\preceq M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>⪯</mo> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L\preceq M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3be7cacab54af1796add5f3fe053a61b77e4ab4c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.124ex; height:2.343ex;" alt="{\displaystyle L\preceq M}" /></span> and <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 M\preceq N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo>⪯</mo> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M\preceq N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a616f9b1c94776da9b86c0a8d5ca46e13da917e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.604ex; height:2.343ex;" alt="{\displaystyle M\preceq N}" /></span>, then <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 L\preceq N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>⪯</mo> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L\preceq N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/20ccd965807441081a6f7cd675ce42aa11e7c4b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.745ex; height:2.343ex;" alt="{\displaystyle L\preceq N}" /></span>.</li> <li>convexity/continuity (Archimedean property): If <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 L\preceq M\preceq N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>⪯</mo> <mi>M</mi> <mo>⪯</mo> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L\preceq M\preceq N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5059a0cade3fe58f7abf5f04e6910e560936aa49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.286ex; height:2.343ex;" alt="{\displaystyle L\preceq M\preceq N}" /></span>, then there is 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 p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}" /></span> between 0 and 1 such that the lottery <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 pL+(1-p)N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mi>L</mi> <mo>+</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle pL+(1-p)N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c9407ba3a3440719a268865c71ac949f47d89542" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:14.727ex; height:2.843ex;" alt="{\displaystyle pL+(1-p)N}" /></span> is equally desirable as <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 M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}" /></span>.</li> <li>independence: for any three lotteries <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 L,M,N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>,</mo> <mi>M</mi> <mo>,</mo> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L,M,N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82ec8e5b50816fc40ef75e37a261c1209964cdd4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.157ex; height:2.509ex;" alt="{\displaystyle L,M,N}" /></span> and any probability <i>p</i>, <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 L\preceq M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>⪯</mo> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L\preceq M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3be7cacab54af1796add5f3fe053a61b77e4ab4c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.124ex; height:2.343ex;" alt="{\displaystyle L\preceq M}" /></span> if and only if <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 pL+(1-p)N\preceq pM+(1-p)N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mi>L</mi> <mo>+</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mi>N</mi> <mo>⪯</mo> <mi>p</mi> <mi>M</mi> <mo>+</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle pL+(1-p)N\preceq pM+(1-p)N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e886fad949d99760646e585ac9666f485cf6d2bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:33.323ex; height:2.843ex;" alt="{\displaystyle pL+(1-p)N\preceq pM+(1-p)N}" /></span>. Intuitively, if the lottery formed by the probabilistic combination of <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 L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}" /></span> and <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/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}" /></span> is no more preferable than the lottery formed by the same probabilistic combination of <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 M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}" /></span> and <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> <mo>,</mo> </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/b2285a1804b7fdcac187d155af09aff63152dd56" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.71ex; height:2.509ex;" alt="{\displaystyle N,}" /></span> then and only then <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 L\preceq M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>⪯</mo> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L\preceq M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3be7cacab54af1796add5f3fe053a61b77e4ab4c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.124ex; height:2.343ex;" alt="{\displaystyle L\preceq M}" /></span>.</li></ol> <p>Axioms 3 and 4 enable us to decide about the relative utilities of two assets or lotteries. </p><p>In more formal language: A von Neumann–Morgenstern utility function is a function from choices to the real numbers: </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 u\colon X\to \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo>:</mo> <mi>X</mi> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u\colon X\to \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eedc6d67e86e9bf65cf3cc825edad82c1ea32bbc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.636ex; height:2.176ex;" alt="{\displaystyle u\colon X\to \mathbb {R} }" /></span></dd></dl> <p>which assigns a real number to every outcome in a way that represents the agent's preferences over simple lotteries. Using the four assumptions mentioned above, the agent will prefer a lottery <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 L_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6a952cfe42c86b7741f55a817da0e251793a358" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.637ex; height:2.509ex;" alt="{\displaystyle L_{2}}" /></span> to a lottery <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 L_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e79dc1b001f8b923df475ed14de023cbc456013" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.637ex; height:2.509ex;" alt="{\displaystyle L_{1}}" /></span> if and only if, for the utility function characterizing that agent, the expected utility of <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 L_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6a952cfe42c86b7741f55a817da0e251793a358" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.637ex; height:2.509ex;" alt="{\displaystyle L_{2}}" /></span> is greater than the expected utility of <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 L_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e79dc1b001f8b923df475ed14de023cbc456013" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.637ex; height:2.509ex;" alt="{\displaystyle L_{1}}" /></span>: </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 L_{1}\preceq L_{2}{\text{ iff }}u(L_{1})\leq u(L_{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>⪯</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mtext> iff </mtext> </mrow> <mi>u</mi> <mo stretchy="false">(</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>≤</mo> <mi>u</mi> <mo stretchy="false">(</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{1}\preceq L_{2}{\text{ iff }}u(L_{1})\leq u(L_{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6471450ccc0d1b0f474576e3bd7aae4179c94cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:26.255ex; height:2.843ex;" alt="{\displaystyle L_{1}\preceq L_{2}{\text{ iff }}u(L_{1})\leq u(L_{2})}" /></span>.</dd></dl> <p>Of all the axioms, independence is the most often discarded. A variety of <a href="/wiki/Generalized_expected_utility" title="Generalized expected utility">generalized expected utility</a> theories have arisen, most of which omit or relax the independence axiom. </p> <div class="mw-heading mw-heading2"><h2 id="Indirect_utility">Indirect utility</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=14" title="Edit section: Indirect utility"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Indirect_utility" class="mw-redirect" title="Indirect utility">Indirect utility</a></div> <p>An indirect utility function gives the <a href="/wiki/Value_function" title="Value function">optimal attainable value</a> of a given utility function, which depends on the prices of the goods and the income or wealth level that the individual possesses. </p> <div class="mw-heading mw-heading3"><h3 id="Money">Money</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=15" title="Edit section: Money"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>One use of the indirect utility concept is the notion of the utility of money. The (indirect) utility function for money is a nonlinear function that is <a href="/wiki/Bounded_function" title="Bounded function">bounded</a> and asymmetric about the origin. The utility function is <a href="/wiki/Concave_function" title="Concave function">concave</a> in the positive region, representing the phenomenon of <a href="/wiki/Diminishing_marginal_utility" class="mw-redirect" title="Diminishing marginal utility">diminishing marginal utility</a>. The boundedness represents the fact that beyond a certain amount money ceases being useful at all, as the size of any economy at that time is itself bounded. The asymmetry about the origin represents the fact that gaining and losing money can have radically different implications both for individuals and businesses. The non-linearity of the utility function for money has profound implications in decision-making processes: in situations where outcomes of choices influence utility by gains or losses of money, which are the norm for most business settings, the optimal choice for a given decision depends on the possible outcomes of all other decisions in the same time-period.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Budget_constraints">Budget constraints</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=16" title="Edit section: Budget constraints"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Individuals' consumptions are constrained by their budget allowance. The graph of budget line is a linear, downward-sloping line between X and Y axes. All the bundles of consumption under the budget line allow individuals to consume without using the whole budget as the total budget is greater than the total cost of bundles (Figure 2). If only considers prices and quantities of two goods in one bundle, a budget constraint could be formulated as <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_{1}X_{1}+p_{2}X_{2}=Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{1}X_{1}+p_{2}X_{2}=Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab1c719a0039c9889fe7d0798d6ad2d9d5934661" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:18.206ex; height:2.509ex;" alt="{\displaystyle p_{1}X_{1}+p_{2}X_{2}=Y}" /></span>, where <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_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b9b58f22283ca46dd5da309cc34303b06a797783" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:2.313ex; height:2.009ex;" alt="{\displaystyle p_{1}}" /></span> and <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_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43f1b08d7d69712872e051c2b33fdfa9f5d42319" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:2.313ex; height:2.009ex;" alt="{\displaystyle p_{2}}" /></span> are prices of the two goods, <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 X_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f70b2694445a5901b24338a2e7a7e58f02a72a32" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.979ex; height:2.509ex;" alt="{\displaystyle X_{1}}" /></span> and <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 X_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ad47c14b8a092f182512e76c96638aea6e3bea1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.979ex; height:2.509ex;" alt="{\displaystyle X_{2}}" /></span> are quantities of the two goods. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:General_version_of_budget_constraint.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/General_version_of_budget_constraint.png/220px-General_version_of_budget_constraint.png" decoding="async" width="220" height="169" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/General_version_of_budget_constraint.png/330px-General_version_of_budget_constraint.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/General_version_of_budget_constraint.png/440px-General_version_of_budget_constraint.png 2x" data-file-width="1018" data-file-height="784" /></a><figcaption>Figure 2</figcaption></figure> <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 {\text{slope}}={\frac {-P(x)}{P(y)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>slope</mtext> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <mi>P</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>P</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{slope}}={\frac {-P(x)}{P(y)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d41196e8a6a2a2444942c7ce47e3aa03ecd9229" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:15.678ex; height:6.509ex;" alt="{\displaystyle {\text{slope}}={\frac {-P(x)}{P(y)}}}" /></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Constrained_utility_optimisation">Constrained utility optimisation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=17" title="Edit section: Constrained utility optimisation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Rational consumers wish to maximise their utility. However, as they have budget constraints, a change of price would affect the quantity of demand. There are two factors could explain this situation: </p> <ul><li>Purchasing power. Individuals obtain greater purchasing power when the price of a good decreases. The reduction of the price allows individuals to increase their savings so they could afford to buy other products.</li> <li>Substitution effect. If the price of good A decreases, then the good becomes relatively cheaper with respect to its substitutes. Thus, individuals would consume more of good A as the utility would increase by doing so.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Discussion_and_criticism">Discussion and criticism</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=18" title="Edit section: Discussion and criticism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Cambridge economist <a href="/wiki/Joan_Robinson" title="Joan Robinson">Joan Robinson</a> famously criticized utility for being a circular concept: "Utility is the quality in <a href="/wiki/Commodities" class="mw-redirect" title="Commodities">commodities</a> that makes individuals want to buy them, and the fact that individuals want to buy commodities shows that they have utility".<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 48">: 48 </span></sup> Robinson also stated that because the theory assumes that preferences are fixed this means that utility is not a <a href="/wiki/Testability" title="Testability">testable</a> assumption. This is so because if we observe changes of peoples' behavior in relation to a change in prices or a change in budget constraint we can never be sure to what extent the change in behavior was due to the change of price or budget constraint and how much was due to a change of preference.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Reliable_sources" title="Wikipedia:Reliable sources"><span title="The material near this tag relies on an unreliable source. A blogpost from a fringe website is not a reliable source, link to a scholarly article (June 2023)">unreliable source</span></a></i>]</sup> This criticism is similar to that of the philosopher <a href="/wiki/Hans_Albert" title="Hans Albert">Hans Albert</a> who argued that the <i><a href="/wiki/Ceteris_paribus" title="Ceteris paribus">ceteris paribus</a></i> (all else equal) conditions on which the <a href="/wiki/Marginalist" class="mw-redirect" title="Marginalist">marginalist</a> theory of demand rested rendered the theory itself a meaningless <a href="/wiki/Tautology_(language)" title="Tautology (language)">tautology</a>, incapable of being tested experimentally.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Reliable_sources" title="Wikipedia:Reliable sources"><span title="The material near this tag relies on an unreliable source. A blogpost from a fringe website is not a reliable source, link to a scholarly article (June 2023)">unreliable source</span></a></i>]</sup> In essence, a curve of demand and supply (a theoretical line of quantity of a product which would have been offered or requested for given price) is purely <a href="/wiki/Ontological" class="mw-redirect" title="Ontological">ontological</a> and could never have been demonstrated <a href="/wiki/Empirically" class="mw-redirect" title="Empirically">empirically</a><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Accuracy_dispute#Disputed_statement" title="Wikipedia:Accuracy dispute"><span title="There have been studies that see a D&S Curve, it's also what you do in Micro classes in Uni. (June 2023)">dubious</span></a> – <a href="/wiki/Talk:Utility#Dubious" title="Talk:Utility">discuss</a></i>]</sup>. </p><p>Other questions of what arguments ought to be included in a utility function are difficult to answer, yet seem necessary to understanding utility. Whether people gain utility from coherence of <a href="/wiki/Wants" class="mw-redirect" title="Wants">wants</a>, <a href="/wiki/Beliefs" class="mw-redirect" title="Beliefs">beliefs</a> or a sense of <a href="/wiki/Duty" title="Duty">duty</a> is important to understanding their behavior in the utility <a href="/wiki/Organon" title="Organon">organon</a>.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> Likewise, choosing between alternatives is itself a process of determining what to consider as alternatives, a question of choice within uncertainty.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p>An <a href="/wiki/Evolutionary_psychology" title="Evolutionary psychology">evolutionary psychology</a> theory is that utility may be better considered as due to preferences that maximized evolutionary <a href="/wiki/Fitness_(biology)" title="Fitness (biology)">fitness</a> in the ancestral environment but not necessarily in the current one.<sup id="cite_ref-AEP_17-0" class="reference"><a href="#cite_note-AEP-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Measuring_utility_functions">Measuring utility functions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=19" title="Edit section: Measuring utility functions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There are many empirical works trying to estimate the form of utility functions of agents with respect to money.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=20" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1266661725">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Emblem-money.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Emblem-money.svg/40px-Emblem-money.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Emblem-money.svg/42px-Emblem-money.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Emblem-money.svg/56px-Emblem-money.svg.png 2x" data-file-width="48" data-file-height="48" /></a></span></span><span class="portalbox-link"><a href="/wiki/Portal:Business_and_Economics" class="mw-redirect" title="Portal:Business and Economics">Business and Economics portal</a></span></li></ul> <ul><li><a href="/wiki/Happiness_economics" title="Happiness economics">Happiness economics</a></li> <li><a href="/wiki/Law_of_demand" title="Law of demand">Law of demand</a></li> <li><a href="/wiki/Marginal_utility" title="Marginal utility">Marginal utility</a></li> <li><a href="/wiki/Utility_maximization_problem" title="Utility maximization problem">Utility maximization problem</a> - a problem faced by consumers in a market: how to maximize their utility given their budget.</li> <li><a href="/wiki/Utility_assessment" title="Utility assessment">Utility assessment</a> - processes for estimating the utility functions of human subjects.</li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=21" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFDebreu1954" class="citation cs2">Debreu, Gérard (1954), "Representation of a preference ordering by a numerical function", in Thrall, Robert M.; <a href="/wiki/Clyde_H._Coombs" class="mw-redirect" title="Clyde H. 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New Delhi: Oxford Higher Education/Oxford University Press. p. 60. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780198062301" title="Special:BookSources/9780198062301"><bdi>9780198062301</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Principles+Of+Microeconomics&rft.place=New+Delhi&rft.pages=60&rft.pub=Oxford+Higher+Education%2FOxford+University+Press&rft.date=2008&rft.isbn=9780198062301&rft.aulast=Dominick&rft.aufirst=Salvatore&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFLinPeng2019" class="citation journal cs1">Lin, Chung-Cheng; Peng, Shi-Shu (2019). <a rel="nofollow" class="external text" href="https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-8454.12151">"The role of diminishing marginal utility in the ordinal and cardinal utility theories"</a>. <i>Australian Economic Papers</i>. <b>58</b> (3): <span class="nowrap">233–</span>246. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2F1467-8454.12151">10.1111/1467-8454.12151</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:159308055">159308055</a> – via Wiley Online Library.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Australian+Economic+Papers&rft.atitle=The+role+of+diminishing+marginal+utility+in+the+ordinal+and+cardinal+utility+theories&rft.volume=58&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E233-%3C%2Fspan%3E246&rft.date=2019&rft_id=info%3Adoi%2F10.1111%2F1467-8454.12151&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A159308055%23id-name%3DS2CID&rft.aulast=Lin&rft.aufirst=Chung-Cheng&rft.au=Peng%2C+Shi-Shu&rft_id=https%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2Fabs%2F10.1111%2F1467-8454.12151&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMoscati2013" class="citation journal cs1">Moscati, Ivan (2013). <a rel="nofollow" class="external text" href="https://doi.org/10.2139%2Fssrn.2296881">"How Cardinal Utility Entered Economic Analysis, 1909-1944"</a>. <i>SSRN Electronic Journal</i>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.2139%2Fssrn.2296881">10.2139/ssrn.2296881</a></span>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/10419%2F149700">10419/149700</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1556-5068">1556-5068</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:55651414">55651414</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=SSRN+Electronic+Journal&rft.atitle=How+Cardinal+Utility+Entered+Economic+Analysis%2C+1909-1944&rft.date=2013&rft_id=info%3Ahdl%2F10419%2F149700&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A55651414%23id-name%3DS2CID&rft.issn=1556-5068&rft_id=info%3Adoi%2F10.2139%2Fssrn.2296881&rft.aulast=Moscati&rft.aufirst=Ivan&rft_id=https%3A%2F%2Fdoi.org%2F10.2139%252Fssrn.2296881&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFIngersoll1987" class="citation book cs1">Ingersoll, Jonathan E. Jr. (1987). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/theoryoffinancia1987inge"><i>Theory of Financial Decision Making</i></a></span>. Totowa: Rowman and Littlefield. p. <a rel="nofollow" class="external text" href="https://archive.org/details/theoryoffinancia1987inge/page/21">21</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8476-7359-6" title="Special:BookSources/0-8476-7359-6"><bdi>0-8476-7359-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Theory+of+Financial+Decision+Making&rft.place=Totowa&rft.pages=21&rft.pub=Rowman+and+Littlefield&rft.date=1987&rft.isbn=0-8476-7359-6&rft.aulast=Ingersoll&rft.aufirst=Jonathan+E.+Jr.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ftheoryoffinancia1987inge&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></span> </li> <li id="cite_note-:1-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_9-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCastroAraujo2019" class="citation journal cs1">Castro, Luiz Carvalho; Araujo, Antônio Souza (2019). <a rel="nofollow" class="external text" href="https://journals.seagullpublications.com/ijtem/archive/f_IJ0320191627.pdf">"Marginal Utility & its Diminishing Methods"</a> <span class="cs1-format">(PDF)</span>. <i>International Journal of Tax Economics and Management</i>: <span class="nowrap">36–</span>47. <a href="/wiki/EISSN_(identifier)" class="mw-redirect" title="EISSN (identifier)">eISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2618-1118">2618-1118</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+of+Tax+Economics+and+Management&rft.atitle=Marginal+Utility+%26+its+Diminishing+Methods&rft.pages=%3Cspan+class%3D%22nowrap%22%3E36-%3C%2Fspan%3E47&rft.date=2019&rft.eissn=2618-1118&rft.aulast=Castro&rft.aufirst=Luiz+Carvalho&rft.au=Araujo%2C+Ant%C3%B4nio+Souza&rft_id=https%3A%2F%2Fjournals.seagullpublications.com%2Fijtem%2Farchive%2Ff_IJ0320191627.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBloomenthal" class="citation web cs1">Bloomenthal, Andrew. <a rel="nofollow" class="external text" href="https://www.investopedia.com/terms/m/marginalutility.asp">"Marginal Utility"</a>. <i>Investopedia</i><span class="reference-accessdate">. Retrieved <span class="nowrap">25 April</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Investopedia&rft.atitle=Marginal+Utility&rft.aulast=Bloomenthal&rft.aufirst=Andrew&rft_id=https%3A%2F%2Fwww.investopedia.com%2Fterms%2Fm%2Fmarginalutility.asp&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBerger1985" class="citation book cs1">Berger, J. O. (1985). "Utility and Loss". <i>Statistical Decision Theory and Bayesian Analysis</i> (2nd ed.). Berlin: Springer-Verlag. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/3-540-96098-8" title="Special:BookSources/3-540-96098-8"><bdi>3-540-96098-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Utility+and+Loss&rft.btitle=Statistical+Decision+Theory+and+Bayesian+Analysis&rft.place=Berlin&rft.edition=2nd&rft.pub=Springer-Verlag&rft.date=1985&rft.isbn=3-540-96098-8&rft.aulast=Berger&rft.aufirst=J.+O.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFRobinson1962" class="citation book cs1">Robinson, Joan (1962). <i>Economic Philosophy</i>. Harmondsworth, Middle-sex, UK: Penguin Books.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Economic+Philosophy&rft.place=Harmondsworth%2C+Middle-sex%2C+UK&rft.pub=Penguin+Books&rft.date=1962&rft.aulast=Robinson&rft.aufirst=Joan&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFPilkington2014" class="citation web cs1">Pilkington, Philip (17 February 2014). <a rel="nofollow" class="external text" href="https://fixingtheeconomists.wordpress.com/2014/02/17/joan-robinsons-critique-of-marginal-utility-theory/">"Joan Robinson's Critique of Marginal Utility Theory"</a>. <i>Fixing the Economists</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150713112846/https://fixingtheeconomists.wordpress.com/2014/02/17/joan-robinsons-critique-of-marginal-utility-theory/">Archived</a> from the original on 13 July 2015.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Fixing+the+Economists&rft.atitle=Joan+Robinson%27s+Critique+of+Marginal+Utility+Theory&rft.date=2014-02-17&rft.aulast=Pilkington&rft.aufirst=Philip&rft_id=https%3A%2F%2Ffixingtheeconomists.wordpress.com%2F2014%2F02%2F17%2Fjoan-robinsons-critique-of-marginal-utility-theory%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFPilkington2014" class="citation web cs1">Pilkington, Philip (27 February 2014). <a rel="nofollow" class="external text" href="https://fixingtheeconomists.wordpress.com/2014/02/27/hans-albert-expands-robinsons-critique-of-marginal-utility-theory-to-the-law-of-demand/">"utility Hans Albert Expands Robinson's Critique of Marginal Utility Theory to the Law of Demand"</a>. <i>Fixing the Economists</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150719164628/https://fixingtheeconomists.wordpress.com/2014/02/27/hans-albert-expands-robinsons-critique-of-marginal-utility-theory-to-the-law-of-demand/">Archived</a> from the original on 19 July 2015.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Fixing+the+Economists&rft.atitle=utility+Hans+Albert+Expands+Robinson%27s+Critique+of+Marginal+Utility+Theory+to+the+Law+of+Demand&rft.date=2014-02-27&rft.aulast=Pilkington&rft.aufirst=Philip&rft_id=https%3A%2F%2Ffixingtheeconomists.wordpress.com%2F2014%2F02%2F27%2Fhans-albert-expands-robinsons-critique-of-marginal-utility-theory-to-the-law-of-demand%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKlein2014" class="citation journal cs1">Klein, Daniel (May 2014). <a rel="nofollow" class="external text" href="http://econjwatch.org/file_download/826/CompleteIssueMay2014.pdf">"Professor"</a> <span class="cs1-format">(PDF)</span>. <i>Econ Journal Watch</i>. <b>11</b> (2): <span class="nowrap">97–</span>105. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20141005153234/http://econjwatch.org/file_download/826/CompleteIssueMay2014.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 5 October 2014<span class="reference-accessdate">. Retrieved <span class="nowrap">15 November</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Econ+Journal+Watch&rft.atitle=Professor&rft.volume=11&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E97-%3C%2Fspan%3E105&rft.date=2014-05&rft.aulast=Klein&rft.aufirst=Daniel&rft_id=http%3A%2F%2Feconjwatch.org%2Ffile_download%2F826%2FCompleteIssueMay2014.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBurke1932" class="citation book cs1">Burke, Kenneth (1932). <i>Towards a Better Life</i>. Berkeley, Calif: University of California Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Towards+a+Better+Life&rft.place=Berkeley%2C+Calif&rft.pub=University+of+California+Press&rft.date=1932&rft.aulast=Burke&rft.aufirst=Kenneth&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></span> </li> <li id="cite_note-AEP-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-AEP_17-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCapraRubin2011" class="citation book cs1">Capra, C. Monica; Rubin, Paul H. (2011). "The Evolutionary Psychology of Economics". <i>Applied Evolutionary Psychology</i>. Oxford University Press. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Facprof%3Aoso%2F9780199586073.003.0002">10.1093/acprof:oso/9780199586073.003.0002</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780191731358" title="Special:BookSources/9780191731358"><bdi>9780191731358</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Evolutionary+Psychology+of+Economics&rft.btitle=Applied+Evolutionary+Psychology&rft.pub=Oxford+University+Press&rft.date=2011&rft_id=info%3Adoi%2F10.1093%2Facprof%3Aoso%2F9780199586073.003.0002&rft.isbn=9780191731358&rft.aulast=Capra&rft.aufirst=C.+Monica&rft.au=Rubin%2C+Paul+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKirby,_Kris_N.2011" class="citation web cs1">Kirby, Kris N. (2011). <a rel="nofollow" class="external text" href="https://psycnet.apa.org/record/2011-03782-002">"An empirical assessment of the form of utility functions"</a>. <i>psycnet.apa.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">31 October</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=psycnet.apa.org&rft.atitle=An+empirical+assessment+of+the+form+of+utility+functions&rft.date=2011&rft.au=Kirby%2C+Kris+N.&rft_id=https%3A%2F%2Fpsycnet.apa.org%2Frecord%2F2011-03782-002&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=22" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFAnand1993" class="citation book cs1">Anand, Paul (1993). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/foundationsofrat00anan"><i>Foundations of Rational Choice Under Risk</i></a></span>. Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-19-823303-5" title="Special:BookSources/0-19-823303-5"><bdi>0-19-823303-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Foundations+of+Rational+Choice+Under+Risk&rft.pub=Oxford+University+Press&rft.date=1993&rft.isbn=0-19-823303-5&rft.aulast=Anand&rft.aufirst=Paul&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ffoundationsofrat00anan&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFFishburn1970" class="citation book cs1"><a href="/wiki/Peter_C._Fishburn" title="Peter C. Fishburn">Fishburn, Peter C.</a> (1970). <i>Utility Theory for Decision Making</i>. Huntington, NY: Robert E. Krieger. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-88275-736-9" title="Special:BookSources/0-88275-736-9"><bdi>0-88275-736-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Utility+Theory+for+Decision+Making&rft.place=Huntington%2C+NY&rft.pub=Robert+E.+Krieger&rft.date=1970&rft.isbn=0-88275-736-9&rft.aulast=Fishburn&rft.aufirst=Peter+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFGeorgescu-Roegen1936" class="citation journal cs1">Georgescu-Roegen, Nicholas (August 1936). "The Pure Theory of Consumer's Behavior". <i>Quarterly Journal of Economics</i>. <b>50</b> (4): <span class="nowrap">545–</span>593. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F1891094">10.2307/1891094</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/1891094">1891094</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Quarterly+Journal+of+Economics&rft.atitle=The+Pure+Theory+of+Consumer%27s+Behavior&rft.volume=50&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E545-%3C%2Fspan%3E593&rft.date=1936-08&rft_id=info%3Adoi%2F10.2307%2F1891094&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1891094%23id-name%3DJSTOR&rft.aulast=Georgescu-Roegen&rft.aufirst=Nicholas&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFGilboa2009" class="citation book cs1"><a href="/wiki/Itzhak_Gilboa" title="Itzhak Gilboa">Gilboa, Itzhak</a> (2009). <i>Theory of Decision under Uncertainty</i>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-74123-1" title="Special:BookSources/978-0-521-74123-1"><bdi>978-0-521-74123-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Theory+of+Decision+under+Uncertainty&rft.pub=Cambridge+University+Press&rft.date=2009&rft.isbn=978-0-521-74123-1&rft.aulast=Gilboa&rft.aufirst=Itzhak&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKreps1988" class="citation book cs1"><a href="/wiki/David_M._Kreps" title="David M. Kreps">Kreps, David M.</a> (1988). <i>Notes on the Theory of Choice</i>. Boulder, CO: West-view Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8133-7553-3" title="Special:BookSources/0-8133-7553-3"><bdi>0-8133-7553-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Notes+on+the+Theory+of+Choice&rft.place=Boulder%2C+CO&rft.pub=West-view+Press&rft.date=1988&rft.isbn=0-8133-7553-3&rft.aulast=Kreps&rft.aufirst=David+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFNash1950" class="citation journal cs1"><a href="/wiki/John_Forbes_Nash_Jr." title="John Forbes Nash Jr.">Nash, John F.</a> (1950). "The Bargaining Problem". <i><a href="/wiki/Econometrica" title="Econometrica">Econometrica</a></i>. <b>18</b> (2): <span class="nowrap">155–</span>162. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F1907266">10.2307/1907266</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/1907266">1907266</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:153422092">153422092</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Econometrica&rft.atitle=The+Bargaining+Problem&rft.volume=18&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E155-%3C%2Fspan%3E162&rft.date=1950&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A153422092%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1907266%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.2307%2F1907266&rft.aulast=Nash&rft.aufirst=John+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFNeumannMorgenstern1944" class="citation book cs1"><a href="/wiki/John_von_Neumann" title="John von Neumann">Neumann, John von</a> & <a href="/wiki/Oskar_Morgenstern" title="Oskar Morgenstern">Morgenstern, Oskar</a> (1944). <a rel="nofollow" class="external text" href="https://archive.org/details/in.ernet.dli.2015.215284"><i>Theory of Games and Economic Behavior</i></a>. Princeton University Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Theory+of+Games+and+Economic+Behavior&rft.pub=Princeton+University+Press&rft.date=1944&rft.aulast=Neumann&rft.aufirst=John+von&rft.au=Morgenstern%2C+Oskar&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fin.ernet.dli.2015.215284&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFNicholson1978" class="citation book cs1">Nicholson, Walter (1978). <i>Micro-economic Theory</i> (Second ed.). Hinsdale: Dryden Press. pp. <span class="nowrap">53–</span>87. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-03-020831-9" title="Special:BookSources/0-03-020831-9"><bdi>0-03-020831-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Micro-economic+Theory&rft.place=Hinsdale&rft.pages=%3Cspan+class%3D%22nowrap%22%3E53-%3C%2Fspan%3E87&rft.edition=Second&rft.pub=Dryden+Press&rft.date=1978&rft.isbn=0-03-020831-9&rft.aulast=Nicholson&rft.aufirst=Walter&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFPlous1993" class="citation book cs1">Plous, S. (1993). <i>The Psychology of Judgement and Decision Making</i>. McGraw-Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-07-050477-6" title="Special:BookSources/0-07-050477-6"><bdi>0-07-050477-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Psychology+of+Judgement+and+Decision+Making&rft.pub=McGraw-Hill&rft.date=1993&rft.isbn=0-07-050477-6&rft.aulast=Plous&rft.aufirst=S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AUtility" class="Z3988"></span></li> <li>Viner, Jacob (1925). "The Utility Concept in Value Theory and Its Critics". <i>Journal of Political Economy</i>. <b>33</b> (4): 369–387.</li> <li>Viner, Jacob (1925). "The Utility Concept in Value Theory and Its Critics". <i>Journal of Political Economy</i>. <b>33</b> (6): 638–659.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Utility&action=edit&section=23" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 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class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/40px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/60px-Commons-logo.svg.png 1.5x" data-file-width="1024" data-file-height="1376" /></a></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Utility_(decision_theory)" class="extiw" title="commons:Category:Utility (decision theory)">Utility (decision theory)</a></span>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="http://www.investopedia.com/terms/u/utility.asp#axzz1eGQlDNsr">Definition of Utility by Investopedia</a></li> <li><a rel="nofollow" class="external text" href="http://www2.hawaii.edu/~fuleky/anatomy/anatomy.html">Anatomy of Cobb-Douglas Type Utility Functions in 3D</a></li> <li><a rel="nofollow" class="external text" href="http://www2.hawaii.edu/~fuleky/anatomy/anatomy2.html">Anatomy of CES Type Utility Functions in 3D</a></li> <li><a rel="nofollow" class="external text" href="http://www.investopedia.com/university/economics/economics5.asp">Simpler Definition with example from Investopedia</a></li> <li><a rel="nofollow" class="external text" href="http://philpapers.org/rec/BRAMOO-2">Maximization of Originality - redefinition of classic utility</a></li> <li><a rel="nofollow" class="external text" href="http://smallbusiness.chron.com/four-types-utility-marketing-24420.html">Utility Model of Marketing</a> - <a rel="nofollow" class="external text" href="http://www.businessdictionary.com/definition/form-utility.html">Form</a>, <a rel="nofollow" class="external text" href="http://www.businessdictionary.com/definition/place-utility.html">Place</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20151112192023/http://www.businessdictionary.com/definition/place-utility.html">Archived</a> 12 November 2015 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, <a rel="nofollow" class="external text" href="http://www.businessdictionary.com/definition/time-utility.html">Time</a></li></ul> <p><a rel="nofollow" class="external text" href="https://web.archive.org/web/20151030091408/http://www.businessdictionary.com/definition/time-utility.html">Archived</a> 30 October 2015 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, <a rel="nofollow" class="external text" href="http://www.allbusiness.com/glossaries/possession-utility/4957292-1.html">Possession</a> and perhaps also <a rel="nofollow" class="external text" href="http://www.witiger.com/marketing/5utilities.htm">Task</a> </p> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output 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style="width:1%;font-weight:normal;">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Barley" title="Barley">Barley</a></li> <li><a href="/wiki/Cocoa_bean" title="Cocoa bean">Cocoa</a></li> <li><a href="/wiki/Coffee" title="Coffee">Coffee</a></li> <li><a href="/wiki/Cotton" title="Cotton">Cotton</a></li> <li><a href="/wiki/Cottonseed_oil" title="Cottonseed oil">Cottonseed oil</a></li> <li><a href="/wiki/Flaxseed" class="mw-redirect" title="Flaxseed">Flaxseed</a></li> <li><a href="/wiki/Maize" title="Maize">Maize</a></li> <li><a href="/wiki/Millet" title="Millet">Millet</a></li> <li><a href="/wiki/Orange_juice" title="Orange juice">Frozen orange juice</a></li> <li><a href="/wiki/Oat" title="Oat">Oat</a></li> <li><a href="/wiki/Olive_oil" title="Olive oil">Olive oil</a></li> <li><a href="/wiki/Palm_oil" title="Palm oil">Palm oil</a></li> <li><a href="/wiki/Peanut_oil" title="Peanut oil">Peanut oil</a></li> <li><a href="/wiki/Potato" title="Potato">Potatoes</a></li> <li><a href="/wiki/Rapeseed" title="Rapeseed">Rapeseed</a></li> <li><a href="/wiki/Rice" title="Rice">Rice</a></li> <li><a href="/wiki/Rye" title="Rye">Rye</a></li> <li><a href="/wiki/Natural_rubber" title="Natural rubber">Rubber</a></li> <li><a href="/wiki/Soybean" title="Soybean">Soybean</a></li> <li><a href="/wiki/Soybean_oil" title="Soybean oil">Soybean oil</a></li> <li><a href="/wiki/Sugar" title="Sugar">Sugar</a></li> <li><a href="/wiki/Tea" title="Tea">Tea</a></li> <li><a href="/wiki/Wheat" title="Wheat">Wheat</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Animals &<br /><a href="/wiki/Animal_product" title="Animal product">animal products</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ambergris" title="Ambergris">Ambergris</a></li> <li><a href="/wiki/Bristle" title="Bristle">Bristle</a></li> <li><a href="/wiki/Butter" title="Butter">Butter</a></li> <li><a href="/wiki/Cashmere_wool" title="Cashmere wool">Cashmere</a></li> <li><a href="/wiki/Civet_(perfumery)" title="Civet (perfumery)">Civet</a></li> <li><a href="/wiki/Feather" title="Feather">Feathers</a></li> <li><a href="/wiki/Feeder_cattle" title="Feeder cattle">Feeder cattle</a></li> <li><a href="/wiki/Lean_Hog" title="Lean Hog">Lean Hog</a></li> <li><a href="/wiki/Cattle" title="Cattle">Live cattle</a></li> <li><a href="/wiki/Goat" title="Goat">Goats</a></li> <li><a href="/wiki/Hide_(skin)" title="Hide (skin)">Hide (skin)</a></li> <li><a href="/wiki/Horse" title="Horse">Horses</a></li> <li><a href="/wiki/Ivory" title="Ivory">Ivory</a></li> <li><a href="/wiki/Lard" title="Lard">Lard</a></li> <li><a href="/wiki/Milk" title="Milk">Milk</a></li> <li><a href="/wiki/Musk" title="Musk">Musk</a></li> <li><a href="/wiki/Pet_industry" title="Pet industry">Pet industry</a></li> <li><a href="/wiki/Pork_bellies" class="mw-redirect" title="Pork bellies">Pork bellies</a> <ul><li><a href="/wiki/Pork_bellies#Futures" class="mw-redirect" title="Pork bellies">Pork belly futures</a></li></ul></li> <li><a href="/wiki/Sheep" title="Sheep">Sheep</a></li> <li><a href="/wiki/Silk" title="Silk">Silk</a></li> <li><a href="/wiki/Sponge" title="Sponge">Sponges</a></li> <li><a href="/wiki/Tallow" title="Tallow">Tallow</a></li> <li><a href="/wiki/Bone" title="Bone">Whalebone</a></li> <li><a href="/wiki/Wool" title="Wool">Wool</a></li> <li><a href="/wiki/Wool_top" title="Wool top">Wool tops</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Hard commodities</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6.5em;font-weight:normal;">Energy</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Coal" title="Coal">Coal</a></li> <li><a href="/wiki/Compressed_hydrogen" title="Compressed hydrogen">Compressed hydrogen</a></li> <li><a href="/wiki/Petroleum" title="Petroleum">Crude oil</a></li> <li><a href="/wiki/Ethanol_fuel" title="Ethanol fuel">Ethanol</a></li> <li><a href="/wiki/Heating_oil" title="Heating oil">Heating oil</a></li> <li><a href="/wiki/Natural_gas" title="Natural gas">Natural gas</a></li> <li><a href="/wiki/Propane" title="Propane">Propane</a></li> <li><a href="/wiki/Thorium" title="Thorium">Thorium</a></li> <li><a href="/wiki/Uranium" title="Uranium">Uranium</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6.5em;font-weight:normal;">Industrial metals</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aluminium" title="Aluminium">Aluminium</a></li> <li><a href="/wiki/Aluminium_alloy" title="Aluminium alloy">Aluminium alloy</a></li> <li><a href="/wiki/Cobalt" title="Cobalt">Cobalt</a></li> <li><a href="/wiki/Copper" title="Copper">Copper</a></li> <li><a href="/wiki/Lead" title="Lead">Lead</a></li> <li><a href="/wiki/Molybdenum" title="Molybdenum">Molybdenum</a></li> <li><a href="/wiki/Nickel" title="Nickel">Nickel</a></li> <li><a href="/wiki/Steel" title="Steel">Steel</a></li> <li><a href="/wiki/Tin" title="Tin">Tin</a></li> <li><a href="/wiki/Zinc" title="Zinc">Zinc</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6.5em;font-weight:normal;">Precious metals</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Gold" title="Gold">Gold</a></li> <li><a href="/wiki/Palladium" title="Palladium">Palladium</a></li> <li><a href="/wiki/Platinum" title="Platinum">Platinum</a></li> <li><a href="/wiki/Silver" title="Silver">Silver</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Organizations</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Commodity_market" title="Commodity market">Commodity market</a></li> <li><a href="/wiki/Futures_contract" title="Futures contract">Futures contract</a></li> <li><a href="/wiki/Futures_exchange" title="Futures exchange">Futures exchange</a></li> <li><a href="/wiki/List_of_commodities_exchanges" title="List of commodities exchanges">List of commodities exchanges</a></li> <li><a href="/wiki/List_of_futures_exchanges" title="List of futures exchanges">List of futures exchanges</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Laws</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Commodity_Exchange_Act" title="Commodity Exchange Act">Commodity Exchange Act</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Miscellaneous</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Commodification" title="Commodification">Commodification</a></li> <li><a href="/wiki/Commoditization" title="Commoditization">Commoditization</a></li> <li><a href="/wiki/Commodification_of_nature" title="Commodification of nature">Commodification of nature</a></li> <li><a href="/wiki/Commodification_of_water" title="Commodification of water">Commodification of water</a></li> <li><a href="/wiki/Commodity_status_of_animals" title="Commodity status of animals">Commodity status of animals</a></li> <li><a href="/wiki/Fictitious_commodities" title="Fictitious commodities">Fictitious commodities</a></li> <li><a href="/wiki/Heritage_commodification" title="Heritage commodification">Heritage commodification</a></li> <li><a href="/wiki/Value_(economics)" title="Value (economics)">Economic value</a></li> <li><a href="/wiki/Exchange_value" title="Exchange value">Exchange value</a></li> <li><a href="/wiki/Price" title="Price">Price</a></li> <li><a href="/wiki/Use_value" title="Use value">Use value</a>/<a class="mw-selflink selflink">utility</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/List_of_traded_commodities" title="List of traded commodities">List of traded commodities</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235" /></div><div role="navigation" class="navbox" aria-labelledby="Microeconomics291" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231" /><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Microeconomics" title="Template:Microeconomics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Microeconomics" title="Template talk:Microeconomics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Microeconomics" title="Special:EditPage/Template:Microeconomics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Microeconomics291" style="font-size:114%;margin:0 4em"><a href="/wiki/Microeconomics" title="Microeconomics">Microeconomics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Major topics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aggregation_problem" title="Aggregation problem">Aggregation</a></li> <li><a href="/wiki/Budget_set" title="Budget set">Budget set</a></li> <li><a href="/wiki/Consumer_choice" title="Consumer choice">Consumer choice</a></li> <li><a href="/wiki/Convexity_in_economics" title="Convexity in economics">Convexity</a> and <a href="/wiki/Non-convexity_(economics)" title="Non-convexity (economics)">non-convexity</a></li> <li><a href="/wiki/Economic_cost" title="Economic cost">Cost</a> <ul><li><a href="/wiki/Average_cost" title="Average cost">Average</a></li> <li><a href="/wiki/Marginal_cost" title="Marginal cost">Marginal</a></li> <li><a href="/wiki/Opportunity_cost" title="Opportunity cost">Opportunity</a> <ul><li><a href="/wiki/Implicit_cost" title="Implicit cost">Implicit</a></li></ul></li> <li><a href="/wiki/Social_cost" title="Social cost">Social</a></li> <li><a href="/wiki/Sunk_cost" title="Sunk cost">Sunk</a></li> <li><a href="/wiki/Transaction_cost" title="Transaction cost">Transaction</a></li></ul></li> <li><a href="/wiki/Cost%E2%80%93benefit_analysis" title="Cost–benefit analysis">Cost–benefit analysis</a></li> <li><a href="/wiki/Deadweight_loss" title="Deadweight loss">Deadweight loss</a></li> <li><a href="/wiki/Distribution_(economics)" title="Distribution (economics)">Distribution</a></li> <li><a href="/wiki/Economies_of_scale" title="Economies of scale">Economies of scale</a></li> <li><a href="/wiki/Economies_of_scope" title="Economies of scope">Economies of scope</a></li> <li><a href="/wiki/Elasticity_(economics)" title="Elasticity (economics)">Elasticity</a> <ul><li><a href="/wiki/Cross_elasticity_of_demand" title="Cross elasticity of demand">Cross elasticity of demand</a></li> <li><a href="/wiki/Income_elasticity_of_demand" title="Income elasticity of demand">Income elasticity of demand</a></li> <li><a href="/wiki/Price_elasticity_of_demand" title="Price elasticity of demand">Price elasticity of demand</a></li> <li><a href="/wiki/Price_elasticity_of_supply" title="Price elasticity of supply">Price elasticity of supply</a></li></ul></li> <li><a href="/wiki/Economic_equilibrium" title="Economic equilibrium">Equilibrium</a> <ul><li><a href="/wiki/General_equilibrium_theory" title="General equilibrium theory">General</a></li></ul></li> <li><a href="/wiki/Trade" title="Trade">Exchange</a></li> <li><a href="/wiki/Externality" title="Externality">Externality</a></li> <li><a href="/wiki/Theory_of_the_firm" title="Theory of the firm">Firms</a></li> <li><a href="/wiki/Goods_and_services" title="Goods and services">Goods and services</a> <ul><li><a href="/wiki/Goods" title="Goods">Goods</a></li> <li><a href="/wiki/Service_(economics)" title="Service (economics)">Service</a></li></ul></li> <li><a href="/wiki/Family_economics" title="Family economics">Household</a></li> <li><a href="/wiki/Income%E2%80%93consumption_curve" title="Income–consumption curve">Income–consumption curve</a></li> <li><a href="/wiki/Information_economics" title="Information economics">Information</a></li> <li><a href="/wiki/Indifference_curve" title="Indifference curve">Indifference curve</a></li> <li><a href="/wiki/Intertemporal_choice" title="Intertemporal choice">Intertemporal choice</a></li> <li><a href="/wiki/Market_(economics)" title="Market (economics)">Market</a></li> <li><a href="/wiki/Market_failure" title="Market failure">Market failure</a></li> <li><a href="/wiki/Market_structure" title="Market structure">Market structure</a> <ul><li><a href="/wiki/Competition_(economics)" title="Competition (economics)">Competition</a> <ul><li><a href="/wiki/Monopolistic_competition" title="Monopolistic competition">Monopolistic</a></li> <li><a href="/wiki/Perfect_competition" title="Perfect competition">Perfect</a></li></ul></li> <li><a href="/wiki/Duopoly" title="Duopoly">Duopoly</a></li> <li><a href="/wiki/Monopoly" title="Monopoly">Monopoly</a> <ul><li><a href="/wiki/Bilateral_monopoly" title="Bilateral monopoly">Bilateral</a></li> <li><a href="/wiki/Complementary_monopoly" title="Complementary monopoly">Complementary</a></li></ul></li> <li><a href="/wiki/Monopsony" title="Monopsony">Monopsony</a></li> <li><a href="/wiki/Oligopoly" title="Oligopoly">Oligopoly</a></li> <li><a href="/wiki/Oligopsony" title="Oligopsony">Oligopsony</a></li></ul></li> <li><a href="/wiki/Pareto_efficiency" title="Pareto efficiency">Pareto efficiency</a></li> <li><a href="/wiki/Preference_(economics)" title="Preference (economics)">Preferences</a></li> <li><a href="/wiki/Price" title="Price">Price</a> <ul><li><a href="/wiki/Price_controls" title="Price controls">Price controls</a></li> <li><a href="/wiki/Price_ceiling" title="Price ceiling">Price ceiling</a></li> <li><a href="/wiki/Price_floor" title="Price floor">Price floor</a></li> <li><a href="/wiki/Price_discrimination" title="Price discrimination">Price discrimination</a></li> <li><a href="/wiki/Price_signal" title="Price signal">Price signal</a></li> <li><a href="/wiki/Price_system" title="Price system">Price system</a>/<a href="/wiki/Free_price_system" title="Free price system">Free</a></li> <li><a href="/wiki/Pricing" title="Pricing">Pricing</a></li></ul></li> <li><a href="/wiki/Production_set" title="Production set">Production</a></li> <li><a href="/wiki/Profit_(economics)" title="Profit (economics)">Profit</a></li> <li><a href="/wiki/Public_good_(economics)" class="mw-redirect" title="Public good (economics)">Public goods</a></li> <li><a href="/wiki/Rationing" title="Rationing">Rationing</a></li> <li><a href="/wiki/Economic_rent" title="Economic rent">Rent</a></li> <li><a href="/wiki/Returns_to_scale" title="Returns to scale">Returns to scale</a></li> <li><a href="/wiki/Risk_aversion" title="Risk aversion">Risk aversion</a></li> <li><a href="/wiki/Scarcity" title="Scarcity">Scarcity</a></li> <li><a href="/wiki/Shortage" title="Shortage">Shortage</a>/<a href="/wiki/Excess_supply" title="Excess supply">Excess supply</a></li> <li><a href="/wiki/Substitution_effect" title="Substitution effect">Substitution effect</a></li> <li><a href="/wiki/Economic_surplus" title="Economic surplus">Surplus</a></li> <li><a href="/wiki/Social_choice_theory" title="Social choice theory">Social choice</a></li> <li><a href="/wiki/Supply_and_demand" title="Supply and demand">Supply and demand</a> <ul><li><a href="/wiki/Demand" title="Demand">Demand</a>/<a href="/wiki/Law_of_demand" title="Law of demand">Law of demand</a></li> <li><a href="/wiki/Supply_(economics)" title="Supply (economics)">Supply</a>/<a href="/wiki/Law_of_supply" title="Law of supply">Law of supply</a></li></ul></li> <li><a href="/wiki/Uncertainty" title="Uncertainty">Uncertainty</a></li> <li><a class="mw-selflink selflink">Utility</a> <ul><li><a href="/wiki/Expected_utility_hypothesis" title="Expected utility hypothesis">Expected</a></li> <li><a href="/wiki/Marginal_utility" title="Marginal utility">Marginal</a></li></ul></li> <li><a href="/wiki/Wage" title="Wage">Wage</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Subfields</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Behavioral_economics" title="Behavioral economics">Behavioral</a></li> <li><a href="/wiki/Business_economics" title="Business economics">Business</a></li> <li><a href="/wiki/Computational_economics" title="Computational economics">Computational</a></li> <li><a href="/wiki/Development_economics" title="Development economics">Development</a></li> <li><a href="/wiki/Statistical_decision_theory" class="mw-redirect" title="Statistical decision theory">Statistical decision theory</a></li> <li><a href="/wiki/Econometrics" title="Econometrics">Econometrics</a></li> <li><a href="/wiki/Engineering_economics" title="Engineering economics">Engineering economics</a></li> <li><a href="/wiki/Engineering_economics_(civil_engineering)" title="Engineering economics (civil engineering)">Civil engineering economics</a></li> <li><a href="/wiki/Evolutionary_economics" title="Evolutionary economics">Evolutionary</a></li> <li><a href="/wiki/Experimental_economics" title="Experimental economics">Experimental</a></li> <li><a href="/wiki/Game_theory" title="Game theory">Game theory</a></li> <li><a href="/wiki/Green_economy" title="Green economy">Green</a></li> <li><a href="/wiki/Industrial_organization" title="Industrial organization">Industrial organization</a></li> <li><a href="/wiki/Institutional_economics" title="Institutional economics">Institutional</a></li> <li><a href="/wiki/Labour_economics" title="Labour economics">Labor</a></li> <li><a href="/wiki/Law_and_economics" title="Law and economics">Law</a></li> <li><a href="/wiki/Managerial_economics" title="Managerial economics">Managerial</a></li> <li><a href="/wiki/Mathematical_economics" title="Mathematical economics">Mathematical</a></li> <li><a href="/wiki/Microfoundations" title="Microfoundations">Microfoundations of macroeconomics</a></li> <li><a href="/wiki/Operations_research" title="Operations research">Operations research</a></li> <li><a href="/wiki/Mathematical_optimization" title="Mathematical optimization">Optimization</a></li> <li><a href="/wiki/Welfare_economics" title="Welfare economics">Welfare</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">See also</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Economics" title="Economics">Economics</a> <ul><li><a href="/wiki/Applied_economics" title="Applied economics">Applied</a></li></ul></li> <li><a href="/wiki/Macroeconomics" title="Macroeconomics">Macroeconomics</a></li> <li><a href="/wiki/Political_economy" title="Political economy">Political economy</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Emblem-money.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Emblem-money.svg/20px-Emblem-money.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Emblem-money.svg/40px-Emblem-money.svg.png 1.5x" data-file-width="48" data-file-height="48" /></a></span> </span><a href="/wiki/Portal:Business" title="Portal:Business">Business portal</a></li> <li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Microeconomics" title="Category:Microeconomics">Category</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235" /><style data-mw-deduplicate="TemplateStyles:r1066933788">.mw-parser-output .excerpt-hat .mw-editsection-like{font-style:normal}</style></div><div role="navigation" class="navbox" aria-labelledby="Economics681" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231" /><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Economics" title="Template:Economics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Economics" title="Template talk:Economics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Economics" title="Special:EditPage/Template:Economics"><abbr title="Edit this 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title="Macroeconomics">Macroeconomics</a></li> <li><a href="/wiki/Mathematical_economics" title="Mathematical economics">Mathematical economics</a></li> <li><a href="/wiki/Complexity_economics" title="Complexity economics">Complexity economics</a></li> <li><a href="/wiki/Computational_economics" title="Computational economics">Computational economics</a> <ul><li><a href="/wiki/Agent-based_computational_economics" title="Agent-based computational economics">Agent-based computational economics</a></li></ul></li> <li><a href="/wiki/Behavioral_economics" title="Behavioral economics">Behavioral economics</a></li> <li><a href="/wiki/Pluralism_in_economics" title="Pluralism in economics">Pluralism in economics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Economics#Empirical_research" title="Economics">Empirical</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> 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economics">Welfare</a></li></ul></div></div> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Schools_of_economic_thought" title="Schools of economic thought">Schools</a><br />(<a href="/wiki/History_of_economic_thought" title="History of economic thought">history</a>)<br /></div></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Attention_economy" title="Attention economy">Attention</a></li> <li><a href="/wiki/Mainstream_economics" title="Mainstream economics">Mainstream</a></li> <li><a href="/wiki/Heterodox_economics" title="Heterodox economics">Heterodox</a></li> <li><a href="/wiki/American_School_(economics)" title="American School (economics)">American (National)</a></li> <li><a href="/wiki/Ancient_economic_thought" title="Ancient economic thought">Ancient thought</a></li> <li><a href="/wiki/Anarchist_economics" class="mw-redirect" title="Anarchist economics">Anarchist</a> <ul><li><a href="/wiki/Mutualism_(economic_theory)" title="Mutualism (economic theory)">Mutualism</a></li></ul></li> <li><a href="/wiki/Austrian_School" class="mw-redirect" title="Austrian School">Austrian</a></li> <li><a href="/wiki/Behavioral_economics" title="Behavioral economics">Behavioral</a></li> <li><a href="/wiki/Buddhist_economics" title="Buddhist economics">Buddhist</a></li> <li><a href="/wiki/Chartalism" title="Chartalism">Chartalism</a> <ul><li><a href="/wiki/Modern_monetary_theory" title="Modern monetary theory">Modern monetary theory</a></li></ul></li> <li><a href="/wiki/Chicago_school_of_economics" title="Chicago school of economics">Chicago</a></li> <li><a href="/wiki/Classical_economics" title="Classical economics">Classical</a></li> <li><a href="/wiki/Critique_of_political_economy" title="Critique of political economy">Critique of political economy</a></li> <li><a href="/wiki/Economic_democracy" title="Economic democracy">Democratic</a></li> <li><a href="/wiki/Disequilibrium_macroeconomics" title="Disequilibrium macroeconomics">Disequilibrium</a></li> <li><a href="/wiki/Ecological_economics" title="Ecological economics">Ecological</a></li> <li><a href="/wiki/Evolutionary_economics" title="Evolutionary economics">Evolutionary</a></li> <li><a href="/wiki/Feminist_economics" title="Feminist economics">Feminist</a></li> <li><a href="/wiki/Georgism" title="Georgism">Georgism</a></li> <li><a href="/wiki/Happiness_economics" title="Happiness economics">Happiness</a></li> <li><a href="/wiki/Historical_school_of_economics" title="Historical school of economics">Historical</a></li> <li><a href="/wiki/Humanistic_economics" title="Humanistic economics">Humanistic</a></li> <li><a href="/wiki/Institutional_economics" title="Institutional economics">Institutional</a></li> <li><a href="/wiki/Keynesian_economics" title="Keynesian economics">Keynesian</a> <ul><li><a href="/wiki/Neo-Keynesian_economics" class="mw-redirect" title="Neo-Keynesian economics">Neo-</a> (<a href="/wiki/Neoclassical_synthesis" title="Neoclassical synthesis">neoclassical–Keynesian synthesis</a>)</li> <li><a href="/wiki/New_Keynesian_economics" title="New Keynesian economics">New</a></li> <li><a href="/wiki/Post-Keynesian_economics" title="Post-Keynesian economics">Post-</a> <ul><li><a href="/wiki/Monetary_circuit_theory" title="Monetary circuit theory">Circuitism</a></li></ul></li></ul></li> <li><a href="/wiki/Malthusianism" title="Malthusianism">Malthusianism</a></li> <li><a href="/wiki/Marginalism" title="Marginalism">Marginalism</a></li> <li><a href="/wiki/Marxian_economics" title="Marxian economics">Marxian</a> <ul><li><a href="/wiki/Neo-Marxian_economics" class="mw-redirect" title="Neo-Marxian economics">Neo-</a></li></ul></li> <li><a href="/wiki/Mercantilism" title="Mercantilism">Mercantilism</a></li> <li><a href="/wiki/Mixed_economy" title="Mixed economy">Mixed</a></li> <li><a href="/wiki/Neoclassical_economics" title="Neoclassical economics">Neoclassical</a> <ul><li><a href="/wiki/Lausanne_School" title="Lausanne School">Lausanne</a></li></ul></li> <li><a href="/wiki/New_classical_macroeconomics" title="New classical macroeconomics">New classical</a> <ul><li><a href="/wiki/Real_business-cycle_theory" title="Real business-cycle theory">Real business-cycle theory</a></li></ul></li> <li><a href="/wiki/New_institutional_economics" title="New institutional economics">New institutional</a></li> <li><a href="/wiki/Physiocracy" title="Physiocracy">Physiocracy</a></li> <li><a href="/wiki/Socialist_economics" title="Socialist economics">Socialist</a></li> <li><a href="/wiki/Stockholm_School_(economics)" title="Stockholm School (economics)">Stockholm</a></li> <li><a href="/wiki/Supply-side_economics" title="Supply-side economics">Supply-side</a></li> <li><a href="/wiki/Thermoeconomics" title="Thermoeconomics">Thermo</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Economist" title="Economist">Economists</a><br /></div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bernard_de_Mandeville" class="mw-redirect" title="Bernard de Mandeville">de Mandeville</a></li> <li><a href="/wiki/Fran%C3%A7ois_Quesnay" title="François Quesnay">Quesnay</a></li> <li><a href="/wiki/Adam_Smith" title="Adam Smith">Smith</a></li> <li><a href="/wiki/Thomas_Robert_Malthus" title="Thomas Robert Malthus">Malthus</a></li> <li><a href="/wiki/Jean-Baptiste_Say" title="Jean-Baptiste Say">Say</a></li> <li><a href="/wiki/David_Ricardo" title="David Ricardo">Ricardo</a></li> <li><a href="/wiki/Johann_Heinrich_von_Th%C3%BCnen" title="Johann Heinrich von Thünen">von Thünen</a></li> <li><a href="/wiki/Friedrich_List" title="Friedrich List">List</a></li> <li><a href="/wiki/Fr%C3%A9d%C3%A9ric_Bastiat" title="Frédéric Bastiat">Bastiat</a></li> <li><a href="/wiki/Antoine_Augustin_Cournot" title="Antoine Augustin Cournot">Cournot</a></li> <li><a href="/wiki/John_Stuart_Mill" title="John Stuart Mill">Mill</a></li> <li><a href="/wiki/Hermann_Heinrich_Gossen" title="Hermann Heinrich Gossen">Gossen</a></li> <li><a href="/wiki/Karl_Marx" title="Karl Marx">Marx</a></li> <li><a href="/wiki/L%C3%A9on_Walras" title="Léon Walras">Walras</a></li> <li><a href="/wiki/William_Stanley_Jevons" title="William Stanley Jevons">Jevons</a></li> <li><a href="/wiki/Henry_George" title="Henry George">George</a></li> <li><a href="/wiki/Carl_Menger" title="Carl Menger">Menger</a></li> <li><a href="/wiki/Alfred_Marshall" title="Alfred Marshall">Marshall</a></li> <li><a href="/wiki/Francis_Ysidro_Edgeworth" title="Francis Ysidro Edgeworth">Edgeworth</a></li> <li><a href="/wiki/John_Bates_Clark" title="John Bates 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