The Utility Function (Graph, Formula & Example)

The Utility Function in Economics adds a degree of measurable, or comparable, analysis for the indifference curves that we use in modeling consumer behavior ... DyingEconomy.com MenuWhat'sNew?MacroeconomicsInflationUnemploymentInequalityMoney&BankingSupply-SideNationalIncomeMicroeconomicsConsumersMarketFailureAboutContact UtilityFunction(Graph,Formula&Example) BySteveBain TheUtilityFunctioninEconomicsaddsadegreeofmeasurable,orcomparable,analysisfortheindifferencecurvesthatweuseinmodelingconsumerbehavior.Thenumbersascribedtothesefunctionsaremeaninglessinthemselves,buttheycanbeusedforcomparisonpurposes.Foreconomiststhewordutilitymeansagreatdeal,andmuchofmicroeconomicsisbuiltonthenotionofmarginalutility,i.e.,thevalueofonemoregood,oronemoreinputunitintheproductionprocess.Totalutilitypalesinsignificancewhencomparedtomarginalutilitywhenconsidering,forexample,themarketpriceofgoods.ThewholeDiamondWaterParadoxisexplainedviathewayinwhichconsumersvaluethemarginalunitratherthangooditself.Withautilityfunction,wecanaddanextradegreeortwoofusefulnesstoouroverallmodelofconsumerbehavior.Whenaconsumerpurchasesagood,thepricepaidisalwaysworthlesstotheconsumerthantheexpectedutilitythatwillbegainedfromthatgood,otherwisenopurchasewouldbemade. MarginalUtility&'Utils' Iftheutilityfunctiongraphbelowlooksfamiliar,that'sbecauseitissimplytheindifferencemapthatfeaturedonmypageaboutindifferencecurves.Theonlydifferenceisthatthistimeeachcurvehasbeengivenanarbitrarynumericalvalue. Thenumericalvaluerelatestowhateconomistscallutilsi.e.,howmuchutilitypertainstoeachindifferencecurve.Ifyouhaveforgottenwhatthesecurvesrepresentandneedarefresher,havealookatmymainarticleabout:IndifferenceCurvesandMaps'Utils'cannotbeboughtorsold,theycan'tbetraded,andtheycan'tbetransferred.That'sbecausetheydon'texistintherealworld,theyarejustanarbitraryconceptthatserveasinglepurpose,andthatistocompare/rankdifferentlevelsofutilitygainedfrombasketsofgoodsandservices.Keepinmindthattheterm'utility'ineconomicsisusedexclusivelyforthispurpose-toassignanumericalvaluetoonebasketofgoods&servicescomparedtoanother. AUtilityFunctionExample Stickingwiththesametwo-goodmodelthatIhaveusedonrelatedpages,let'sconsidertheutilitygainedfromabasketofbiscuitsandcheese.Byobservinghowconsumersspendtheirmoneyontheseitemsatvariouspricesitispossibletodeducetheirpreference-it'saprocesscalledrevealedpreference.Fromthiswecanconstructtypicalutilityfunctionstoestimatetheutilitygainedfromdifferentcombinationsofbiscuitsandcheese.Let'skeepthisexamplereallysimple: UtilityFunctionFormula U(B,C)=B+10C Inwordsthismeansthattheutilityfrombiscuitsandcheeseequalsonemultipliedbytheservingsofbiscuitsplustenmultipliedbytheservingsofcheese.So,ifwehavetwobasketsofthesegoodswithdifferentquantitiesofeachgood,wecancomparetheoverallutilityofeachbasket:BasketAhas5servingsofbiscuitsand2servingsofcheese,yielding25utils.BasketBhas10servingsofbiscuitsand1servingofcheese,yielding20utils.Twothingsshouldbenotedhere:BasketAispreferredtoBasketBbecauseitgivesmoreutility.Thisistheimportantbit-whilstAispreferred,wecannotdeterminebyhowmuch!Takegoodnoteofpoint2here,becausethenumbersassignedherearenotcomparableinamathematicalsense.Inotherwords,wecannotsaythat4basketsofAwouldgive100utilsandthat5basketsofBwouldalsogive100utils.Utilsarenotadditiveinthismanner,theycanonlybeusedtorankonebasketaspreferredtoanother,theycannotbeusedtomeasurebyhowmuchoneispreferredtoanother. DifferentUtilityFunctions-Ordinal&Cardinal Theformofrankingdifferentbasketsofgoodswithindividualutilityfunctionshasaspecificname,itisreferredtoasordinalranking.Weranktheorderinwhichbasketsarepreferred,butwedonotknowbyhowmuchtheyarepreferred.Utilityfunctionsbasedonordinalrankingsarealsospecifictoeachconsumer.IfJackgains12utilsfromaservingofcheeseandJanegains10utils,wecannotdeducethatJackgainsmoreutilityfromcheesethanJanedoes.Weonlyknowthatthe12utilshegainsarebetterforhimpersonallythansomeothergoodthatgiveshim10utils.Inotherwords,agivennumberofutilsforonepersonmayrepresentanentirelydifferentamountofutilitythanitrepresentsforadifferentperson.Therestrictionsonwhatcanbededucedfromordinalutilitymayseemsevere,andmayappeartorenderthewholeconceptsomewhatuseless.Certainlywewouldliketobeabletoquantifyandcompareexactlyhowmuchutilitywegainfromconsuminggoods,andifwecoulddothiswewouldbeabletoconstruct'cardinalutilityfunctions'.However,wesimplycannottellexactlyhowmuchutilityaconsumergainsfromconsumingagood.Eventhesameconsumeratagiventimeexperiencesdiminishingmarginalutilityfromadditionalunitsofthesamegood,soquantifyingthisovertime,acrossdifferentconsumers,andfordifferingquantitiesisimpossible.Happily,cardinalutilityfunctionsareunnecessary.Ordinalutilityisquitesufficientforustobeabletoformusefulmodelsofconsumerbehavior. ExpectedUtilityforDifferentGoods Theexpectedutilityfromconsuminggoodsvariesdependingonthetypeofgoodsbeingconsumed.Onthispage(andonallothersunlessstatedotherwise)Ireferto'normalgoods'i.e.,thoseforwhichthethreeassumptionsunderlyingconsumerbehaviortheoryaresatisfied.Those3assumptionsrelatetocompleteness,transitivity,andnon-satiation.Formoredetailsontheseassumptions,seemymainarticleat:ConsumerBehaviorTheoryWeshould,however,keepinmindthattherearemanyothertypesofgoods.I'llbecoveringtheseinseparatearticlesasIbuildupthemicroeconomicssectionofthesite.Seetherelatedpagesbelowforinfo. RelatedPages:MarginalUtilityMarginalRateofSubstitutionBudgetLine&BudgetConstraintEngelCurveTypesofEconomicGoodsRationalChoiceTheory Togetmylatestupdatessentstraighttoyourinbox,justaddyourdetailsbelow: Email Iamatleast16yearsofage. Ihavereadandaccepttheprivacypolicy. Iunderstandthatyouwillusemyinformationtosendmeanewsletter. 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