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> <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">Herfindahl–Hirschman index</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 19 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-19" 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">19 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Herfindal_%E2%80%93_Hir%C5%9Fman_indeksi" title="Herfindal – Hirşman indeksi – Azerbaijani" lang="az" hreflang="az" data-title="Herfindal – Hirşman indeksi" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/%C3%8Dndex_de_Herfindahl" title="Índex de Herfindahl – Catalan" lang="ca" hreflang="ca" data-title="Índex de Herfindahl" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Herfindahl-Index" title="Herfindahl-Index – German" lang="de" hreflang="de" data-title="Herfindahl-Index" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Herfindahli-Hirschmani_indeks" title="Herfindahli-Hirschmani indeks – Estonian" lang="et" hreflang="et" data-title="Herfindahli-Hirschmani indeks" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/%C3%8Dndice_de_Herfindahl" title="Índice de Herfindahl – Spanish" lang="es" hreflang="es" data-title="Índice de Herfindahl" 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/Herfindahl_adierazlea" title="Herfindahl adierazlea – Basque" lang="eu" hreflang="eu" data-title="Herfindahl adierazlea" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Indice_de_Herfindahl-Hirschmann" title="Indice de Herfindahl-Hirschmann – French" lang="fr" hreflang="fr" data-title="Indice de Herfindahl-Hirschmann" 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%97%88%ED%95%80%EB%8B%AC-%ED%97%88%EC%89%AC%EB%A7%8C_%EC%A7%80%EC%88%98" title="허핀달-허쉬만 지수 – Korean" lang="ko" hreflang="ko" data-title="허핀달-허쉬만 지수" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Indice_di_concentrazione#Indice_di_concentrazione_di_Herfindahl-Hirschman" title="Indice di concentrazione – Italian" lang="it" hreflang="it" data-title="Indice di concentrazione" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%93%D7%93_%D7%94%D7%A8%D7%A4%D7%99%D7%A0%D7%93%D7%9C-%D7%94%D7%99%D7%A8%D7%A9%D7%9E%D7%9F" title="מדד הרפינדל-הירשמן – Hebrew" lang="he" hreflang="he" data-title="מדד הרפינדל-הירשמן" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Herfindahl%E2%80%93Hirschman-index" title="Herfindahl–Hirschman-index – Hungarian" lang="hu" hreflang="hu" data-title="Herfindahl–Hirschman-index" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Herfindahl-index" title="Herfindahl-index – Dutch" lang="nl" hreflang="nl" data-title="Herfindahl-index" 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/%E3%83%8F%E3%83%BC%E3%83%95%E3%82%A3%E3%83%B3%E3%83%80%E3%83%BC%E3%83%AB%E3%83%BB%E3%83%8F%E3%83%BC%E3%82%B7%E3%83%A5%E3%83%9E%E3%83%B3%E3%83%BB%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9" title="ハーフィンダール・ハーシュマン・インデックス – Japanese" lang="ja" hreflang="ja" data-title="ハーフィンダール・ハーシュマン・インデックス" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Wska%C5%BAnik_Herfindahla-Hirschmana" title="Wskaźnik Herfindahla-Hirschmana – Polish" lang="pl" hreflang="pl" data-title="Wskaźnik Herfindahla-Hirschmana" 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/%C3%8Dndice_Herfindahl" title="Índice Herfindahl – Portuguese" lang="pt" hreflang="pt" data-title="Índice Herfindahl" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%98%D0%BD%D0%B4%D0%B5%D0%BA%D1%81_%D0%A5%D0%B5%D1%80%D1%84%D0%B8%D0%BD%D0%B4%D0%B0%D0%BB%D1%8F" title="Индекс Херфиндаля – Russian" lang="ru" hreflang="ru" data-title="Индекс Херфиндаля" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Herfindahlin_indeksi" title="Herfindahlin indeksi – Finnish" lang="fi" hreflang="fi" data-title="Herfindahlin indeksi" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Herfindahl-Hirschman_endeksi" title="Herfindahl-Hirschman endeksi – Turkish" lang="tr" hreflang="tr" data-title="Herfindahl-Hirschman endeksi" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%86%D0%BD%D0%B4%D0%B5%D0%BA%D1%81_%D0%93%D0%B5%D1%80%D1%84%D1%96%D0%BD%D0%B4%D0%B0%D0%BB%D1%8F_%E2%80%94_%D0%93%D1%96%D1%80%D1%88%D0%BC%D0%B0%D0%BD%D0%B0" title="Індекс Герфіндаля — Гіршмана – Ukrainian" lang="uk" hreflang="uk" data-title="Індекс Герфіндаля — Гіршмана" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li> </ul> <div 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data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">(Redirected from <a href="/w/index.php?title=Herfindahl_index&redirect=no" class="mw-redirect" title="Herfindahl index">Herfindahl index</a>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Measure of the relative size of firms</div> <style 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 measure. For the author-level metric, see <a href="/wiki/H-index" title="H-index">H-index</a>.</div> <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 .hlist dd::after,.mw-parser-output .hlist li::after{content:" · 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.sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar nomobile nowraplinks" style="width: 18em;"><tbody><tr><th class="sidebar-title"><a href="/wiki/Competition_law" title="Competition law">Competition law</a></th></tr><tr><td class="sidebar-image"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/File:Scale_of_justice_2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Scale_of_justice_2.svg/100px-Scale_of_justice_2.svg.png" decoding="async" width="100" height="102" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Scale_of_justice_2.svg/150px-Scale_of_justice_2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Scale_of_justice_2.svg/200px-Scale_of_justice_2.svg.png 2x" data-file-width="204" data-file-height="208" /></a><figcaption></figcaption></figure></td></tr><tr><th class="sidebar-heading" style="background:#98FB98;"> Basic concepts</th></tr><tr><td class="sidebar-content" style="text-align: left"> <ul><li><a href="/wiki/History_of_competition_law" title="History of competition law">History of competition law</a></li> <li><a href="/wiki/Monopoly" title="Monopoly">Monopoly</a> and <a href="/wiki/Oligopoly" title="Oligopoly">oligopoly</a> <ul><li><a href="/wiki/Coercive_monopoly" title="Coercive monopoly">Coercive monopoly</a></li> <li><a href="/wiki/Natural_monopoly" title="Natural monopoly">Natural monopoly</a></li></ul></li> <li><a href="/wiki/Barriers_to_entry" title="Barriers to entry">Barriers to entry</a></li> <li><a class="mw-selflink selflink">Herfindahl–Hirschman index</a></li> <li><a href="/wiki/Market_concentration" title="Market concentration">Market concentration</a></li> <li><a href="/wiki/Market_power" title="Market power">Market power</a></li> <li><a href="/wiki/Small_but_significant_and_non-transitory_increase_in_price" title="Small but significant and non-transitory increase in price">SSNIP test</a></li> <li><a href="/wiki/Relevant_market" title="Relevant market">Relevant market</a></li> <li><a href="/wiki/Merger_control" title="Merger control">Merger control</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#98FB98;"> <a href="/wiki/Anti-competitive_practices" title="Anti-competitive practices">Anti-competitive practices</a></th></tr><tr><td class="sidebar-content" style="text-align: left"> <ul><li><a href="/wiki/Monopolization" title="Monopolization">Monopolization</a></li> <li><a href="/wiki/Collusion" title="Collusion">Collusion</a> <ul><li>Formation of <a href="/wiki/Cartel" title="Cartel">cartels</a></li> <li><a href="/wiki/Price_fixing" title="Price fixing">Price fixing</a> (<a href="/wiki/Price_fixing_cases" class="mw-redirect" title="Price fixing cases">cases</a>)</li> <li><a href="/wiki/Bid_rigging" title="Bid rigging">Bid rigging</a></li> <li><a href="/wiki/Tacit_collusion" title="Tacit collusion">Tacit collusion</a></li> <li><a href="/wiki/Occupational_licensing" title="Occupational licensing">Occupational licensing</a></li></ul></li> <li><a href="/wiki/Product_bundling" title="Product bundling">Product bundling</a> and <a href="/wiki/Tying_(commerce)" title="Tying (commerce)">tying</a></li> <li><a href="/wiki/Refusal_to_deal" title="Refusal to deal">Refusal to deal</a> <ul><li><a href="/wiki/Group_boycott" title="Group boycott">Group boycott</a></li> <li><a href="/wiki/Essential_facilities_doctrine" title="Essential facilities doctrine">Essential facilities</a></li></ul></li> <li><a href="/wiki/Exclusive_dealing" title="Exclusive dealing">Exclusive dealing</a></li> <li><a href="/wiki/Dividing_territories" title="Dividing territories">Dividing territories</a></li> <li><a href="/wiki/Occupational_closure" title="Occupational closure">Occupational closure</a></li> <li><a href="/wiki/Predatory_pricing" title="Predatory pricing">Predatory pricing</a></li> <li><a href="/wiki/Patent_misuse" title="Patent misuse">Misuse of patents</a> and <a href="/wiki/Copyright_misuse" title="Copyright misuse">copyrights</a></li> <li><a href="/wiki/Regulatory_capture" title="Regulatory capture">Regulatory capture</a></li> <li><a href="/wiki/Rent-seeking" title="Rent-seeking">Rent-seeking</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#98FB98;"> Enforcement authorities and organizations</th></tr><tr><td class="sidebar-content" style="text-align: left"> <ul><li><a href="/wiki/International_Competition_Network" title="International Competition Network">International Competition Network</a></li> <li><a href="/wiki/Competition_regulator" title="Competition regulator">List of competition regulators</a></li></ul></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:Competition_law" title="Template:Competition law"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Competition_law" title="Template talk:Competition law"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Competition_law" title="Special:EditPage/Template:Competition law"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>The <b>Herfindahl index</b> (also known as <b>Herfindahl–Hirschman Index</b>, <b>HHI</b>, or sometimes <b>HHI-score</b>) is a measure of the size of <a href="/wiki/Corporation" title="Corporation">firms</a> in relation to the <a href="/wiki/Industry_(economics)" title="Industry (economics)">industry</a> they are in and is an indicator of the amount of competition among them. Named after economists <a href="/wiki/Orris_C._Herfindahl" title="Orris C. Herfindahl">Orris C. Herfindahl</a> and <a href="/wiki/Albert_O._Hirschman" title="Albert O. Hirschman">Albert O. Hirschman</a>, it is an <a href="/wiki/Economics" title="Economics">economic</a> concept widely applied in <a href="/wiki/Competition_law" title="Competition law">competition law</a>, <a href="/wiki/Antitrust" class="mw-redirect" title="Antitrust">antitrust</a> regulation,<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> and technology management.<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> HHI has continued to be used by antitrust authorities, primarily to evaluate and understand how mergers will affect their associated markets.<sup id="cite_ref-:0_3-0" class="reference"><a href="#cite_note-:0-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> HHI is calculated by squaring the market share of each competing firm in the industry and then summing the resulting numbers<sup id="cite_ref-dojhhi_4-0" class="reference"><a href="#cite_note-dojhhi-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> (sometimes limited to the 50 largest firms<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><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>). The result is proportional to the average market share, weighted by market share. As such, it can range from 0 to 1.0, moving from a huge number of very small firms to a single <a href="/wiki/Monopoly" title="Monopoly">monopolistic</a> producer. Increases in the HHI generally indicate a decrease in competition and an increase of <a href="/wiki/Market_power" title="Market power">market power</a>, whereas decreases indicate the opposite. Alternatively, the index can be expressed per 10,000 "<a href="/wiki/Basis_point" title="Basis point">points</a>". For example, an index of .25 is the same as 2,500 points. </p><p>The major benefit of the Herfindahl index in relation to measures such as the <a href="/wiki/Concentration_ratio" title="Concentration ratio">concentration ratio</a> is that the HHI gives more weight to larger firms. Other advantages of the HHI include its simple calculation method and the small amount of often easily obtainable data required for the calculation.<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>The HHI has the same formula as the <a href="/wiki/Simpson_diversity_index" class="mw-redirect" title="Simpson diversity index">Simpson diversity index</a>, which is a <a href="/wiki/Diversity_index" title="Diversity index">diversity index</a> used in ecology; the <a href="/wiki/Purity_(quantum_mechanics)#Inverse_Participation_Ratio_(IPR)" title="Purity (quantum mechanics)">inverse participation ratio (IPR)</a> in physics; and the inverse of the <a href="/wiki/Effective_number_of_parties" title="Effective number of parties">effective number of parties</a> index in political science. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Example">Example</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Herfindahl%E2%80%93Hirschman_index&action=edit&section=1" title="Edit section: Example"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Consider an example of 3 firms before and after a merger, with the top 2 firms producing 40% of goods each, and the other firm producing 20%. </p><p><b>Prior to Merger:</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 0.4^{2}+0.4^{2}+0.2^{2}=0.36=36\%}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>0.4</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mn>0.4</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mn>0.2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>0.36</mn> <mo>=</mo> <mn>36</mn> <mi mathvariant="normal">%</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0.4^{2}+0.4^{2}+0.2^{2}=0.36=36\%}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9821b468c5915fdee6885d2f311b61c1dd6bd669" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:32.351ex; height:2.843ex;" alt="{\displaystyle 0.4^{2}+0.4^{2}+0.2^{2}=0.36=36\%}"></span><sup id="cite_ref-:1_8-0" class="reference"><a href="#cite_note-:1-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>Now let's consider the top 2 firms merging. </p><p><b>Post Merger:</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 (0.4+0.4)^{2}+0.2^{2}=0.68=68\%}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>0.4</mn> <mo>+</mo> <mn>0.4</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mn>0.2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>0.68</mn> <mo>=</mo> <mn>68</mn> <mi mathvariant="normal">%</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (0.4+0.4)^{2}+0.2^{2}=0.68=68\%}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ae10c61bef82dfbbbc02c4953f5a5c541aa84e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:33.106ex; height:3.176ex;" alt="{\displaystyle (0.4+0.4)^{2}+0.2^{2}=0.68=68\%}"></span><sup id="cite_ref-:1_8-1" class="reference"><a href="#cite_note-:1-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>As can be seen prior to the merger, the HHI, while not low, is in a range that allows for strong competition. However, post merger the HHI reaches 68%, approaching a HHI consistent with monopolies. This high HHI would lead to weak competition.<sup id="cite_ref-:1_8-2" class="reference"><a href="#cite_note-:1-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>This demonstrates how the HHI enables antitrust authorities to understand the impact that mergers have on the market.<sup id="cite_ref-:0_3-1" class="reference"><a href="#cite_note-:0-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>The index involves taking the market share of the respective market competitors, squaring it, and adding them together (e.g. in the market for X, company A has 30%, B, C, D, E and F have 10% each and G through to Z have 1% each). When calculating HHI the post merger level of the HHI score and the total increase of the HHI score are considered when reviewing the outcome. If the resulting figure is above a certain threshold then economists will consider the market to have a high concentration (e.g. market X's concentration is 0.142 or 14.2%). This threshold is considered to be 0.25 in the U.S.,<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> while the EU prefers to focus on the level of change, for instance that concern is raised if there is a 0.025 change when the index already shows a concentration of 0.1.<sup id="cite_ref-dojguidelines_10-0" class="reference"><a href="#cite_note-dojguidelines-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> So to take the example, if in market X company B (with 10% market share) suddenly bought out the shares of company C (with 10% also) then this new <a href="/wiki/Market_concentration" title="Market concentration">market concentration</a> would make the index jump to 0.162. Here it can be seen that it would not be relevant for merger law in the U.S. (being under 0.18) or in the EU (because there is not a change over 0.025). </p> <div class="mw-heading mw-heading2"><h2 id="Formula">Formula</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Herfindahl%E2%80%93Hirschman_index&action=edit&section=2" title="Edit section: Formula"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle HHI=\sum _{i=1}^{N}(MS_{i})^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mi>H</mi> <mi>I</mi> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <mo stretchy="false">(</mo> <mi>M</mi> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle HHI=\sum _{i=1}^{N}(MS_{i})^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5198a3d96af3da9ab1cf44409dc649b1efc9eee" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:19.283ex; height:7.343ex;" alt="{\displaystyle HHI=\sum _{i=1}^{N}(MS_{i})^{2}}"></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="{\textstyle MS_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>M</mi> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle MS_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba0a94e7e5f34f95bdb6229b167c61e6862fc17c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.667ex; height:2.509ex;" alt="{\textstyle MS_{i}}"></span> is the market share of firm <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 i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> in the market, 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 the number of firms.<sup id="cite_ref-:1_8-3" class="reference"><a href="#cite_note-:1-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Therefore, in a market with 5 firms each producing 20%, the HHI would be <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 0.2^{2}+0.2^{2}+0.2^{2}+0.2^{2}+0.2^{2}=0.20}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>0.2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mn>0.2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mn>0.2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mn>0.2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mn>0.2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>0.20</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0.2^{2}+0.2^{2}+0.2^{2}+0.2^{2}+0.2^{2}=0.20}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8384caea699b41e57709b07d93a87252a9a109c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:38.724ex; height:2.843ex;" alt="{\displaystyle 0.2^{2}+0.2^{2}+0.2^{2}+0.2^{2}+0.2^{2}=0.20}"></span>. </p><p>The Herfindahl Index (<i>HHI</i>) ranges from 1/<i>N</i> (in case of <a href="/wiki/Perfect_competition" title="Perfect competition">perfect competition</a>) to 1 (in case of <a href="/wiki/Monopoly" title="Monopoly">monopoly</a>), where <i>N</i> is the number of firms in the market. Equivalently, if percents are used as whole numbers, as in 75 instead of 0.75, the index can range up to 100<sup>2</sup>, or 10,000. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Herfindahls_index.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Herfindahls_index.jpg/220px-Herfindahls_index.jpg" decoding="async" width="220" height="62" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Herfindahls_index.jpg/330px-Herfindahls_index.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Herfindahls_index.jpg/440px-Herfindahls_index.jpg 2x" data-file-width="1335" data-file-height="378" /></a><figcaption>Herfindahl-Hirschman Index</figcaption></figure> <p><b>An <i>HHI</i> below 0.01 (or 100)</b> indicates a highly competitive industry, Mergers and acquisitions with an increase of 100 points or less will usually not have any anti competitive effects and will require no further analysis.<sup id="cite_ref-dojguidelines_10-1" class="reference"><a href="#cite_note-dojguidelines-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> <br /><b>An <i>HHI</i> below 0.15 (or 1,500)</b> indicates an unconcentrated industry. Mergers and acquisitions between 100 and 1500 points are unlikely to have anti-competitive effects and will most likely not need further analysis.<sup id="cite_ref-dojguidelines_10-2" class="reference"><a href="#cite_note-dojguidelines-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><br /><b>An <i>HHI</i> between 0.15 and 0.25 (or 1,500 to 2,500)</b> indicates moderate concentration. Mergers and acquisitions that result in moderate market concentration from HHI increases will raise anti-competitive concerns and will require further analysis.<sup id="cite_ref-dojguidelines_10-3" class="reference"><a href="#cite_note-dojguidelines-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><br /><b>An <i>HHI</i> above 0.25 (above 2,500)</b> indicates high concentration.<sup id="cite_ref-dojguidelines_10-4" class="reference"><a href="#cite_note-dojguidelines-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Mergers and acquisitions with HHI scores of 2,500 or above will be considered anti competitive and an in-depth analysis produced, if the scores are well above 2,500 they are considered to enhance market power they may only be allowed to progress when significant evidence is shown that the merger or acquisition will not increase market power.<sup id="cite_ref-dojguidelines_10-5" class="reference"><a href="#cite_note-dojguidelines-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>A small index indicates a competitive industry with no dominant players. If all firms have an equal share the reciprocal of the index shows the number of firms in the industry. When firms have unequal shares, the reciprocal of the index indicates the "equivalent" number of firms in the industry. Using case 2, we find that the <a href="/wiki/Market_structure" title="Market structure">market structure</a> is equivalent to having 1.55521 firms of the same size. </p><p>There is also a normalized Herfindahl index. Whereas the Herfindahl index ranges from 1/<i>N</i> to one, the normalized Herfindahl index ranges from 0 to 1. It is computed as: </p> <ul><li><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="{\textstyle HHI^{*}={\cfrac {\left(HHI-{\dfrac {1}{N}}\right)}{1-{\dfrac {1}{N}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>H</mi> <mi>H</mi> <msup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow> <mi>H</mi> <mi>H</mi> <mi>I</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> </mstyle> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> </mstyle> </mrow> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle HHI^{*}={\cfrac {\left(HHI-{\dfrac {1}{N}}\right)}{1-{\dfrac {1}{N}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e2ff023a7d7ea6ea8b24cfbdab52e9d84da56df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.838ex; width:24.793ex; height:11.676ex;" alt="{\textstyle HHI^{*}={\cfrac {\left(HHI-{\dfrac {1}{N}}\right)}{1-{\dfrac {1}{N}}}}}"></span> for <i>N</i> > 1 and</li> <li><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 HHI^{*}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mi>H</mi> <msup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle HHI^{*}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90bb0ab3779e42b3e466ac4b30d668b05ef4b40f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.659ex; height:2.343ex;" alt="{\displaystyle HHI^{*}=1}"></span> for <i>N</i> = 1</li></ul> <p>where again, <i>N</i> is the number of firms in the market, and <i>HHI</i> is the usual Herfindahl Index, as above. </p><p>Using the normalized Herfindahl index, information about the total number of players (<i>N</i>) is lost, as shown in the following example: </p><p>Assume a market with two players and equally distributed market share; <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="{\textstyle H={\dfrac {1}{N}}={\dfrac {1}{2}}=0.5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>H</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> </mstyle> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo>=</mo> <mn>0.5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle H={\dfrac {1}{N}}={\dfrac {1}{2}}=0.5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fea7310e8708a673673e206bbef693e64b68fe29" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.229ex; height:5.176ex;" alt="{\textstyle H={\dfrac {1}{N}}={\dfrac {1}{2}}=0.5}"></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 H^{*}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H^{*}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d347d6f4c18885adb0004f44b459138689c2f0a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.419ex; height:2.343ex;" alt="{\displaystyle H^{*}=0}"></span>. Now compare that to a situation with three players and again an equally distributed market share; <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 H={\dfrac {1}{N}}={\frac {1}{3}}\approx 0.{\overline {333}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> </mstyle> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> <mo>≈</mo> <mn>0.</mn> <mrow class="MJX-TeXAtom-ORD"> <mover> <mn>333</mn> <mo accent="false">¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H={\dfrac {1}{N}}={\frac {1}{3}}\approx 0.{\overline {333}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/591644867693805c55838f495a231d208e04ce81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:21.669ex; height:5.176ex;" alt="{\displaystyle H={\dfrac {1}{N}}={\frac {1}{3}}\approx 0.{\overline {333}}}"></span>, note 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 H^{*}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H^{*}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d347d6f4c18885adb0004f44b459138689c2f0a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.419ex; height:2.343ex;" alt="{\displaystyle H^{*}=0}"></span> like the situation with two players. The market with three players is less concentrated, but this is not obvious looking at just <i>H*</i>. Thus, the normalized Herfindahl index can serve as a measure for the equality of distributions, but is less suitable for concentration. </p> <div class="mw-heading mw-heading2"><h2 id="Problems">Problems</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Herfindahl%E2%80%93Hirschman_index&action=edit&section=3" title="Edit section: Problems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The usefulness of this statistic to detect monopoly formation is directly dependent on a proper definition of a particular market (which hinges primarily on the notion of substitutability). The index fails to take into consideration the complex nature of the market being tested.<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> <ul><li>For example, if the statistic were to look at a hypothetical financial services industry as a whole, and found that it contained 6 main firms with 15% market share apiece, then the industry would look non-monopolistic. However, suppose one of those firms handles 90% of the checking and savings accounts and physical branches (and overcharges for them because of its monopoly), and the others primarily do commercial banking and investments. In this scenario, the index hints at <a href="/wiki/Dominance_(economics)" class="mw-redirect" title="Dominance (economics)">dominance</a> by one firm. The market is not properly defined because checking accounts are not substitutable with commercial and investment banking. The problems of defining a market work the other way as well. To take another example, one cinema may have 90% of the movie market, but if movie theaters compete against video stores, pubs and nightclubs then people are less likely to be suffering due to market dominance.</li> <li>Another typical problem in defining the market is choosing a geographic scope. For example, firms may have 20% market share each, but may occupy five areas of the country in which they are monopoly providers and thus do not compete against each other. A service provider or manufacturer in one city is not necessarily substitutable with a service provider or manufacturer in another city, depending on the importance of being local for the business—for example, telemarketing services are rather global in scope, while shoe repair services are local.</li></ul> <p>The United States federal anti-trust authorities such as the <a href="/wiki/United_States_Department_of_Justice" title="United States Department of Justice">Department of Justice</a> and the <a href="/wiki/Federal_Trade_Commission" title="Federal Trade Commission">Federal Trade Commission</a> use the Herfindahl index as a screening tool to determine whether a proposed merger or acquisition is likely to raise antitrust concerns. Increases of over 0.01 (100) generally provoke scrutiny, although this varies from case to case. The <a href="/wiki/United_States_Department_of_Justice_Antitrust_Division" title="United States Department of Justice Antitrust Division">Antitrust Division</a> of the Department of Justice considers Herfindahl indices between 0.15 (1,500) and 0.25 (2,500) to be "moderately concentrated" and indices above 0.25 to be "highly concentrated".<sup id="cite_ref-dojhhi_4-1" class="reference"><a href="#cite_note-dojhhi-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> However, these indices scores are not rigid guidelines that must be followed, while high levels of concentration is concerning, they indices scores provide ways to identify which mergers and acquisitions are potentially noncompetitive. There are other factors that need to be considered that will either help reinforce or counter the harmful effects of higher market concentration. The Herfindahl-Hirschman index is used as a starting point to gauge initial market power and then determine if additional information is needed to conduct further analysis on any potential anti-competitive concerns.<sup id="cite_ref-dojguidelines_10-6" class="reference"><a href="#cite_note-dojguidelines-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Intuition">Intuition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Herfindahl%E2%80%93Hirschman_index&action=edit&section=4" title="Edit section: Intuition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When all the firms in an industry have equal market shares, <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="{\textstyle H=N\left({\dfrac {1}{N}}\right)^{2}={\dfrac {1}{N}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>H</mi> <mo>=</mo> <mi>N</mi> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> </mstyle> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle H=N\left({\dfrac {1}{N}}\right)^{2}={\dfrac {1}{N}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d22873ad819ab62b4c5350384955484c4628cc74" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:20.599ex; height:6.509ex;" alt="{\textstyle H=N\left({\dfrac {1}{N}}\right)^{2}={\dfrac {1}{N}}}"></span>. The Herfindahl is correlated with the number of firms in an industry because its lower bound when there are <i>N</i> firms is 1/<i>N</i>. In the more general case of unequal market share, 1/<i>H</i> is called "equivalent (or effective) number of firms in the industry", <i>N</i><sub>eqi</sub> or <i>N</i><sub>eff</sub>.<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 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 id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> An industry with 3 firms cannot have a lower Herfindahl than an industry with 20 firms when firms have equal market shares. But as market shares of the 20-firm industry diverge from equality the Herfindahl can exceed that of the equal-market-share 3-firm industry (e.g., if one firm has 81% of the market and the remaining 19 have 1% each, 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 H=0.658}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mo>=</mo> <mn>0.658</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H=0.658}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b6d5616a728aabe070a8adc7fc5d16482fff2527" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.459ex; height:2.176ex;" alt="{\displaystyle H=0.658}"></span>). A higher Herfindahl signifies a less competitive (i.e., more concentrated) industry. </p> <div class="mw-heading mw-heading3"><h3 id="Appearance_in_market_structure">Appearance in market structure</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Herfindahl%E2%80%93Hirschman_index&action=edit&section=5" title="Edit section: Appearance in market structure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>It can be shown that the Herfindahl index arises as a natural consequence of assuming that a given market's structure is described by <a href="/wiki/Cournot_competition" title="Cournot competition">Cournot competition</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> Suppose that we have a Cournot model for competition between <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> firms with different linear marginal costs and a homogeneous product. Then the profit of the <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 i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span>-th firm <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 \pi _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51bb06f24c5ba78c53df3a04cb60ba05ef6f08aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.125ex; height:2.009ex;" alt="{\displaystyle \pi _{i}}"></span> is: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi _{i}=P(Q)q_{i}-c_{i}q_{i},\quad Q=\sum _{i=1}^{n}q_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mi>P</mi> <mo stretchy="false">(</mo> <mi>Q</mi> <mo stretchy="false">)</mo> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> <mspace width="1em" /> <mi>Q</mi> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi _{i}=P(Q)q_{i}-c_{i}q_{i},\quad Q=\sum _{i=1}^{n}q_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f35f5b8de268bdf0893b70601003d7d55342f3f" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:32.809ex; height:6.843ex;" alt="{\displaystyle \pi _{i}=P(Q)q_{i}-c_{i}q_{i},\quad Q=\sum _{i=1}^{n}q_{i}}"></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 q_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2752dcbff884354069fe332b8e51eb0a70a531b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.837ex; height:2.009ex;" alt="{\displaystyle q_{i}}"></span> is the quantity produced by each firm, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01acb7953ba52c2aa44264b5d0f8fd223aa178a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.807ex; height:2.009ex;" alt="{\displaystyle c_{i}}"></span> is the <a href="/wiki/Marginal_cost" title="Marginal cost">marginal cost</a> of production for each firm, 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(Q)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo stretchy="false">(</mo> <mi>Q</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P(Q)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9ce6f2bcd64e0ca3b45dd73cec6cd918f5db4dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.393ex; height:2.843ex;" alt="{\displaystyle P(Q)}"></span> is the price of the product. Taking the derivative of the firm's profit function with respect to its output to maximize its profit gives us: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\partial \pi _{i}}{\partial q_{i}}}=0\implies P'(Q)q_{i}+P(Q)-c_{i}=0\implies -{\frac {dP}{dQ}}q_{i}=P-c_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mspace width="thickmathspace" /> <mo stretchy="false">⟹</mo> <mspace width="thickmathspace" /> <msup> <mi>P</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>Q</mi> <mo stretchy="false">)</mo> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>+</mo> <mi>P</mi> <mo stretchy="false">(</mo> <mi>Q</mi> <mo stretchy="false">)</mo> <mo>−</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mspace width="thickmathspace" /> <mo stretchy="false">⟹</mo> <mspace width="thickmathspace" /> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>P</mi> </mrow> <mrow> <mi>d</mi> <mi>Q</mi> </mrow> </mfrac> </mrow> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mi>P</mi> <mo>−</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial \pi _{i}}{\partial q_{i}}}=0\implies P'(Q)q_{i}+P(Q)-c_{i}=0\implies -{\frac {dP}{dQ}}q_{i}=P-c_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87922d70bc1ad8b6126fa23a09e3024fc3e52fe8" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:63.47ex; height:5.843ex;" alt="{\displaystyle {\frac {\partial \pi _{i}}{\partial q_{i}}}=0\implies P'(Q)q_{i}+P(Q)-c_{i}=0\implies -{\frac {dP}{dQ}}q_{i}=P-c_{i}}"></span> Dividing by <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/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> gives us each firm's <a href="/wiki/Profit_margin" title="Profit margin">profit margin</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {P-c_{i} \over {P}}=-{dP \over {dQ}}{q_{i} \over {P}}=-{dP/P \over {dQ/Q}}{q_{i} \over {Q}}={s_{i} \over {\eta }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>P</mi> <mo>−</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>P</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> <mi>Q</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>P</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>Q</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi>Q</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi>η</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {P-c_{i} \over {P}}=-{dP \over {dQ}}{q_{i} \over {P}}=-{dP/P \over {dQ/Q}}{q_{i} \over {Q}}={s_{i} \over {\eta }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32721d672052e2905a6c6ae614d1272eaa51b525" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:38.995ex; height:6.509ex;" alt="{\displaystyle {P-c_{i} \over {P}}=-{dP \over {dQ}}{q_{i} \over {P}}=-{dP/P \over {dQ/Q}}{q_{i} \over {Q}}={s_{i} \over {\eta }}}"></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 s_{i}=q_{i}/Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s_{i}=q_{i}/Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4bff8f6542bcac6313845be4a6aece356d183680" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.826ex; height:2.843ex;" alt="{\displaystyle s_{i}=q_{i}/Q}"></span> is the market share 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 \eta =-d\log Q/d\log P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>η</mi> <mo>=</mo> <mo>−</mo> <mi>d</mi> <mi>log</mi> <mo>⁡</mo> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> <mi>log</mi> <mo>⁡</mo> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \eta =-d\log Q/d\log P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c4a8ab5cd75122bd8201ba7be188da87ada496b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.746ex; height:2.843ex;" alt="{\displaystyle \eta =-d\log Q/d\log P}"></span> is the <a href="/wiki/Price_elasticity_of_demand" title="Price elasticity of demand">price elasticity of demand</a>. Multiplying each firm's profit margin by its market share gives us: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s_{1}\left({P-c_{1} \over {P}}\right)+\cdots +s_{n}\left({P-c_{n} \over {P}}\right)={H \over {\eta }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>P</mi> <mo>−</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>P</mi> <mo>−</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>η</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s_{1}\left({P-c_{1} \over {P}}\right)+\cdots +s_{n}\left({P-c_{n} \over {P}}\right)={H \over {\eta }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5249d9aefc95e2296cb285520d5c60bc63a2ba4" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:41.603ex; height:6.176ex;" alt="{\displaystyle s_{1}\left({P-c_{1} \over {P}}\right)+\cdots +s_{n}\left({P-c_{n} \over {P}}\right)={H \over {\eta }}}"></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 H}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75a9edddcca2f782014371f75dca39d7e13a9c1b" 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 H}"></span> is the Herfindahl index. Therefore, the Herfindahl index is directly related to the weighted average of the profit margins of firms under Cournot competition with linear marginal costs. </p> <div class="mw-heading mw-heading3"><h3 id="Effective_assets_in_a_portfolio">Effective assets in a portfolio</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Herfindahl%E2%80%93Hirschman_index&action=edit&section=6" title="Edit section: Effective assets in a portfolio"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Herfindahl index is also a widely used metric for <a href="/wiki/Portfolio_(finance)" title="Portfolio (finance)">portfolio</a> concentration.<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> In portfolio theory, the Herfindahl index is related to the effective number of positions <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_{\text{eff}}=1/H}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>eff</mtext> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{\text{eff}}=1/H}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e66845adebe78f8348eb57433cc99618cf45fb2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.322ex; height:2.843ex;" alt="{\displaystyle N_{\text{eff}}=1/H}"></span><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> held in a portfolio, 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="{\textstyle H=\sum \|w\|^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>H</mi> <mo>=</mo> <mo>∑</mo> <mo fence="false" stretchy="false">‖</mo> <mi>w</mi> <msup> <mo fence="false" stretchy="false">‖</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle H=\sum \|w\|^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/951d441925625effbef7b0d9a38ce8abc4b5b18c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.046ex; height:3.009ex;" alt="{\textstyle H=\sum \|w\|^{2}}"></span> is computed as the sum of the squares of the proportion of market value invested in each security. A low H-index implies a very diversified portfolio: as an example, a portfolio with <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 H=0.02}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mo>=</mo> <mn>0.02</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H=0.02}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8185aab61d9768985263507ed0f08429f10c33a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.296ex; height:2.176ex;" alt="{\displaystyle H=0.02}"></span> is equivalent to a portfolio with <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_{\text{eff}}=50}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>eff</mtext> </mrow> </msub> <mo>=</mo> <mn>50</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{\text{eff}}=50}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f9b7bf56aeead462c748818b33fedcdceafa2fe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.259ex; height:2.509ex;" alt="{\displaystyle N_{\text{eff}}=50}"></span> equally weighted positions. The H-index has been shown to be one of the most efficient measures of portfolio diversification.<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><p>It may also be used as a <a href="/wiki/Constraint_(mathematics)" title="Constraint (mathematics)">constraint</a> to force a portfolio to hold a minimum number of effective assets: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \|w\|^{2}\leq N_{\text{eff}}^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">‖</mo> <mi>w</mi> <msup> <mo fence="false" stretchy="false">‖</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>≤</mo> <msubsup> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>eff</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \|w\|^{2}\leq N_{\text{eff}}^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc4d9f66d2abee0d2afb0b181c7ca3bf0b277db6" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:12.597ex; height:3.343ex;" alt="{\displaystyle \|w\|^{2}\leq N_{\text{eff}}^{-1}}"></span> For commonly used <a href="/wiki/Portfolio_optimization" title="Portfolio optimization">portfolio optimization</a> techniques, such as <a href="/wiki/Modern_portfolio_theory" title="Modern portfolio theory">mean-variance</a> and <a href="/wiki/Expected_shortfall" title="Expected shortfall">CVaR</a>, the optimal solution may be found using <a href="/wiki/Second-order_cone_programming" title="Second-order cone programming">second-order cone programming</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Decomposition">Decomposition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Herfindahl%E2%80%93Hirschman_index&action=edit&section=7" title="Edit section: Decomposition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Supposing 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 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> firms share all the market, each one with a participation 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 x_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e87000dd6142b81d041896a30fe58f0c3acb2158" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.129ex; height:2.009ex;" alt="{\displaystyle x_{i}}"></span> and market share <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="{\textstyle s_{i}=x_{i}/\sum _{j=1}^{N}x_{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle s_{i}=x_{i}/\sum _{j=1}^{N}x_{j}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/914fdca5bf241dfe91388ecb89d2b7d9038fd926" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:16.758ex; height:3.843ex;" alt="{\textstyle s_{i}=x_{i}/\sum _{j=1}^{N}x_{j}}"></span>, then the index can be expressed 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="{\textstyle H={\frac {1}{N}}+(N-1)\sigma ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>H</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> </mrow> <mo>+</mo> <mo stretchy="false">(</mo> <mi>N</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle H={\frac {1}{N}}+(N-1)\sigma ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/25de9f88b32976119f80a414ffb14b9861196a11" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:20.558ex; height:3.509ex;" alt="{\textstyle H={\frac {1}{N}}+(N-1)\sigma ^{2}}"></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 \sigma ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53a5c55e536acf250c1d3e0f754be5692b843ef5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.385ex; height:2.676ex;" alt="{\displaystyle \sigma ^{2}}"></span> is the <a href="/wiki/Variance" title="Variance">statistical variance</a> of the firm shares, defined 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="{\textstyle \sigma ^{2}={\frac {1}{N-1}}\sum _{i=1}^{N}\left(s_{i}-\mu \right)^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>N</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>−</mo> <mi>μ</mi> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \sigma ^{2}={\frac {1}{N-1}}\sum _{i=1}^{N}\left(s_{i}-\mu \right)^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d9b7e2f5b334bb4fc2c85e178e32c70622dfe29" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:25.003ex; height:3.843ex;" alt="{\textstyle \sigma ^{2}={\frac {1}{N-1}}\sum _{i=1}^{N}\left(s_{i}-\mu \right)^{2}}"></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="{\textstyle \mu ={\frac {1}{N}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>μ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \mu ={\frac {1}{N}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d928f91ec6edc31e60b4173c965cc50bd872dc5a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:6.795ex; height:3.509ex;" alt="{\textstyle \mu ={\frac {1}{N}}}"></span> is the mean of participations. If all firms have equal (identical) shares (that is, if the market structure is completely <i><a href="/wiki/Symmetric" class="mw-redirect" title="Symmetric">symmetric</a></i>, in which case <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 s_{i}=1/N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s_{i}=1/N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/146c4f32829d2a14d4a59d5e6e0f2886a2c8879c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.377ex; height:2.843ex;" alt="{\displaystyle s_{i}=1/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 \sigma ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53a5c55e536acf250c1d3e0f754be5692b843ef5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.385ex; height:2.676ex;" alt="{\displaystyle \sigma ^{2}}"></span> is zero 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 H}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75a9edddcca2f782014371f75dca39d7e13a9c1b" 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 H}"></span> equals <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 1/N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1/N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa5c2544725c51dfe75eea07ee1f487feb8664c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.389ex; height:2.843ex;" alt="{\displaystyle 1/N}"></span>. If the number of firms in the market is held constant, then a higher variance due to a higher level of asymmetry between firms' shares (that is, a higher <i>share dispersion</i>) will result in a higher index value. See the Brown and Warren-Boulton (1988) and Warren-Boulton (1990) texts cited below. </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=Herfindahl%E2%80%93Hirschman_index&action=edit&section=8" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Concentration_ratio" title="Concentration ratio">Concentration ratio</a></li> <li><a href="/wiki/Marketing_strategy" title="Marketing strategy">Marketing strategy</a></li> <li><a href="/wiki/Microeconomics" title="Microeconomics">Microeconomics</a></li> <li><a href="/wiki/N50_statistic" class="mw-redirect" title="N50 statistic">N50 statistic</a> – a measure of concentration used in genomics</li> <li><a href="/wiki/Small_but_significant_and_non-transitory_increase_in_price" title="Small but significant and non-transitory increase in price">Small but significant and non-transitory increase in price</a> – a test to determine the relevant market</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=Herfindahl%E2%80%93Hirschman_index&action=edit&section=9" 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"><a href="#CITEREFUnited_States_Department_of_Justice2010">United States Department of Justice 2010</a>, § 5.3</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output 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West Publishing Company. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780314414434" title="Special:BookSources/9780314414434"><bdi>9780314414434</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Banking+and+Financial+Institutions+Law+in+a+Nutshell&rft.edition=2nd&rft.pub=West+Publishing+Company&rft.date=1988&rft.isbn=9780314414434&rft.aulast=Lovett&rft.aufirst=William+Anthony&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHerfindahl%E2%80%93Hirschman+index" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBouchaudPottersAguilar1997" class="citation arxiv cs1">Bouchaud, Jean-Philippe; Potters, Marc; Aguilar, Jean-Pierre (July 1997). "Missing Information and Asset Allocation". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/cond-mat/9707042">cond-mat/9707042</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=Missing+Information+and+Asset+Allocation&rft.date=1997-07&rft_id=info%3Aarxiv%2Fcond-mat%2F9707042&rft.aulast=Bouchaud&rft.aufirst=Jean-Philippe&rft.au=Potters%2C+Marc&rft.au=Aguilar%2C+Jean-Pierre&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHerfindahl%E2%80%93Hirschman+index" class="Z3988"></span><a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1997cond.mat..7042B/abstract">1997cond.mat..7042B</a></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="CITEREFWoerheidePersson1993" class="citation journal cs1">Woerheide, Walt J.; Persson, Don (1993). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20180323220210/https://pdfs.semanticscholar.org/0a5e/ec924dae3ea30b6cae8e66f7070344d47631.pdf">"An Index of Portfolio Diversification"</a> <span class="cs1-format">(PDF)</span>. <i>Financial Services Review</i>. <b>2</b> (2): 73–85. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F1057-0810%2892%2990003-U">10.1016/1057-0810(92)90003-U</a>. <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/1057-0810">1057-0810</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:18548005">18548005</a>. Archived from <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://pdfs.semanticscholar.org/0a5e/ec924dae3ea30b6cae8e66f7070344d47631.pdf">the original</a></span> <span class="cs1-format">(PDF)</span> on 2018-03-23.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Financial+Services+Review&rft.atitle=An+Index+of+Portfolio+Diversification&rft.volume=2&rft.issue=2&rft.pages=73-85&rft.date=1993&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A18548005%23id-name%3DS2CID&rft.issn=1057-0810&rft_id=info%3Adoi%2F10.1016%2F1057-0810%2892%2990003-U&rft.aulast=Woerheide&rft.aufirst=Walt+J.&rft.au=Persson%2C+Don&rft_id=https%3A%2F%2Fpdfs.semanticscholar.org%2F0a5e%2Fec924dae3ea30b6cae8e66f7070344d47631.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHerfindahl%E2%80%93Hirschman+index" 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=Herfindahl%E2%80%93Hirschman_index&action=edit&section=10" 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="CITEREFBrownWarren-Boulton,_Frederick_R.1988" class="citation report cs1">Brown, Donald M.; Warren-Boulton, Frederick R. (May 11, 1988). Testing the Structure-Competition Relationship on Cross-Sectional Firm Data (Report). Discussion paper 88-6. <a href="/wiki/Washington,_D.C." title="Washington, D.C.">Washington, D.C.</a>: Economic Analysis Group, U.S. Department of Justice, Antitrust Division. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/221796344">221796344</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=report&rft.btitle=Testing+the+Structure-Competition+Relationship+on+Cross-Sectional+Firm+Data&rft.place=Washington%2C+D.C.&rft.series=Discussion+paper+88-6&rft.pub=Economic+Analysis+Group%2C+U.S.+Department+of+Justice%2C+Antitrust+Division&rft.date=1988-05-11&rft_id=info%3Aoclcnum%2F221796344&rft.aulast=Brown&rft.aufirst=Donald+M.&rft.au=Warren-Boulton%2C+Frederick+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHerfindahl%E2%80%93Hirschman+index" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCapozzaLee,_Sohan1996" class="citation journal cs1">Capozza, Dennis R.; Lee, Sohan (1996). "Portfolio Characteristics and Net Asset Values in REITs". <i>The Canadian Journal of Economics</i>. <b>29</b> (Special Issue: Part 2): S520–S526. <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%2F136100">10.2307/136100</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/136100">136100</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Canadian+Journal+of+Economics&rft.atitle=Portfolio+Characteristics+and+Net+Asset+Values+in+REITs&rft.volume=29&rft.issue=Special+Issue%3A+Part+2&rft.pages=S520-S526&rft.date=1996&rft_id=info%3Adoi%2F10.2307%2F136100&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F136100%23id-name%3DJSTOR&rft.aulast=Capozza&rft.aufirst=Dennis+R.&rft.au=Lee%2C+Sohan&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHerfindahl%E2%80%93Hirschman+index" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHirschman1964" class="citation journal cs1"><a href="/wiki/Albert_O._Hirschman" title="Albert O. Hirschman">Hirschman, Albert O.</a> (1964). "The Paternity of an Index". <i><a href="/wiki/The_American_Economic_Review" class="mw-redirect" title="The American Economic Review">The American Economic Review</a></i>. <b>54</b> (5). <a href="/wiki/American_Economic_Association" title="American Economic Association">American Economic Association</a>: 761–762. <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/1818582">1818582</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+American+Economic+Review&rft.atitle=The+Paternity+of+an+Index&rft.volume=54&rft.issue=5&rft.pages=761-762&rft.date=1964&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1818582%23id-name%3DJSTOR&rft.aulast=Hirschman&rft.aufirst=Albert+O.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHerfindahl%E2%80%93Hirschman+index" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKwoka1977" class="citation journal cs1">Kwoka, John E. Jr. (1977). "Large Firm Dominance and Price-Cost Margins in Manufacturing Industries". <i><a href="/wiki/Southern_Economic_Journal" class="mw-redirect" title="Southern Economic Journal">Southern Economic Journal</a></i>. <b>44</b> (1): 183–189. <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%2F1057315">10.2307/1057315</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/1057315">1057315</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Southern+Economic+Journal&rft.atitle=Large+Firm+Dominance+and+Price-Cost+Margins+in+Manufacturing+Industries&rft.volume=44&rft.issue=1&rft.pages=183-189&rft.date=1977&rft_id=info%3Adoi%2F10.2307%2F1057315&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1057315%23id-name%3DJSTOR&rft.aulast=Kwoka&rft.aufirst=John+E.+Jr.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHerfindahl%E2%80%93Hirschman+index" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWarren-Boulton1990" class="citation book cs1">Warren-Boulton, Frederick R. (1990). "Implications of U.S. Experience with Horizontal Mergers and Takeovers for Canadian Competition Policy". In Mathewson, Frank; Trebilcock, Michael; Walker, Michael (eds.). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/laweconomicsofco0000unse"><i>The Law and Economics of Competition Policy</i></a></span>. <a href="/wiki/Vancouver" title="Vancouver">Vancouver, B.C.</a>: <a href="/wiki/The_Fraser_Institute" class="mw-redirect" title="The Fraser Institute">The Fraser Institute</a>. pp. 337–368. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-88975-121-7" title="Special:BookSources/978-0-88975-121-7"><bdi>978-0-88975-121-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Implications+of+U.S.+Experience+with+Horizontal+Mergers+and+Takeovers+for+Canadian+Competition+Policy&rft.btitle=The+Law+and+Economics+of+Competition+Policy&rft.place=Vancouver%2C+B.C.&rft.pages=337-368&rft.pub=The+Fraser+Institute&rft.date=1990&rft.isbn=978-0-88975-121-7&rft.aulast=Warren-Boulton&rft.aufirst=Frederick+R.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Flaweconomicsofco0000unse&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHerfindahl%E2%80%93Hirschman+index" class="Z3988"></span></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=Herfindahl%E2%80%93Hirschman_index&action=edit&section=11" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Orris Herfindahl, "Concentration in the steel industry", 1950, published on Archive.org with consent of his heirs in June 2021, <a rel="nofollow" class="external text" href="https://archive.org/details/herfindahl-concentration-in-the-steel-industry-1950-publish/">Dissertation on Archive.org</a></li> <li><a rel="nofollow" class="external text" href="http://wits.worldbank.org">World Integrated Trade Solution</a>, <i>Calculate Herfindahl-Hirschman Index using UNSD COMTRADE data</i></li> <li><a rel="nofollow" class="external text" href="https://www.justice.gov/atr/herfindahl-hirschman-index">US Department of Justice market concentration cutoffs</a>.</li> <li><a rel="nofollow" class="external text" href="http://www.unclaw.com/chin/teaching/antitrust/herfindahl.htm">Herfindahl-Hirschman Index Calculator</a>. Web tool for calculating pre- and post-merger Herfindahl index.</li> <li><a rel="nofollow" class="external text" href="https://www.justice.gov/atr/public/guidelines/hmg-2010.html">Department of Justice and Federal Trade Commission 2010 Horizontal Merger Guidelines</a>. More detailed information about mergers, market concentration, and competition (from the <a href="/wiki/United_States_Department_of_Justice" title="United States Department of Justice">Department of Justice</a>).</li></ul> <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 .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Institutional_economics" style="padding:3px"><table class="nowraplinks 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:Instecon" title="Template:Instecon"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Instecon" title="Template talk:Instecon"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Instecon" title="Special:EditPage/Template:Instecon"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Institutional_economics" style="font-size:114%;margin:0 4em"><a href="/wiki/Institutional_economics" title="Institutional economics">Institutional economics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Institutional economists</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Werner_Abelshauser" title="Werner Abelshauser">Werner Abelshauser</a></li> <li><a href="/wiki/Clarence_Edwin_Ayres" title="Clarence Edwin Ayres">Clarence Edwin Ayres</a></li> <li><a href="/wiki/Joe_S._Bain" class="mw-redirect" title="Joe S. Bain">Joe S. Bain</a></li> <li><a href="/wiki/Shimshon_Bichler" title="Shimshon Bichler">Shimshon Bichler</a></li> <li><a href="/wiki/Robert_A._Brady" title="Robert A. Brady">Robert A. Brady</a></li> <li><a href="/wiki/Daniel_Bromley" title="Daniel Bromley">Daniel Bromley</a></li> <li><a href="/wiki/Ha-Joon_Chang" title="Ha-Joon Chang">Ha-Joon Chang</a></li> <li><a href="/wiki/John_Maurice_Clark" title="John Maurice Clark">John Maurice Clark</a></li> <li><a href="/wiki/John_R._Commons" title="John R. Commons">John R. Commons</a></li> <li><a href="/wiki/Richard_T._Ely" title="Richard T. Ely">Richard T. Ely</a></li> <li><a href="/wiki/Robert_H._Frank" title="Robert H. Frank">Robert H. Frank</a></li> <li><a href="/wiki/John_Kenneth_Galbraith" title="John Kenneth Galbraith">John Kenneth Galbraith</a></li> <li><a href="/wiki/Walton_Hale_Hamilton" title="Walton Hale Hamilton">Walton Hale Hamilton</a></li> <li><a href="/wiki/Orris_C._Herfindahl" title="Orris C. Herfindahl">Orris C. Herfindahl</a></li> <li><a href="/wiki/Albert_O._Hirschman" title="Albert O. Hirschman">Albert O. Hirschman</a></li> <li><a href="/wiki/Geoffrey_Hodgson" title="Geoffrey Hodgson">Geoffrey Hodgson</a></li> <li><a href="/wiki/J%C3%A1nos_Kornai" title="János Kornai">János Kornai</a></li> <li><a href="/wiki/Simon_Kuznets" title="Simon Kuznets">Simon Kuznets</a></li> <li><a href="/wiki/Hunter_Lewis" title="Hunter Lewis">Hunter Lewis</a></li> <li><a href="/wiki/Jesse_W._Markham" title="Jesse W. Markham">Jesse W. Markham</a></li> <li><a href="/wiki/Wesley_Clair_Mitchell" title="Wesley Clair Mitchell">Wesley Clair Mitchell</a></li> <li><a href="/wiki/Gunnar_Myrdal" title="Gunnar Myrdal">Gunnar Myrdal</a></li> <li><a href="/wiki/Jonathan_Nitzan" title="Jonathan Nitzan">Jonathan Nitzan</a></li> <li><a href="/wiki/Warren_Samuels" title="Warren Samuels">Warren Samuels</a></li> <li><a href="/wiki/Fran%C3%A7ois_Simiand" title="François Simiand">François Simiand</a></li> <li><a href="/wiki/Herbert_A._Simon" title="Herbert A. Simon">Herbert A. Simon</a></li> <li><a href="/wiki/Frank_Stilwell_(economist)" title="Frank Stilwell (economist)">Frank Stilwell</a></li> <li><a href="/wiki/George_W._Stocking_Sr." title="George W. Stocking Sr.">George W. Stocking Sr.</a></li> <li><a href="/wiki/Lars_P%C3%A5lsson_Syll" title="Lars Pålsson Syll">Lars Pålsson Syll</a></li> <li><a href="/wiki/Thorstein_Veblen" title="Thorstein Veblen">Thorstein Veblen</a></li> <li><a href="/wiki/Edward_Lawrence_Wheelwright" title="Edward Lawrence Wheelwright">Edward Lawrence Wheelwright</a></li> <li><a href="/wiki/Erich_Zimmermann" title="Erich Zimmermann">Erich Zimmermann</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/New_institutional_economics" title="New institutional economics">New institutional economists</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Daron_Acemoglu" title="Daron Acemoglu">Daron Acemoglu</a></li> <li><a href="/wiki/Armen_Alchian" title="Armen Alchian">Armen Alchian </a></li> <li><a href="/wiki/Masahiko_Aoki" title="Masahiko Aoki">Masahiko Aoki</a></li> <li><a href="/wiki/Steven_N._S._Cheung" title="Steven N. S. Cheung">Steven N. S. Cheung</a></li> <li><a href="/wiki/Ronald_Coase" title="Ronald Coase">Ronald Coase</a></li> <li><a href="/wiki/Harold_Demsetz" title="Harold Demsetz">Harold Demsetz</a></li> <li><a href="/wiki/Avner_Greif" title="Avner Greif">Avner Greif</a></li> <li><a href="/wiki/Claude_M%C3%A9nard_(economist)" title="Claude Ménard (economist)">Claude Ménard</a></li> <li><a href="/wiki/Douglass_North" title="Douglass North">Douglass North</a></li> <li><a href="/wiki/Mancur_Olson" title="Mancur Olson">Mancur Olson</a></li> <li><a href="/wiki/Elinor_Ostrom" title="Elinor Ostrom">Elinor Ostrom</a></li> <li><a href="/wiki/Oliver_E._Williamson" title="Oliver E. Williamson">Oliver E. Williamson</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Behavioral_economics" title="Behavioral economics">Behavioral economists</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/George_Ainslie_(psychologist)" title="George Ainslie (psychologist)">George Ainslie</a></li> <li><a href="/wiki/Dan_Ariely" title="Dan Ariely">Dan Ariely</a></li> <li><a href="/wiki/Nava_Ashraf" title="Nava Ashraf">Nava Ashraf</a></li> <li><a href="/wiki/Ofer_Azar" title="Ofer Azar">Ofer Azar</a></li> <li><a href="/wiki/Douglas_Bernheim" title="Douglas Bernheim">Douglas Bernheim</a></li> <li><a href="/wiki/Samuel_Bowles_(economist)" title="Samuel Bowles (economist)">Samuel Bowles</a></li> <li><a href="/wiki/Sarah_Brosnan" title="Sarah Brosnan">Sarah Brosnan</a></li> <li><a href="/wiki/Colin_Camerer" title="Colin Camerer">Colin Camerer</a></li> <li><a href="/wiki/David_Cesarini" title="David Cesarini">David Cesarini</a></li> <li><a href="/wiki/Kay-Yut_Chen" title="Kay-Yut Chen">Kay-Yut Chen</a></li> <li><a href="/wiki/Rachel_Croson" title="Rachel Croson">Rachel Croson</a></li> <li><a href="/wiki/Werner_De_Bondt" title="Werner De Bondt">Werner De Bondt</a></li> <li><a href="/wiki/Paul_Dolan_(academic)" class="mw-redirect" title="Paul Dolan (academic)">Paul Dolan</a></li> <li><a href="/wiki/Stephen_Duneier" title="Stephen Duneier">Stephen Duneier</a></li> <li><a href="/wiki/Catherine_C._Eckel" title="Catherine C. Eckel">Catherine C. Eckel</a></li> <li><a href="/wiki/Armin_Falk" title="Armin Falk">Armin Falk</a></li> <li><a href="/wiki/Urs_Fischbacher" title="Urs Fischbacher">Urs Fischbacher</a></li> <li><a href="/wiki/Herbert_Gintis" title="Herbert Gintis">Herbert Gintis</a></li> <li><a href="/wiki/Uri_Gneezy" title="Uri Gneezy">Uri Gneezy</a></li> <li><a href="/wiki/David_Halpern_(psychologist)" title="David Halpern (psychologist)">David Halpern</a></li> <li><a href="/wiki/Charles_A._Holt" title="Charles A. Holt">Charles A. Holt</a></li> <li><a href="/wiki/David_Ryan_Just" title="David Ryan Just">David Ryan Just</a></li> <li><a href="/wiki/Daniel_Kahneman" title="Daniel Kahneman">Daniel Kahneman</a></li> <li><a href="/wiki/Ariel_Kalil" title="Ariel Kalil">Ariel Kalil</a></li> <li><a href="/wiki/George_Katona" title="George Katona">George Katona</a></li> <li><a href="/wiki/Jeffrey_R._Kling" title="Jeffrey R. Kling">Jeffrey R. Kling</a></li> <li><a href="/wiki/George_Loewenstein" title="George Loewenstein">George Loewenstein</a></li> <li><a href="/wiki/Graham_Loomes" title="Graham Loomes">Graham Loomes</a></li> <li><a href="/wiki/Brigitte_C._Madrian" title="Brigitte C. Madrian">Brigitte C. Madrian</a></li> <li><a href="/wiki/Gary_McClelland" title="Gary McClelland">Gary McClelland</a></li> <li><a href="/wiki/Matteo_Motterlini" title="Matteo Motterlini">Matteo Motterlini</a></li> <li><a href="/wiki/Sendhil_Mullainathan" title="Sendhil Mullainathan">Sendhil Mullainathan</a></li> <li><a href="/wiki/Michael_Norton_(professor)" title="Michael Norton (professor)">Michael Norton</a></li> <li><a href="/wiki/Matthew_Rabin" title="Matthew Rabin">Matthew Rabin</a></li> <li><a href="/wiki/Howard_Rachlin" title="Howard Rachlin">Howard Rachlin</a></li> <li><a href="/wiki/Klaus_M._Schmidt" title="Klaus M. Schmidt">Klaus M. Schmidt</a></li> <li><a href="/wiki/Eldar_Shafir" title="Eldar Shafir">Eldar Shafir</a></li> <li><a href="/wiki/Hersh_Shefrin" title="Hersh Shefrin">Hersh Shefrin</a></li> <li><a href="/wiki/Robert_J._Shiller" title="Robert J. Shiller">Robert J. Shiller</a></li> <li><a href="/wiki/Uwe_Sunde" title="Uwe Sunde">Uwe Sunde</a></li> <li><a href="/wiki/Richard_Thaler" title="Richard Thaler">Richard Thaler</a></li> <li><a href="/wiki/Amos_Tversky" title="Amos Tversky">Amos Tversky</a></li> <li><a href="/wiki/Robert_W._Vishny" title="Robert W. Vishny">Robert W. Vishny</a></li> <li><a href="/wiki/Georg_Weizs%C3%A4cker" title="Georg Weizsäcker">Georg Weizsäcker</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Economic_sociology" title="Economic sociology">Economic sociologists</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Jens_Beckert" title="Jens Beckert">Jens Beckert</a></li> <li><a href="/wiki/Fred_L._Block" title="Fred L. Block">Fred L. Block</a></li> <li><a href="/wiki/James_Smoot_Coleman" title="James Smoot Coleman">James S. Coleman</a></li> <li><a href="/wiki/Paul_DiMaggio" title="Paul DiMaggio">Paul DiMaggio</a></li> <li><a href="/wiki/Paula_England" title="Paula England">Paula England</a></li> <li><a href="/wiki/Mark_Granovetter" title="Mark Granovetter">Mark Granovetter</a></li> <li><a href="/wiki/Donald_Angus_MacKenzie" class="mw-redirect" title="Donald Angus MacKenzie">Donald Angus MacKenzie</a></li> <li><a href="/wiki/Joel_M._Podolny" title="Joel M. Podolny">Joel M. Podolny</a></li> <li><a href="/wiki/Lynette_Spillman" title="Lynette Spillman">Lynette Spillman</a></li> <li><a href="/wiki/Richard_Swedberg" title="Richard Swedberg">Richard Swedberg</a></li> <li><a href="/wiki/Laurent_Th%C3%A9venot" title="Laurent Thévenot">Laurent Thévenot</a></li> <li><a href="/wiki/Carlo_Trigilia" title="Carlo Trigilia">Carlo Trigilia</a></li> <li><a href="/wiki/Harrison_White" title="Harrison White">Harrison White</a></li> <li><a href="/wiki/Viviana_Zelizer" title="Viviana Zelizer">Viviana Zelizer</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Key concepts and ideas</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Accelerator_effect" title="Accelerator effect">Accelerator effect</a></li> <li><a href="/wiki/Administered_prices" title="Administered prices">Administered prices</a></li> <li><a href="/wiki/Barriers_to_entry" title="Barriers to entry">Barriers to entry</a></li> <li><a href="/wiki/Bounded_rationality" title="Bounded rationality">Bounded rationality</a></li> <li><a href="/wiki/Conspicuous_consumption" title="Conspicuous consumption">Conspicuous consumption</a></li> <li><a href="/wiki/Conspicuous_leisure" title="Conspicuous leisure">Conspicuous leisure</a></li> <li><a href="/wiki/Conventional_wisdom" title="Conventional wisdom">Conventional wisdom</a></li> <li><a href="/wiki/Countervailing_power" title="Countervailing power">Countervailing power</a></li> <li><a href="/wiki/Effective_competition" title="Effective competition">Effective competition</a></li> <li><a href="/wiki/Herfindahl_index" class="mw-redirect" title="Herfindahl index">Herfindahl index</a></li> <li><a href="/wiki/Hiding_hand_principle" title="Hiding hand principle">Hiding hand principle</a></li> <li><a href="/wiki/Hirschman_cycle" title="Hirschman cycle">Hirschman cycle</a></li> <li><a href="/wiki/Instrumentalism" title="Instrumentalism">Instrumentalism</a></li> <li><a href="/wiki/Kuznets_swing" title="Kuznets swing">Kuznets cycles</a></li> <li><a href="/wiki/Market_concentration" title="Market concentration">Market concentration</a></li> <li><a href="/wiki/Market_power" title="Market power">Market power</a></li> <li><a href="/wiki/Market_structure" title="Market structure">Market structure</a></li> <li><a href="/wiki/Backwardness" title="Backwardness">Penalty of taking the lead</a></li> <li><a href="/wiki/Satisficing" title="Satisficing">Satisficing</a></li> <li><a href="/wiki/Shortage_economy" title="Shortage economy">Shortage economy</a></li> <li><a href="/wiki/Structure%E2%80%93conduct%E2%80%93performance_paradigm" title="Structure–conduct–performance paradigm">Structure–conduct–performance paradigm</a></li> <li><a href="/wiki/Technostructure" title="Technostructure">Technostructure</a></li> <li><a href="/wiki/Theory_of_two-level_planning" title="Theory of two-level planning">Theory of two-level planning</a></li> <li><a href="/wiki/Veblen_good" title="Veblen good">Veblen goods</a></li> <li><a href="/wiki/Veblenian_dichotomy" class="mw-redirect" title="Veblenian dichotomy">Veblenian dichotomy</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related fields</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cultural_economics" title="Cultural economics">Cultural economics</a></li> <li><a href="/wiki/Development_economics" title="Development economics">Development economics</a></li> <li><a href="/wiki/English_historical_school_of_economics" title="English historical school of economics">English historical school of economics</a></li> <li><a href="/wiki/Evolutionary_economics" title="Evolutionary economics">Evolutionary economics</a></li> <li><a href="/wiki/Evolutionary_psychology" title="Evolutionary psychology">Evolutionary psychology</a></li> <li><a href="/wiki/Schools_of_economic_thought#French_historical_school" title="Schools of economic thought">French historical school</a></li> <li><a href="/wiki/Historical_school_of_economics" title="Historical school of economics">Historical school of economics</a></li> <li><a href="/wiki/Legal_realism" title="Legal realism">Legal realism</a></li> <li><a href="/wiki/Microeconomics" title="Microeconomics">Microeconomics</a></li> <li><a href="/wiki/Post-Keynesian_economics" title="Post-Keynesian economics">Post-Keynesian economics</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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