Utility Maximization - ECON 150: Microeconomics

We assume that the goal of the consumer is to maximize his/her level of satisfaction or joy, ... Summing the marginal utilities gives us the total utility. Section01:ConsumerBehavior Utility Inthissection,wearegoingtotakeacloserlookatwhatisbehindthedemandcurveandthebehaviorofconsumers.Howdoesaconsumerdecidetospendhis/herincomeonthemanydifferentthingsthathe/shewants,i.e.,food,clothing,housing,entertainment?Weassumethatthegoaloftheconsumeristomaximizehis/herlevelofsatisfactionorjoy,constrainedbyhis/herincome. Economistsusethetermutilityasameasureofsatisfaction,joy,orhappiness.Howmuchsatisfactiondoesapersongainfromeatingapizzaorwatchingamovie? Measuringutilityisbasedsolelyonthepreferencesoftheindividualandhasnothingtodowiththepriceofthegood. Let’sdoanexperimentinutility. Step01:Getsomeofyourfavoritecandy,pastries,orcookies. Step02:Takeabiteandevaluate,onascalefrom0to100(with100beingthegreatestutility),thelevelofutilityfromthatbite.Recordthemarginalutilityofthatbite(i.e.,howmuchyougetfromthatoneadditionalbite). Step03:Repeatstep02.Itisimportanttobeconsistentwitheachunitconsumed,i.e.,thesamesizeandnodrinkingmilkorwaterpartwaythough. Whenyourunoutofcandyoryourmarginalutilitygoestozeroyoucanstop. LawofDiminishingMarginalUtility Thelawofdiminishingmarginalutilitystatesthatasmoreofthegoodisconsumed,theadditionalsatisfactionfromanotherbitewilleventuallydecline.Themarginalutilityisthesatisfactiongainedfromeachadditionalbite.Asmoreofthegoodisconsumed,wegainlessadditionalsatisfactionfromconsuminganotherunit. Thusevenifagoodwerefreeandyoucouldconsumeasmuchasyouwanted,therewouldbealimittotheamountyouwouldconsumeduetothelawofdiminishingmarginalutility. Summingthemarginalutilitiesgivesusthetotalutility. Forexample,let’ssaythefirstchocolatewasan85andthesecondchocolatehadamarginalutilityof79,thenthetotalutilityfromconsumingtwochocolatesis164.Thetotalutilityfromconsumingthreechocolatesis85+79+73=237. Aslongasourmarginalutilityispositiveourtotalutilityincreasesalthoughwithdiminishingmarginalutilityitincreasesatadecreasingrate. Canmarginalutilitybenegative?Yes.Ataholidaydinner,youmayovereatandsufferfromindigestionafterwardstoapointwhereyouregrethavingeatentoomuch,butatthetimeofthedinner,youexpectedgreaterutilityfromeatingthelastofthemeal.Wewouldnotwillinglyconsumeanitemthatgaveusnegativemarginalutility. Thenwhywouldanindividualstuffthemselvesduringahotdogeatingcontestwhereclearlythelasthotdogsconsumedaremakingthemworseoff? Althoughthemarginalutilityfromthelasthotdogitselfmakesthepersonworseoff,theutilityfromwinningthecontestisgreatermakingthemarginalutilitypositive.  Themarginalutilityofanitemcanchange.Forexample,duringadroughtwaterprovidesahighpositivemarginalutility,andwithmorerainthemarginalutilitydeclines.Atsomepoint,thereistoomuchrain,itturnsfrombeingagoodutilitytoabadoneandthemarginalutilityofmorerain, whenitisalreadyflooding, isnegative. MaximizingUtility Utilityvaluescanbedeterminedbyanindividualrankinghis/herpreferencesfromleastpreferredtomostpreferred. Theresultingrankingorutilityvaluesaresubjectiveorindividual. Theyarealsoordinalratherthancardinal. Ordinalmeansthattheutilityvaluessimplydefinearankingofpreferencesratherthananactualcardinalmeasurement. Imagineaclasshas10studentsintheclassandtheteacherlinedthestudentsupaccordingtoheight. Hethennumberedthemoffaccordingtoheight,assigningtheshorteststudenta1andthetalleststudenta10. Isittruethatstudentnumber4istwicetallasstudentnumber2? Ofcoursenot. Allweknowfromtherankingisthatstudentnumber4istallerthanstudentnumber2. Now,imaginethatinanotherclassanotherteacherhasalsoranked10studentsaccordingtoheight. Isittruethatstudentnumber10fromthesecondclassroomistallerthanstudent1fromthefirstclassroom? Wecannotsaysincetherankingisonlyvalidwithinaparticularcourse. Inordertosayastudentistwiceastallasanotherstudentortobeabletocomparestudentsbetweenclasses,wewouldneedacardinalmeasureofheightlikeinchesorcentimeters.  Sinceutilityisordinalandnotcardinalwecannotmakeinterpersonalcomparisonsofutility. Doesarichpersonvalueadollarmoreorlessthanapoorperson? Whilesomewouldsaythatapoorpersonlikelyhasmoreunmetneedsandthushewouldvaluethedollarmore.Theansweristhatitalldependsonthepreferencesoftheindividuals.Apoorpersonmayprefertoliveamoresimplisticlifeandplacealowervalueonhavinganextradollarthanarichpersonwhohasa“loveofmoney”(1Timothy6:10). Wesimplycannotmakesuchaninterpersonalcomparisonofutility.  Sohowdoestheconsumerdecidewhattopurchase? Unfortunatelyeverythinghasapriceandconsumersonlyhavesomuchmoneytospend.Consequentlyconsumerstrytospendthelimitedmoneytheyhaveonwhatwillgivethemthegreatestamountofsatisfaction.Thedecisionruleforutilitymaximizationistopurchasethoseitemsthatgivethegreatestmarginalutilityperdollarandareaffordableorwithinthebudget. Manygrocerystoresprovideatagthatindicatesthepriceperpoundforthegood.Thisallowsconsumerstocomparethecostperpoundfordifferentbrandsordifferentsizes.Thesameconceptisusedformaximizingutilitybutwedividethemarginalutilitybythepricetogetthemarginalutilityperdollar. Let’ssaythatweeatonlytwogoods:milkshakesandpizzawherethepriceofeachsliceofpizzais$2andthepriceofeachshakeis$1andweonlyhave$11tospend.Sincethepriceofeachgoodisdifferentweneedtodividethemarginalutilitybythepricetoallowforacommoncomparison.Wethencomparethemarginalutilityperdollarforpizzasversesshakes.Forthefirstunitthemarginalutilityperdollarofashakeis50comparedtoonly45forthepizza,sowewouldpurchasethefirstshake.Wethencomparethemarginalutilityperdollarofthefirstpizza(45)tothemarginalutilityperdollarofthesecondshake(40)andpurchasethefirstsliceofpizza.Ifthemarginalutility perdollaristhesameforthetwogoodsandwehaveincometopurchaseboththenwewoulddoso,asseeninthesecondsliceofpizzaandthesecondshake.  Wecontinuetoallocateonbudgetonthosegoodsthatyieldthehighestmarginalutilityperdollar.Inthisexample,wewouldpurchasefourslicesorpizzaandthreemilkshakesandspendourentirebudgetof$11.Thetotalutilityfromthispurchasewouldbethesumofthemarginalutilities:50+90+80+40+70+60+30=420.Atthelastitemspurchasedthemarginalutilityperdollarspentonthetwogoodsisthesame,noothercombinationofpizzasandmilkshakeswillgiveusgreaterutilitygivenourbudget. Practice Hereisyourchancetopractice. Hollyhas$20tospendoneithermoviesorbowlingandwantstomaximizeherutility.Completethetableanddeterminehowmanymoviesandroundsofbowlingwillmaximizeherutility. Ourfirststepistodividethemarginalutilityofeachitembytheprice.Withanincomeof$20sheislimitedinwhatshecanpurchase. Sincethemarginalutilityperdollarforbowling(15)isgreaterthanthemarginalutilityofthefirstmovie(12.5)shewouldinitiallygobowling,spending$4. Comparingthefirstmovie(12.5)tothesecondroundofbowling(10)shewouldgotothemoviespendinganadditional$8andatotalof$12. Thedecisionisalittleharder.Hollyhaseightdollarsstilltospendandthemarginalutilityperdollaristhesameforeachgood.Ifshechoosesthemovieshewillspendalleightdollars,butifshegoesbowlingshewillspendfourdollarsandstillhavefourtospend.Wehaveassumedthatshewantstospendallhermoneyandgainsnoutilityfromholdingthecash.Sinceshecan’taffordtobuyanothermoviebutwouldinsteadbyathirdroundofbowling,whichonlyhasamarginalutilityperdollarof7.5. Thusweseethattomaximizeherutility,shewouldpurchaseoneroundofbowlingandtwomoviesgivingheratotalutilityof(60+100+80)=240. Recallourdecisionruleistohavethemarginalutilityperdollarspentonthelastitemsbethesameforallgoods.Inthiscase,weareunabletohavethatexactlybutwetrytogetascloseaspossible.Thereisnoothercombinationthatwouldgiveusgreaterutilitygivenourincome. DerivingDemand Knowinghowtheconsumerbehavesallowsustoderiveademandcurve. Let’ssaythatSuzetteeatseitheranappleoranorangeasasnack.Shehas$12tospend. Giventhateachfruitcoststwodollars,shewillmaximizeherutilitybypurchasing3applesand3oranges.Ifwearelookingatthedemandfororanges,thiswillgiveusonepointonthedemandcurve. Atapriceof$2.00,thequantitydemandedoforangesis3.  Recallthataswemovealongthedemandcurve,theonlythingthatchangesisthepriceofthegood(ceterisparibusorholdingallelseconstant). Ifthepriceoforangesdecreasesto$1,thequantityoforangesdemandedincreasesto6. Wecanplotthetwopointsandcreateademandcurvefororanges.Atapriceof$2thequantitydemandedis3andatapriceof$1thequantitydemandedis6.Recallthatthedemandcurvereflectsthemarginalbenefitorthewillingnesstopayoftheconsumer. Thedemandcurvecanbeseeninthediamond-waterparadox.Whydoeswaterthatisessentialtosustainlifecostsomuchlessthandiamondsthatareatheisticallypleasing,butarerelativelyunnecessary?Recallthatpricereflectsthescarcityofagood.Overall,thesupplyofwaterisrelativelyabundantwhilethesupplyofdiamondsisrelativelylimited.Thusthepricewepayforwaterislowcomparedtothepriceofdiamonds. Isitlogicalforsomeonewhoismaximizinghisutilitytopurchasebothwateranddiamonds?Whendecidingwhattopurchasewecomparethemarginalutilitydividedbytheprice.Withlotsofwaterconsumption,thetotalutilityofwaterisverylargebutthemarginalutilityofthelastgallonconsumedisrelativelylow.Fewdiamondsarepurchasedsowhilethemarginalutilityisverylarge,saythediamondringyoujustpurchasedforyourfuturespouse,thetotalutilityislowsincefewdiamondsarepurchased. HowBusinessesReact Knowingthatindividualsexperiencediminishingmarginalutility,howdobusinessesreact? Recallthatconsumersurplusistheareabelowthedemandcurvebutabovetheprice.Thinkofsomeexamplesofhowbusinessesreactgiventhelawofdiminishingmarginalutility. Oneexampleisthepriceperunitbasedonpackagesize. Anicecreamstorehasthreedifferentservingsizes-a6,10,and12ouncecup.Thepriceofthesmallestsize,"LikeIt,"is$4.29or71.5centsperounce.Forjust32centsmore,onecanhavefourmoreounces,"LoveIt,"makingthemarginalcostperounce8centsandtheaveragecostperounce46cents.Upgradingtothe"GottaHaveIt"sizeaddsanadditionaltwoounceswithonly15.5centsperouncemoreandanaveragecostperounceofonly41cents.Certainlythelargesizeischeaperperounce,butnoteveryonewantstoeatthatlargeofaserving.Forthoseonlywantingasmallserving,thestoretakesadvantageoftheirgreaterwillingnesstopayforthatportionsize. Whetheritsicecream,eggs,milk,popcorn,orcereal,itiscommonpracticetochargeahigherpriceperunitforasmallerpackagesize.Howeveritpaysforconsumerstodothemathsincebusinesseswillattimeschargeahigherpriceonthelargerpackagessize. Ifcustomersbelievethatbiggerisalwayscheaperandfailtodothemath,theymaygetcaughtpayingahigherpriceperunit. Servicesoftenfollowasimilarpricingschemewithloweraveragepricesformorefrequentattendance.Forexample,belowarethepricesforthe“hopperpass”atDisneyland.Ticketstosportingeventsfollowasimilarpricingapproachwiththepergamepricebeinglowerifmultiplegamesarepurchased,suchastheseasonpass. Regularpricesasof1/18/10 http://disneyland.disney.go.com/disneyland/en_US/reserve/ticketListing?name=TicketListingPage Considerthisexample.Youareonalongairplaneride,seatednexttoaneccentriclookingwomanandabusinessman.Halfwayintotheflight,thewomansaystoyouandthebusinessman,thatsheisveryrichandboredofflying.Tobreakupthemonotony,sheoffersyouandthebusinessmanachancetosplit$5,000. Therulesareasfollows:thebusinessmanmakesanofferofhowtosplitthemoneyandyoueitheracceptorreject.Ifyouaccept,yougettheagreeduponsplit.Ifyoudon’t,youbothgetnothing.Thisisaonetimeoffer.Thebusinessmanthinksandoffersthefollowingsplit$4,995forhimand$5foryou.Doyouacceptorrejecttheoffer?Why? Theanswertothesequestionswillvaryamongindividuals.Somewillacceptstatingtheyhavefivedollarsmorethantheydidbefore.Otherswillrejecttheoffer,sayingthatitisworthatleastfivedollarstothemtodenytheybusinessmanthe$4,995.Rememberthatwhenwetalkaboututility,itincludesnotonlymonetaryitemsbutalsothenonmonetary. InTheTheoryofMoralSentiments,AdamSmithwrote:"Howselfishsoevermanmaybesupposed,thereareevidentlysomeprinciplesinhisnaturewhichinteresthiminthefortuneofothersandrendertheirhappinessnecessarytohimthoughhederivesnothingfromitexceptthepleasureofseeingit.”Rememberthatutilityisderivedfrommanydifferentareasincludingserviceandphilanthropicacts. Reference:http://www.econlib.org/Library/Enc/bios/Smith.html   Section02:IndifferenceCurvesandBudgetConstraints IndifferenceCurves Indifferencecurvesandbudgetconstraintsallowforamorein-depthanalysisofdemand.Formodelingpurposeswewilllookatthetwogoods. Anindifferencecurveshowsthedifferentcombinationsofthetwogoodsthatyieldthesamelevelofutility,independentofthepriceofthegoods.Duetothelawofdiminishingmarginalutility,theindifferencecurvebetweenthetwogoodsisconvextotheorigin.Allcombinationsofthetwogoods(pizzaandshakes)thatareontheindifferencecurve(A,B,andC)yieldthesamelevelofutility,sayUtility=100. Havingmoreofgood,yieldsahigherlevelofutility(combinationD)andhavinglessofthegoodsyieldsalowerlevelofutility(combinationE). Anindifferencecurvemapshowsthefamilyofindifferencecurves.Therecouldbeaninfinitenumberofindifferencecurvesthatwouldreflectthelevelofutilityatdifferentcombinationsofthetwogoods.Justasalineonatopographicalmapindicatesthedifferentpointsthatareatthesameelevation,thedifferentpointsalonganindifferencecurve,indicatethatsamelevelofutility. Source:U.S.GeologicalSurvey   MarginalRateofSubstitution Themarginalrateofsubstitutionistheslopeofthecurveandmeasurestherateatwhichtheconsumerwouldbewillingtogiveuponegoodfortheotherwhilemaintainingthesamelevelofutility.Thusthemarginalrateofsubstitutionreflectstheratioofmarginalutilitiesbetweenthetwogoods. Forexample,atpointA,theconsumerwouldbewillingtotradeoneshakeforoneadditionalsliceofpizza. AtpointB,theconsumeralreadyhasalotofpizzabutfewshakessothemarginalutilityfromanadditionalpizzaisrelativelylowerandthemarginalutilityfromtheshakehewouldhavetogiveupwouldberelativelylarge,thustomaintainthesamelevelofutilityhewouldhavetogain3pizzastowillinglygiveuponehalfashake. Sinceanycombinationofthetwogoodswillonlyyieldonelevelofutilityataparticularpointintime,indifferencecurveswillnevercrosseachother. BudgetConstraint Thebudgetconstraintindicatesthecombinationsofthetwogoodsthatcanbepurchasedgiventheconsumer’sincomeandpricesofthetwogoods.Theinterceptpointsofthebudgetconstraintarecomputingbydividingtheincomebythepriceofthegood.Forexample,iftheconsumerhad$8tospendandthepriceofpizzawas$2andshakeswere$1,thentheconsumercouldbuyfourpizzas($8/$2)oreightshakes($8/$1).Anycombinationofthetwogoodsthatareonorbeneaththebudgetconstraintareaffordable,whilethosetotheoutside(fartherfromtheorigin)areunaffordable. Agreaterincomewillcauseaparallelshiftrightwardofthebudgetconstraintwhileadecreaseinincomewillcauseaparallelshiftleftward. Changingthepricesofthegoodschangestheslopeofthebudgetconstraint. Iftheconsumer’sincomeis$8andthepriceofpizzais$2andthepriceofshakesis$1,thenthebudgetconstraintwouldbeBC1.Ifthepriceofpizzadropsto$1,thenthebudgetconstraintwouldrotateoutonthex-axistoBC2.Alternatively,ifthepriceofshakesincreasedtotwodollarsthenthebudgetconstraintwouldbecomeBC3. Theslopeofthebudgetconstraintisthenegativeratiooftheprices(-Px/Py).Forexample,giventhepriceofpizza(onthex-axis)is$2andthepriceofshakes(onthey-axis)is$1,thentheslopeofthebudgetconstraintwouldbe-2. UtlityMaximization Giventhegoalofconsumersistomaximizeutilitygiventheirbudgetconstraints,theyseekthatcombinationofgoodsthatallowsthemtoreachthehighestindifferencecurvegiventheirbudgetconstraint.Thisoccurswheretheindifferencecurveistangenttothebudgetconstraint(combinationA).NotethatcombinationsBandCcostthesameamountasA;however,Aisonahigherindifferencecurve.Combination DyieldsthatsameutilityasCandBbutdoesn’tusealloftheincome,thustheconsumercanincreaseutilitybyconsumingmore.CombinationEispreferredtocombinationA,butisunattainablegiventhebudgetconstraint. Wepreviouslymentionedthatutilityismaximizedwherethemarginalutilityperdollarspentisthesameforeachofthegoods.Atthepointwheretheindifferencecurveistangenttothebudgetconstraint,theslopeoftheindifferencecurvewhichistheratioofmarginalutilities(-MUx/Muy)isequaltotheslopeofthebudgetconstraint(-Pricex/Pricey). Thisequationcanberewrittentoshowthatthemarginalutilityperdollarspentwillbethesameforbothgoods. Thedemandcurvecanbederivedfromtheindifferencecurvesandbudgetconstraintsbychangingthepriceofthegood.Forexample,ifthepriceofpizzais$4,thequantitydemandedofpizzaistwo.Ifthepriceofpizzadecreases,thebudgetconstraintbecomesflatterandtheconsumercanpurchasemorepizza,saythepriceofpizzadropsto$2andconsumerpurchases4units.Ifthepricedropsto$1.33,thequantitydemandedincreasesto5.Plottingeachofthepriceandquantitydemandedpointscreatesthedemandcurveforpizza. IncomeandSubstitutionEffects Whendiscussingwhythedemandcurveisdownwardsloping,weoutlinedthesubstitutioneffectandincomeeffect. Wecanobservethechangesinquantitydemandedalongthedemandcurveduetothechangeinprice;however,theindifferencecurvesandbudgetconstraintscanhelpusanalyzethesizeoftheincomeandsubstitutioneffects. Forexample,saytheconsumersincomeis$15andthepriceofapplesis$1andthepriceoforangesis$3. Atthesepricestheconsumerpurchasessixapplesandthreeoranges.Whenthepriceoforangesfallsto$1,theconsumerpurchaseseightapplesandsevenoranges. Thusonthedemandcurvefororanges,theconsumerpurchasesthreeorangeswhenthepriceisthreedollarsandsevenorangeswhenthepriceisonedollar. Bringingthenewbudgetconstraintbacktotheoriginalindifferencecurveallowsustobreakdowntheincomeandsubstitutioneffects.Sincetheslopeofthebudgetconstraintreflectstheratioofprices,thesubstitutioneffectistheincreaseinthenumberoforangesthatwouldbepurchasedgiventhenewprices,whilestayingontheoriginalindifferencecurvethatismovingfrompointAtopointB. ThemovementfrompointBtopointCistheincomeeffect,theadditionalconsumptionoforangesduetotheincreasedpurchasingpower.Withadecreaseinthepriceoforanges,therelativepriceofappleshasincreasedandfewerappleswouldbeconsumedduetothesubstitutioneffect;however,duetoincreasedpurchasingpower,moreapplesarepurchasedaswellasmoreoranges. Recallfromourelasticitydiscussionthattheincomeelasticityforaninferiorgoodisnegative.Forexample,asincomerisesthedemandforusedclothingdecreases.Lookingatsecond-handclothingonthex-axis,asthepricedeclinesthesubstitutionwillbepositive(movementfrompointAtopointB);however,theincomeeffect(movementfromBtoC)willbenegative. ExtremeCases Whenexaminingindifferencecurvesandbudgetconstraints,wecanlookatafewextremes.Oneextremecasewouldbeifthetwogoodsareperfectcomplements.Forexample,youdonotgetadditionalsatisfactionfromhavinganotherrightshoe,unlessyouhavealeftshoetogowithit.Inthecaseofperfectcomplements,youalwaysconsumeattheminimumcombinationofthetwogoods. Anotherextremeisperfectsubstitutes.Youpurchasepaperineitherthe100or200sheetpacksandonlyvaluethenumberofsheets. Youareindifferentbetweenhavingtwoone-hundredsheetpackagesoronetwo-hundredsheetpackage.Inthecaseofperfectsubstitutes,therearethreedifferentoutcomesthatwillmaximizeutility.Ifthepriceofonepackage,yieldsalowerpersheetcost,theconsumerwillbuyonlythatgood,soconsumptionwilltakeplaceatoneofthetwointercepts.Thethirdoutcomeiswhenthebudgetconstrainthasthesameslopeastheindifferencecurve.Inthiscase,anycombinationalongthebudgetconstraintwillyieldthesamelevelofutility. GovernmentFoodStampsExample Whydoesthegovernmentgivewelfarerecipientsfoodstampsinsteadofcash? Whyarefoodstampssoldontheblackmarketforadiscount?Let’sassumeapersonhas$75ofincomeandreceives$75offoodstampsfromthegovernment.Forsimplicity,wewillassumethatthepriceofeachunitoffoodandthepriceofclothingareeachonedollar.Thebudgetconstraintallowstheconsumertopurchaseupto150unitsoffood,butsincefoodstampscanonlybeusedtopurchasefood,theconsumerislimitedtoonlybeingabletopurchase75unitsofotheritems. Theamountoffoodandothergoods,theindividualwillpurchasedependsontheshapeofhisindifferencecurve. Providedthatthepersonspendsatleast75dollarsonfood,heisnotconstrainedbyreceivingfoodstampsinsteadofcash.   Unfortunately,forthoseindividualswithstrongaddictions,suchascigarettesoralcohol,theirindifferencecurvesreflectthegreatervaluereceivedfromtheaddictsubstance.Sincefoodstampsonlyapplytopurchasingfood,theconsumerisnotabletogetasmuchutilityandisrestrictedtopointA. Ifthefoodstampshadbeenintheformofcash,theconsumerwouldhavepurchased40unitsoffoodand110unitsofalcohol,pointB,whichwouldyieldahigherlevelofutility. Iftheconsumercouldconvertaportionofthefoodstampstocash,evenatadiscount,hewouldbeabletoreachahigherindifferencecurve.Assumethathecantradefoodstampsontheblackmarketfor50centsonthedollarwhichextendshisbudgetconstraintincreasingtheamountofalcoholthatcanbepurchased.SellingfoodstampsatadiscountallowstheconsumertomovetopointC,whichyieldsahigherutilitythanpointA. Wecanalsomodelwhyindividualspurchaseitemstodayandcarrythedebtontheircreditcardspayingahighinterestrate.Forexample,let’ssaythepriceofeachgoodis$1.AssumeWillhas$100ofincomewhichhecouldspendtodayorinvestthemoneyandreceive$150inthefuture.Bywaiting,Willwouldhaveagreaterpurchasingpower,buthisconsumptionbundlewilldependonhispreferences.Ifhehasastrongpreferenceforhavingconsumptiontoday,hewouldbewillingtopayahigherpriceforthosegoodstoday.Thesameistrueforthosewhobuyitemsoncredit.Theyarewillingto paythepurchasepriceplusalltheinterest,sothattheycanhaveittoday(sotheindifferencecurvetouchesthebudgetconstraintatapointclosertothex-axisasseeninthefigure). Similarly,someindividualsarewillingtopaytogototheexpensivetheaterstoseeamoviewhenitisfirstreleased.OtherswillwaituntilitcomestothecheaptheatersorevenuntilitcomesoutonDVD/Blu-ray.Althoughindividualsarepayingforthe“movieexperience”andnotjustthefilmitself, wecanseethetimepreferencesofindividualsandthepricedifferentialsovertime(asrepresentedbydifferentplacementsoftheindifferencecurves).