中级微观经济学 笔记

ECONS301-INTERMEDIATEMICROECONOMICSLECTURENOTESFelixMunoz-Garcia1SchoolofEconomicSciencesWashingtonStateUniversityThisdocumentcontainsasetofpartiallecturenotesthatareintendedtoserveasastartingpointwhencomingtoclass,soeverystudentcancomplementthemwithadditionalexamples,exercisesandapplicationsdiscussedinclass.(Donotquote).1103GHulbertHall,SchoolofEconomicSciences,WashingtonStateUniversity,Pullman,WA99164-6210.e-mail:fmunoz@wsu.edu.Tel.+1-509-335-8402.1  EconS301–IntermediateMicroeconomicsChapter2–DemandandSupply–LecturenotesInchapter2wedealwithdemandandsupplyanalysisinperfectlycompetitivemarkets.Perfectlycompetitivemarketsconsistofalargenumberofbuyersandsellers.Incompetitivemarkets,thetransactionsofanyindividualbuyerorselleraresosmallincomparisontotheoverallvolumeofthegoodortheservicetradedinthemarketthatthebuyerorselleressentially“takes”thepricesetbythemarket.Therefore,weconsiderthistheperfectcompetitionmodelasamodelofprice-takingbehavior.DemandCurve:MarketDemandCurve:Acurvethatshowsusthequantityofgoodthatconsumersarewillingtobuyatdifferentprices.•Forinstance,inthegraphbelow,thedemandcurveshowsustheamountofcornabuyerwouldbewillingtobuyatdifferentprices.Thisillustrationbringsustoacruciallawineconomics,theLawofDemand…LawofDemand:Theinverserelationshipbetweenthepriceofagoodandthequantitydemanded,whenallotherfactorsthatinfluencedemandareheldfixed.Thislawisintuitive,asahigherpricewillmakeconsumerslesswillingtopurchasethatgood.Withalmostallgoods,theconsumerwillbehaveinthismanner,treatingpriceandquantitydemandedasinverselyrelated.Ademandcurvewilltaketheform...Q=a–bPwhere‘a’=verticalintercept,and‘b’=slopeRearrangingandsolvingforP,weget2  P=(a/b)–(Q/b)ThisistheInverseDemandCurve,whichissimplythedemandcurvewhereP=somefunctionofQExample:Demand:Q=100-2PInverseDemand:P=50–(Q/2)•Theverticalinterceptistherefore50andrepresentstheChokePrice,orthepriceatwhichconsumersoftheproductwillnotdesireanyofthegood.•Thehorizontalinterceptistherefore100,andrepresentstheamountofthegoodtheconsumerwouldwanttopurchaseatapriceof0.Ormoregenerally…Demand:Q=a–bPInverseDemand:P=(a/b)–(Q/bChoke Price 3  SupplyCurveMarketSupplyCurve:Acurvethatshowsusthetotalquantityofgoodsthattheirsuppliersarewillingtosellatdifferentprices.Example:SupplyCurve:QS=0.15+Pa)SupplyofwheatifP=$2→QS=.15(2)=2.15P=$3→QS=.15(3)=3.15b)Sketchthesupplycurve…QS=0.15+PandsolvingforP,wegetP=QS–0.15•Sotheslope=1(coefficientofQS)•Intercept=-0.154  EquilibriumAsyoumightguess,themarketequilibriuminaperfectlycompetitivemarketistheintersectionofthesupplyanddemandcurves.Thatis,inequilibrium,aperfectlycompetitivemarketwillsetapriceandquantitysuchthatthereisnoexcesssupplyandnoexcessdemand,hencedemandequalssupply.Example:DemandCurve:Qd=500–4PSupplyCurve:QS=-100+2Pa)Letussketchthesecurvesonthesamegraphwithquantityonthehorizontalaxisandpriceontheverticalaxis.InverseDemandCurve→P=(500/4)–(Qd/4)InverseSupplyCurve→P=(QS/2)+50b)Atwhatpriceandquantitydoyoureachequilibrium?QS=Qd500–4P=-100+2P600=6P100=PAndthentakethisp=100andplugitintoeitherthedemandorsupplycurvetofindtheequilibriumquantity…QS=500–4(100)=100Andso,equilibriumoccursatp=100andQ=100AnIncreaseinDemand,foranygivenpriceWhen P=0, Qd=500‐4.0=500 5  Anincreaseindemandastheonedepictedaboutcanoriginatefromanincreaseinincome,orinconsumer’spreferenceforthegood.Foranygivenprice,thequantitythatconsumersdemandhasnowgoneup.Youcanvisuallyseethatbyextendingalonghorizontaldottedlinewhichmaintainsyourfocusonagiven(fixedprice).Thepointwherethedottedlinecrosseseachdemandcurverepresentsthequantitydemanded.Adecreaseinsupply,foranygivenprice6  Adecreaseinsupplymightoriginatefromanincreaseinproductioncosts,whichleadproducersofthegoodtosupplyloweramountsofthegoodatanygivenprice.[Followsimilargraphicalrepresentationasabove]Example:MarketforAluminumQd=500–50P+10IwhereP=priceandI=incomeQS=-400+50Pa)EquilibriumwhenI=10PluginI=10intoQdtogetQd=500–50P+10(10)=600–50PNowequateQdtoQS,600–50P=-400+50P1000=100P10=P→QS=-400+50(10)=100b)EquilibriumwhenI=5PlugI=5intoQdtogetQd=500–50P+10(5)=550–50PNowequateQdtoQS,550–50P=-400+50P950+100P9.5=P→QS=-400+50(9.5)=75Summarize…Supply P=10 P=9.5 10075P Q 7  AchangeinboththedemandandsupplycurveAdecreaseindemandandanincreaseinsupply:•Unambiguouslyproduceareductionintheequilibriumprice;but…•theeffectontheequilibriumquantityismoreambiguous.Inthefigure,theoutwardshiftinthesupplycurvedominatestheinwardshiftinthedemandcurve,producinganoverallincreaseintheequilibriumquantity.Otherwise,theequilibriumquantitywoulddecrease.PriceElasticityofDemandThepriceelasticityofdemandmeasuresthesensitivityofthequantitydemandedtopricechanges.PriceElasticityofDemand:Ameasureoftherateofpercentagechangeofquantitydemandedwithrespecttoprice,holdingallotherdeterminantsofdemandconstant.Or,itisthepercentagechangeinquantitydemanded(Q)broughtaboutbya1%changeintheprice.ߝொ,௉ൌ%݄ܿܽ݊݃݁݅݊ܳ%݄ܿܽ݊݃݁݅݊ܲൌ∆ܳܳ∆ܲܲൌ∆ܳ∆ܲൈܲܳExample:WhenP=10,quantityisQ=50WhenP=12,quantityisQ=45(So∆Q=-5)ߝொ,௉ൌ∆ܳ∆ܲൈܲܳൌെ52ൈ1050ൌെ0.5Remember,(P/Q)representstheinitialpriceandquantity8  Whyistheelasticityofdemandalwaysnegative?Because(∆Q/∆P)istheslopeofthedemandcurve,whichisnegativebythelawofdemandand(P/Q)isalwayspositivebecauseneitherPnorQcaneverbenegative.ExampleLet’sfindtheelasticitiesfordifferentpricesalongthedemandcurveQ=100–2(P),firstwhen…oA)P=40,soQ=20oB)P=25,soQ=50oC)P=10,soQ=80Remember,thedemandcurveisintheformQ=a–bP,sotheelasticityequationisєd=-b(P/Q)A)Єd=-2(40/20)=-4B)Єd=-2(25/50)=-1C)Єd=-2(10/80)=-(1/4)VerticalIntercept:єd=-2(50/0)=-∞HorizontalIntercept:Єd=-2(0/100)=0Elasticityofdemandinthelineardemandcurve,Q=a-bP9  Usualmistake:saythattheprice-elasticityofdemandisequaltotheslopeofthedemandcurve.NO!Wejustsawthatademandcurvewithaconstantslope(-b)canhavedifferentprice-elasticitiesofdemand,dependingonthepriceatwhichtheelasticityisevaluated.Whydowemakethingssodifficult?Wouldn’titbeeasiertosimplytalkabouttheslopeofthedemandcurve,ratherthantheprice-elasticity?Thereasonweusepriceelasticityofdemand(andnotsimplytheslopeofthedemandcurve)isbecausebyusingtheformerwecanproduceaunit-freemeasureofhowsensitiveisthedemandcurvetochangesinprices.Indeed,notethatunitscanceloutwhenyouusetheformulaofprice-elasticityofdemand,buttheywouldn’tifyouweresimplyusingtheslopeofthedemandcurve.DifferentTypesofElasticitiesofDemandAswehaveseen,elasticitiesshowushowonecomponentofademandequationchangeswithanothercomponent.Sofarwehaveonlycomparedhowquantitydemandedvarieswithprice,inordertoseehowpricesensitivecertaincommoditiesare.Thisanalysis,however,canbeextendedtocomparemorethanjustquantitywithprice.Aswewillshow,wecancomparechangesinquantitywithchangesinincome,orevenwiththepriceofothergoods.ConstantElasticityDemandCurve:AdemandcurveoftheformQ=aP-bwhere‘a’and‘b’arepositiveconstants.Theterm–bisthepriceelasticityofdemandalongthiscurve.•IfwetakethederivativeofQwithrespecttoP,wecanseethattheelasticityissimplythe–bexponentIncomeElasticityofDemand:Theratioofthepercentagechangeinquantitydemandedtothepercentagechangeinincome,holdingpriceandallotherdeterminantsofdemandconstant.ߝொ,ூൌ∆ܳܳ∆ܫܫܽ݊݀ݎ݁ܽݎݎܽ݊݃݅݊݃ߝொ,ூൌ∆ܳ∆ܫܫܳCross-PriceElasticityofDemand:Theratioofthepercentagechangeofthequantityofonegooddemandedwithrespecttothepercentagechangeinthepriceofanothergood.ߝொ೔௉ೕൌ∆ܳ௜ܳ௜∆௝ܲ௝ܲܽ݊݀ݎ݁ܽݎݎܽ݊݃݅݊݃ൌ∆ܳ௜∆௝ܲ௝ܲܳ௜•Forexample,researchshowsthata1%increaseinthepriceoftheNissanSeutracausea0.454%changeinthequantitydemandedoftheFordEscortCokevs.Pepsi10  CokePepsiPriceElasticityofDemandєQ,P-1.47-1.55Cross-PriceElasticityofDemand0.520.64IncomeElasticityofDemand0.581.38SO…a∆1%inthepriceofCokecausesa1.47%dropintheQdofcoke,buta0.52%increaseintheQdofpepsi.Thisshowsusthattheyaresubstitutes,soasthepriceofonerisesconsumerswilldemandlessofthatproductandmoreofitssubstitute.PriceElasticityofSupplyThisisaverysimilaranalysistopriceelasticityofdemand,exceptweareseeinghowsupplyreactstoa1%increaseintheprice.Simply,thiselasticitywilltellushowsensitivequantitysuppliedistothepriceofthatgood.ߝொೄ,௉ൌ∆ܳௌ∆ܲܲܳௌFittingLinearDemandCurvesNowthatweknowhowademandcurveisconstructedandhowtouseitsvariouspartstoanalysistherelationshipbetweenquantitydemand,quantitysupplied,andprice,wecanworkbackwardstoactuallyconstructademandcurve.Moresimply,ifweknowtheprevailingmarketQandPandєQ,P,wecanhaveallthecomponentsweneedtoconstructtheactualdemandcurveequationofQd=a-bP1)ЄQ,P=-b(P/Q)→So…b=-єQ,P(Q/P)2)Q=a–bP→So…a=Q+bPa=Q+(-єQ,P(Q/P))Pa=Q+(-єQ,P(Q))a=(1-єQ,P)Q1 CHAPTER3-ConsumerPreferencesandUtility•Bundle(food,clothing)-eachbundle/basketisrepresentedbyapointonthegraphbelow.Therearethreeassumptionsthatmustholdtrueinconsumerpreferencetheory.•Consumerpreferences:Thesethreepreferencesmustholdtrueand1.CompleteÆÆabilitytocompare,eitherA>BorB>A,orA~B(inotherwordstheconsumerhastostatetheirpreferences.WhethertheypreferAoverB,orBoverAoriftheybothmakethemequallyhappy.)2.TransitiveÆÆifA>BandB>C,thenA>C(thechoicesthattheconsumermakesmustbeconsistentwitheachother.Explainingthesymbolsabove,theconsumerprefersAoverB,andBoverC,suchthattheconsumershouldpreferAoverC)Exampleofnon-transitivepreferences:“Iwouldratherhavetwocookiesthanaglassofmilk.AndIwouldratherhaveaglassofmilkthanasliceofpizza.However(puzzlingly)Iwouldratherhaveasliceofpizzathantwocookies.”3.Nonsatiated(moreisbetter)-afairlyeasyconcepttounderstandbecauseaconsumershouldprefertwohotdogstoone,andthreehotdogstotwo.Asconsumerswewantmore.•RankingSystems:•Therearetwotypeofrankingsystemsthatthebookreferences.Rationality 2 1)OrdinalRanking:allowsustogatherinformationabouttheorderinwhichaconsumerranksabundle.WecanknowthataconsumerprefersbasketAtoBbutnothowmuchmoretheypreferit.2)CardinalRanking:allowsustoanswertheintensityatwhichaconsumerprefersonebundletoanother.Forexample,IlikebasketAtwiceasmuchasbasketB.Itisusuallyhardforconsumerstoarticulatetheirintensitybutbothrankingsystemsareimportanttorecognize.•UtilityFunction:measuresthelevelofsatisfactionfromconsumingdifferentbundles.Itrepresentstheconsumer’spreferences.TheunitofmeasurementisUtils,whichdoesnothaveareallifetranslation.Insteadofconsideringtheabsoluteornumericalvalueforthelevelofsatisfactionwecomparerelativevalues.Forexample,theconsumerreceivesmoreutilityfromconsuminganorangethanfromconsuminganapple.Differentconsumersmayhavedifferentutilityfunctions.ThusknowingthatJohnreceives5UtilsfromconsuminganappleandJillreceives6Utilsdoesnotgiveusanyusefulinformation.IfweknewJohnreceived7UtilsfromconsuminganorangewecouldsaythatJohnwouldprefertoconsumeanorangemorethananapple.Butagainwecanonlycomparerelativevalues.WecanthinkofUtilsasaconsumerslevelofhappinessinconsumingonegood.Let’sbeginwithjustonegood,u(y)=(y)1/2.Thisutilityfunctionrepresentsconsumerpreferencesthatsatisfy:1)CompletenessForanyA,Bwehaveu(A)≥or≤u(B)thatindicateseitherA>B,A<B,orA~B.2)TransitiveForexamplewhatif:A=1,B=4,C=5,thenu(A)=(1)1/2=1u(B)=(4)1/2=2u(C)=(3)1/2>2Thusifu(A)>u(B)andu(B)>u(C),thenwehavethatu(A)>u(C).ThereforethepreferencesaretransitivebecauseifA>BandB>CthenA>C3)Non-satiation(moreisbetter)Indeedissatisfiedsinceu(C)>u(B)>u(A)3 Marginalutility:rateatwhichutilitychangesasconsumptionincreases.Oftenthoughtofas,howmuchbetteroffwewouldbeifwereceivedonemoreofsomething.Inmathematicaltermsasyouwillseebelow,themarginalutilityisthefirstderivativeoftheutilityfunction.MUy=du/dy=changeinu/changeinyEachrepresentationisequivalent.MUy=∆u/∆y=∂U(y)/∂yExample:Ifu(y)=(y)1/2,then∂u/∂y=½y1/2-1=½y-1/2=½(1/y1/2)=1/(2y1/2)MUy (at y=4)=slope of U at y=4 4 Diminishingmarginalutility:additionalunitsaddlessutility(∆Usmallerandsmaller)butwewillassumethat∆U>0always.Thatis,moreisalwaysbetter,althoughitisnotasgoodasthelastunitconsumed.Therearethreeimportantpointsinmindwhendrawingtotalandmarginalutilitycurves.1)TotalUtilityandmarginalutilitycannotbeplottedonthesamegraph,becausetheY-axisvariablediffersoneachgraph.2)Themarginalutilityfunctionistheslopeofthetotalutilityfunction.3)Therelationshipbetweentotalandmarginalutilityholdsforothermeasuresineconomicsthatwillbediscussedlateron.Forexample:copiesofthesameDVDmovie.Whenyougetthefirstoneyou’reveryexcitedandvaluetheDVDmoviegreatly.Whenyougetasecondoneyou’renotashappybecauseyoualreadyownacopyoftheDVD.Thepropertythatyoureceivelessutilityfromthe2ndcopyoftheDVDthanthe1stcopyandlessutilityfromthe3rdcopythanfromthe2ndcopyiscalleddiminishingmarginalutility.Ismorealwaysbetter?MorethanonegoodExampleUtilityfunction:U(x,y)=(x×y)1/2=x1/2×y1/2Ifx=2,y=8thenweplugintotheutilityfunctiontofindÎ(2×8)1/2=(16)1/2=4utils.Inthe3DgraphbelowpointsA,B,andCallrepresentthesamelevelofutilityx=4,y=4Î4utilsx=8,y=2Î4utilsx=2,y=8Î4utils5 MUx=∆U/∆x│yisheldconstant=∂U(x,y)/∂x│yisheldconstantMUy=∆U/∆y│xisheldconstant=∂U(x,y)/∂y│xisheldconstantThisnotationrepresentspartialderivatives.Whenwetakeaderivativewithrespecttoxwemustholdyconstant.Forexampleifxisapplesandyisoranges.Wewouldtakeapartialderivativewithrespecttoxinordertofindouthowmuchutilityincreasesfromconsumingonemoreapple.Wemustholdthenumberoforangesconsumedconstantbecauseconsumingmoreorangeswouldalsocauseutilitytoincrease.Calculusexample:ThenMUx=∂U(x,y)/∂x=½x-1/2×y1/2=1/(2x1/2)y1/2MUy=∂U(x,y)/∂y=½x1/2×y-1/2=1/(2y1/2)x1/2Learning-by-doing3.1U(x,y)=(x×y)1/21.Satisfiesmoreisbetter?2.Satisfiesdiminishingmarginalutility?1.Moreisbettercanbecheckedintwodifferentways:a)IncreaseinxÎincreaseinUandincreaseinyÎincreaseinUb)MUx>0andMUy>0foranyx,y>02.Diminishingmarginalutilityjusttellsusthattheadditionalutilitywegetfromconsumingamountofgoodsissmallerandsmaller.TheadditionalutilitywegetfromconsumingadditionalgoodsisMUxandMUy.Sowenoticethat:6 MUxisdecreasinginx(xisinthedenominator)MUyisdecreasinginy(yisinthedenominator)Mathematicallywemaytakeaderivativetwicetocheckfordiminishingmarginalutility.a)MUxx<0andMUyy<0foranyx,y>0Indifferencecurves:curvesconnectingconsumptionbundlesthatyieldthesamelevelofutility.Properties:1)Whentheconsumerlikesbothgoods(MUx>0,MUy>0),indifferencecurvesarenegativelysloped(Figure)2)Indifferencecurvescannotintercept.Theycannotintersectbecauseiftheydid,thenabundlecouldcreattwodifferentlevelsofutilitywhichwoulddestroyrationalthinking.IntheFiguretheICsincreasetotheNortheast(upperright)3)EveryconsumptionbundleliesononeandonlyoneIC(Figure)4)ICsarenotthickTheyarenotthickbecausethenitwouldviolatethemoreisbetterassumptionifabundlewithmoreofonegoodandaconstantamountoftheotherwouldcreatethesameutils.7 MRS(marginalrateofsubstitution)Therateatwhichaconsumerwillgiveuponegoodtogetoneadditionalunitofanothergood,keepinghisorherutilitylevelconstant.Inourearlierexampletheconsumergetsthesameutilityfrom4xand4yasshedoesfrom8xand2y.Thisinthesecondsituationshe’dbeexactlyindifferentbetweenatradeof4xfor2y.InthissituationwewouldsaytheMRSofxforyis4for2,or2for1,orjust2.GraphdepictingMRSMovingalongthecurveweseeiftheconsumerhasalotofgoodxshewilltradealotofgoodxforasingleunitofgoody.Inthesamewayiftheconsumerhasalotofgoodyshewilltradealotofgoodyforasingleunitofgoodx.ThisisknownasdiminishingMRS.∆y/∆xistherateatwhichtheconsumerisgivingupyinordertogetanadditionalunitofx.MRSx,y=-slopeofI.C.=MUx/MUyTotallydifferentiatingDiminishingMRSInitiallyyouarewillingtogiveupmanyglassesoflemonade(y)formadditionalhamburgers(x).Whenyouhavefewglassesoflemonadeandmanyhamburgersyouwillnotbewillingtogiveupasmany(ornone)glassesoflemonadeinordertogetanadditionalhamburger.8 Totallydifferentiallyxandy(sinceIamloweringyinordertogetmoreofx),weobtain-MRS=slopeofInd.CurveMRS=-slopeofInd.CurveICsarebowedintowardtheorigin.Application3.2.DemandforattributesincarsU(x,y)=(x×y)1/2wherexishorsepoweryisgasmileageMRSx,yrepresentshowatypicalconsumerwillbewillingtoforgohorsepowerxinordertogetanadditionalmilepergallon(y).In1969,MRSx,y=3.79Δu=MUxΔx+MUyΔy−MUxΔx=MUyΔy−MUxMUy=ΔyΔx9 In1986,MRSx,y=0.71Thedecreasemeansthatpeoplebecamemorewillingtogiveuphorsepowerinordertogetanadditionalmilepergallon(y).Learning-by-doing3.3U(x,y)=x×yMUx=∂U(x,y)/∂x=yMUy=∂U(x,y)/∂y=xa)•DrawtheICcorrespondinglytoU1=128x×y=128inmanyofitscombinationsForexample,G:x=8,y=16H:x=16,y=8I:x=32,y=4•DoesI.C.intersecteitheraxis?No,ifICintersectsx-axis,theny=0,ÆU1=0≠128y-axis,thenx=0,ÆU1=0≠128•DoesICindicatethatMRSx,yisdiminishing?Yes,sinceICisbowedintowardtheorigin.and connect them  10 NotethatMRSx,y=MUx/MUy=y/xsowemorefromlefttotheright(∆x),wegetsmallerratios,ÎsmallerMRSx,y(diminishing).b)Similar,butforU2=200Notgraded:Learning-by-doing3.4.IncreasingMRSx,yU=Ax2+By2ÆMUx=2AxMUy=2BySpecialUtilityFunctions-Therearecertaingoodsthatwillcreateuniqueutilityfunctions.ThesefunctionsareimportanttorecognizebecausetheywillnotalwayshavediminishingMRS,anditisimportanttocheckwhattypeofutilityfunctionyourworkingwith.PerfectSubstitutes:AquafinaversusDasanibottledwaterorKingstonversusScandiskmemorysticks.Closesubstitutes:butterversusmargarineorcoffeeversusblacktea.MRSB,M=MRSM,B=1ÅbutitcanbeanyconstantExampleMRS = 2Ax/2By = Ax/By, which increases in x MRSx,y=MUxMUy=2Ax2Ay=AxBy,whichincreasesinx11 U=aB+aM,thenMUB=aandMUM=aHence,MRSB,M=MUB/MUM=a/a=1Then,slopeofIC=-1Example:PancakesandWafflesU=P+2W,MUp=1andMUW=2Theconsumerisalwayswillingtotrade2pancakesfor1waffle.MRSP,W=MUP/MUW=½ÎslopeofIC=-1/2ConstantslopeofIC-perfectsubstituteswillalwayshavealinearindifferencecurveandarethesimplesttosketch.ConstantMRS(notdiminishingasinpreviousexamples)Similarly,U=ax+by,MRSx,y=a/bPerfectcomplimentsleftshoeandrightshoe(consumerwantstheminfixedproportions),ortwoscoopsofpeanutbuttertoonescoopofjellyfortheperfectPB&Jsandwhich.Example:U=10×min(R,L)12 GÆR=2andL=2,thenU2=10×2=20HÆR=3andL=2,thenU2=10×2=20(consumptionchoicesshouldbeatthekink)�SlopeofIC(MRS)is:�ZeroattheflatsegmentoftheIC�InfinityattheverticalsegmentoftheICUndefinedatthekinkoftheIC(infinitelymanyslopesCobb-DouglasU=(x×y)1/2andU=x×yareexamplesofCobb-DouglasutilityfunctionsGenerally,U=Axαyβifα=β=½,thenU=Ax1/2y1/2=A(xy)1/2ifα=β=1andA=1,thenU=xyProperties:1)MUx>0andMUy>0.Thatis,“moreisbetter”issatisfiedMUx=∂U(x,y)/∂x=Aαxα-1yβ>0foranyxMUy=∂U(x,y)/∂y=Aβxαyβ-1>0foranyy2)SinceMUx>0andMUy>0,thenICisdownwardslopping(recallproperty1ofICs)[whataboutthecaseinwhichtheconsumerdislikessomegoods,MUx<0?ReviewSession]13 3)DiminishingMRSx,y:MRSx,y=Aαxα-1yβ/Aβxαyβ-1=α/β×xα-1-α×yβ-(β-1)=α/β×1/x×y=α/β×y/xThemovementsfromlefttoright(∆x)willshrinkthisratio,andreduceMRSx,yÎDiminishingMRSx,yQuasi-LinearpreferencesUsedineconomicapplicationsforsituationsinwhichtheamountofacommodity(suchastoothpasteorgarlic)doesn’tchangeverymuchtoincome.ICsareparalleldisplacementstoeachotherGeneralformU(x,y)=ν(x)+by(lineariny,butnotgenerallylinearinx)whereν(x)isafunctionthatincreasesinx,suchasν(x)=(x)1/2orν(x)=x2.whereb>0.Forexampleyoumake$400dollarsandspend$5ontoothpasteand$395onpizza.Withquasi-linearpreferencesifgotabetterjobandmade$500dollarsyouwouldstillspend$5