范里安微觀經(jīng)濟學現(xiàn)代觀點原版講義

ChapterOneTheMarketTheTheoryofEconomicsdoesnot

furnishabodyofsettledconclusions

immediatelyapplicabletopolicy.Itis

amethodratherthanadoctrine,an

apparatusofthemind,atechniqueof

thinkingwhichhelpsitspossessorto

drawcorrectconclusions

---JohnMaynardKeynesEconomicModelingWhatcauseswhatineconomicsystems?Atwhatlevelofdetailshallwemodelaneconomicphenomenon?Whichvariablesaredeterminedoutsidethemodel(exogenous)andwhicharetobedeterminedbythemodel(endogenous)?ModelingtheApartmentMarketHowareapartmentrentsdetermined?Supposeapartmentsarecloseordistant,butotherwiseidenticaldistantapartmentsrentsareexogenousandknownmanypotentialrentersandlandlordsModelingtheApartmentMarketWhowillrentcloseapartments?Atwhatprice?Willtheallocationofapartmentsbedesirableinanysense?

Howcanweconstructaninsightfulmodeltoanswerthesequestions?EconomicModelingAssumptionsTwobasicpostulates:RationalChoice:Eachpersontriestochoosethebestalternativeavailabletohimorher.Equilibrium:Marketpriceadjustsuntilquantitydemandedequalsquantitysupplied.ModelingApartmentDemandDemand:Supposethemostanyonepersoniswillingtopaytorentacloseapartmentis$500/month.Then p=$500

QD=1.Supposethepricehastodropto$490beforea2ndpersonwouldrent.Then p=$490

QD=2.ModelingApartmentDemandTheloweristherentalratep,thelargeristhequantityofcloseapartmentsdemanded

p

QD

.Thequantitydemandedvs.pricegraphisthemarketdemandcurveforcloseapartments.MarketDemandCurveforApartmentspQDModelingApartmentSupplySupply:Ittakestimetobuildmorecloseapartmentssointhisshort-runthequantityavailableisfixed(atsay100).MarketSupplyCurveforApartmentspQS100CompetitiveMarketEquilibrium“l(fā)ow”rentalprice

quantitydemandedofcloseapartmentsexceedsquantityavailable

pricewillrise.“high”rentalprice

quantitydemandedlessthanquantityavailable

pricewillfall.CompetitiveMarketEquilibriumQuantitydemanded=quantityavailable

pricewillneitherrisenorfallsothemarketisatacompetitiveequilibrium.CompetitiveMarketEquilibriumpQD,QS100CompetitiveMarketEquilibriumpQD,QSpe100CompetitiveMarketEquilibriumpQD,QSpe100Peoplewillingtopaypeforcloseapartmentsgetcloseapartments.CompetitiveMarketEquilibriumpQD,QSpe100Peoplewillingtopaypeforcloseapartmentsgetcloseapartments.Peoplenotwillingtopay

peforcloseapartments

getdistantapartments.CompetitiveMarketEquilibriumQ:Whorentsthecloseapartments?A:Thosemostwillingtopay.Q:Whorentsthedistantapartments?A:Thoseleastwillingtopay.Sothecompetitivemarketallocationisby“willingness-to-pay”.ComparativeStaticsWhatisexogenousinthemodel?priceofdistantapartmentsquantityofcloseapartmentsincomesofpotentialrenters.Whathappensiftheseexogenousvariableschange?ComparativeStaticsSupposethepriceofdistantapartmentrises.Demandforcloseapartmentsincreases(rightwardshift),causingahigherpriceforcloseapartments.MarketEquilibriumpQD,QSpe100MarketEquilibriumpQD,QSpe100HigherdemandMarketEquilibriumpQD,QSpe100Higherdemandcauseshigher

marketprice;samequantity

traded.ComparativeStaticsSupposethereweremorecloseapartments.Supplyisgreater,sothepriceforcloseapartmentsfalls.MarketEquilibriumpQD,QSpe100MarketEquilibriumpQD,QS100HighersupplypeMarketEquilibriumpQD,QSpe100Highersupplycausesa

lowermarketpriceanda

largerquantitytraded.ComparativeStaticsSupposepotentialrenters’incomesrise,increasingtheirwillingness-to-payforcloseapartments.Demandrises(upwardshift),causinghigherpriceforcloseapartments.MarketEquilibriumpQD,QSpe100MarketEquilibriumpQD,QSpe100Higherincomescause

higherwillingness-to-payMarketEquilibriumpQD,QSpe100Higherincomescause

higherwillingness-to-pay,

highermarketprice,and

thesamequantitytraded.

TaxationPolicyAnalysisLocalgovernmenttaxesapartmentowners.Whathappenstopricequantityofcloseapartmentsrented?Isanyofthetax“passed”torenters?TaxationPolicyAnalysisMarketsupplyisunaffected.Marketdemandisunaffected.Sothecompetitivemarketequilibriumisunaffectedbythetax.Priceandthequantityofcloseapartmentsrentedarenotchanged.Landlordspayallofthetax.ImperfectlyCompetitiveMarketsAmongstmanypossibilitiesare:amonopolisticlandlordaperfectlydiscriminatorymonopolisticlandlordacompetitivemarketsubjecttorentcontrol.AMonopolisticLandlordWhenthelandlordsetsarentalpricepherentsD(p)apartments.Revenue=pD(p).Revenueislowifp

0RevenueislowifpissohighthatD(p)0.Anintermediatevalueforpmaximizesrevenue.MonopolisticMarketEquilibriumpQDLow

priceLowprice,highquantity

demanded,lowrevenue.MonopolisticMarketEquilibriumpQDHigh

priceHighprice,lowquantity

demanded,lowrevenue.MonopolisticMarketEquilibriumpQDMiddle

priceMiddleprice,mediumquantity

demanded,largerrevenue.MonopolisticMarketEquilibriumpQD,QSMiddle

priceMiddleprice,mediumquantity

demanded,largerrevenue.

Monopolistdoesnotrentallthe

closeapartments.100MonopolisticMarketEquilibriumpQD,QSMiddle

priceMiddleprice,mediumquantity

demanded,largerrevenue.

Monopolistdoesnotrentallthe

closeapartments.100Vacantcloseapartments.PerfectlyDiscriminatoryMonopolisticLandlordImaginethemonopolistkneweveryone’swillingness-to-pay.Charge$500tothemostwilling-to-pay,charge$490tothe2ndmostwilling-to-pay,etc.DiscriminatoryMonopolisticMarketEquilibriumpQD,QS100p1=$5001DiscriminatoryMonopolisticMarketEquilibriumpQD,QS100p1=$500p2=$49012DiscriminatoryMonopolisticMarketEquilibriumpQD,QS100p1=$500p2=$49012p3=$4753DiscriminatoryMonopolisticMarketEquilibriumpQD,QS100p1=$500p2=$49012p3=$4753DiscriminatoryMonopolisticMarketEquilibriumpQD,QS100p1=$500p2=$49012p3=$4753peDiscriminatorymonopolist

chargesthecompetitivemarket

pricetothelastrenter,and

rentsthecompetitivequantity

ofcloseapartments.RentControlLocalgovernmentimposesamaximumlegalprice,pmax<pe,thecompetitiveprice.MarketEquilibriumpQD,QSpe100MarketEquilibriumpQD,QSpe100pmaxMarketEquilibriumpQD,QSpe100pmaxExcessdemandMarketEquilibriumpQD,QSpe100pmaxExcessdemandThe100closeapartmentsarenolongerallocatedby

willingness-to-pay(lottery,lines,

largefamiliesfirst?).WhichMarketOutcomesAreDesirable?Whichisbetter?RentcontrolPerfectcompetitionMonopolyDiscriminatorymonopolyParetoEfficiencyVilfredoPareto;1848-1923.AParetooutcomeallowsno“wastedwelfare”;i.e.theonlywayoneperson’swelfarecanbeimprovedistoloweranotherperson’swelfare.ParetoEfficiencyJillhasanapartment;Jackdoesnot.Jillvaluestheapartmentat$200;Jackwouldpay$400forit.JillcouldsublettheapartmenttoJackfor$300.Bothgain,soitwasParetoinefficientforJilltohavetheapartment.ParetoEfficiencyAParetoinefficientoutcomemeansthereremainunrealizedmutualgains-to-trade.Anymarketoutcomethatachievesallpossiblegains-to-trademustbeParetoefficient.ParetoEfficiencyCompetitiveequilibrium:allcloseapartmentrentersvaluethematthemarketpricepeormoreallothersvaluecloseapartmentsatlessthanpesonomutuallybeneficialtradesremainsotheoutcomeisParetoefficient.ParetoEfficiencyDiscriminatoryMonopoly:assignmentofapartmentsisthesameaswiththeperfectlycompetitivemarketsothediscriminatorymonopolyoutcomeisalsoParetoefficient.ParetoEfficiencyMonopoly:notallapartmentsareoccupiedsoadistantapartmentrentercouldbeassignedacloseapartmentandhavehigherwelfarewithoutloweringanybodyelse’swelfare.sothemonopolyoutcomeisParetoinefficient.ParetoEfficiencyRentControl:somecloseapartmentsareassignedtorentersvaluingthematbelowthecompetitivepricepesomerentersvaluingacloseapartmentabovepedon’tgetcloseapartmentsParetoinefficientoutcome.HarderQuestionsOvertime,willthesupplyofcloseapartmentsincrease?rentcontroldecreasethesupplyofapartments?amonopolistsupplymoreapartmentsthanacompetitiverentalmarket?ChapterTwoBudgetaryandOtherConstraintsonChoiceConsumptionChoiceSetsAconsumptionchoicesetisthecollectionofallconsumptionchoicesavailabletotheconsumer.Whatconstrainsconsumptionchoice?Budgetary,timeandotherresourcelimitations.BudgetConstraintsAconsumptionbundlecontainingx1unitsofcommodity1,x2unitsofcommodity2andsoonuptoxnunitsofcommoditynisdenotedbythevector(x1,x2,…,xn).Commoditypricesarep1,p2,…,pn.BudgetConstraintsQ:Whenisaconsumptionbundle

(x1,…,xn)affordableatgivenpricesp1,…,pn?BudgetConstraintsQ:Whenisabundle(x1,…,xn)affordableatpricesp1,…,pn?A:When

p1x1+…+pnxn

￡

m

wheremistheconsumer’s(disposable)income.BudgetConstraintsThebundlesthatareonlyjustaffordableformtheconsumer’sbudgetconstraint.Thisistheset

{(x1,…,xn)|x130,…,xn

30and

p1x1+…+pnxn

=

m}.

BudgetConstraintsTheconsumer’sbudgetsetisthesetofallaffordablebundles;

B(p1,…,pn,m)=

{(x1,…,xn)|x1

30,…,xn

30and

p1x1+…+pnxn

￡

m}Thebudgetconstraintistheupperboundaryofthebudgetset.BudgetSetandConstraintforTwoCommoditiesx2x1Budgetconstraintisp1x1+p2x2=m.m/p1m/p2BudgetSetandConstraintforTwoCommoditiesx2x1Budgetconstraintisp1x1+p2x2=m.m/p2m/p1BudgetSetandConstraintforTwoCommoditiesx2x1Budgetconstraintisp1x1+p2x2=m.m/p1Justaffordablem/p2BudgetSetandConstraintforTwoCommoditiesx2x1Budgetconstraintisp1x1+p2x2=m.m/p1JustaffordableNotaffordablem/p2BudgetSetandConstraintforTwoCommoditiesx2x1Budgetconstraintisp1x1+p2x2=m.m/p1AffordableJustaffordableNotaffordablem/p2BudgetSetandConstraintforTwoCommoditiesx2x1Budgetconstraintisp1x1+p2x2=m.m/p1BudgetSet

thecollection

ofallaffordablebundles.m/p2BudgetSetandConstraintforTwoCommoditiesx2x1p1x1+p2x2=misx2=-(p1/p2)x1+m/p2soslopeis-p1/p2.m/p1BudgetSetm/p2BudgetConstraintsIfn=3whatdothebudgetconstraintandthebudgetsetlooklike?BudgetConstraintforThreeCommoditiesx2x1x3m/p2m/p1m/p3p1x1+p2x2+p3x3=mBudgetSetforThreeCommoditiesx2x1x3m/p2m/p1m/p3{(x1,x2,x3)|x1

30,x230,x3

3

0andp1x1+p2x2+p3x3

￡

m}BudgetConstraintsForn=2andx1onthehorizontalaxis,theconstraint’sslopeis-p1/p2.Whatdoesitmean?

BudgetConstraintsForn=2andx1onthehorizontalaxis,theconstraint’sslopeis-p1/p2.Whatdoesitmean?

Increasingx1by1mustreducex2byp1/p2.BudgetConstraintsx2x1Slopeis-p1/p2+1-p1/p2BudgetConstraintsx2x1+1-p1/p2Opp.costofanextraunitof

commodity1isp1/p2units

foregoneofcommodity2.BudgetConstraintsx2x1Opp.costofanextraunitof

commodity1isp1/p2units

foregoneofcommodity2.And

theopp.costofanextra

unitofcommodity2is

p2/p1unitsforegone

ofcommodity1.-p2/p1+1BudgetSets&Constraints;IncomeandPriceChangesThebudgetconstraintandbudgetsetdependuponpricesandincome.Whathappensaspricesorincomechange?Howdothebudgetsetandbudgetconstraintchangeasincomemincreases?Originalbudgetsetx2x1HigherincomegivesmorechoiceOriginalbudgetsetNewaffordableconsumption

choicesx2x1Originalandnewbudgetconstraintsareparallel(sameslope).Howdothebudgetsetandbudgetconstraintchangeasincomemdecreases?Originalbudgetsetx2x1Howdothebudgetsetandbudgetconstraintchangeasincomemdecreases?x2x1New,smallerbudgetsetConsumptionbundlesthatarenolongeraffordable.Oldandnewconstraintsareparallel.BudgetConstraints-IncomeChangesIncreasesinincomemshifttheconstraintoutwardinaparallelmanner,therebyenlargingthebudgetsetandimprovingchoice.BudgetConstraints-IncomeChangesIncreasesinincomemshifttheconstraintoutwardinaparallelmanner,therebyenlargingthebudgetsetandimprovingchoice.Decreasesinincomemshifttheconstraintinwardinaparallelmanner,therebyshrinkingthebudgetsetandreducingchoice.BudgetConstraints-IncomeChangesNooriginalchoiceislostandnewchoicesareaddedwhenincomeincreases,sohigherincomecannotmakeaconsumerworseoff.Anincomedecreasemay(typicallywill)maketheconsumerworseoff.BudgetConstraints-PriceChangesWhathappensifjustonepricedecreases?Supposep1decreases.Howdothebudgetsetandbudgetconstraintchangeasp1

decreasesfromp1’top1”?Originalbudgetsetx2x1m/p2m/p1’m/p1”-p1’/p2Howdothebudgetsetandbudgetconstraintchangeasp1

decreasesfromp1’top1”?Originalbudgetsetx2x1m/p2m/p1’m/p1”Newaffordablechoices-p1’/p2Howdothebudgetsetandbudgetconstraintchangeasp1

decreasesfromp1’top1”?Originalbudgetsetx2x1m/p2m/p1’m/p1”NewaffordablechoicesBudgetconstraintpivots;slopeflattensfrom-p1’/p2to-p1”/p2-p1’/p2-p1”/p2BudgetConstraints-PriceChangesReducingthepriceofonecommoditypivotstheconstraintoutward.Nooldchoiceislostandnewchoicesareadded,soreducingonepricecannotmaketheconsumerworseoff.BudgetConstraints-PriceChangesSimilarly,increasingonepricepivotstheconstraintinwards,reduceschoiceandmay(typicallywill)maketheconsumerworseoff.UniformAdValoremSalesTaxesAnadvaloremsalestaxleviedatarateof5%increasesallpricesby5%,frompto(1+0×05)p=1×05p.Anadvaloremsalestaxleviedatarateoftincreasesallpricesbytpfrompto(1+t)p.Auniformsalestaxisapplieduniformlytoallcommodities.UniformAdValoremSalesTaxesAuniformsalestaxleviedatratetchangestheconstraintfrom

p1x1+p2x2=m

to

(1+t)p1x1+(1+t)p2x2=mUniformAdValoremSalesTaxesAuniformsalestaxleviedatratetchangestheconstraintfrom

p1x1+p2x2=m

to

(1+t)p1x1+(1+t)p2x2=m

i.e.

p1x1+p2x2=m/(1+t).UniformAdValoremSalesTaxesx2x1p1x1+p2x2=mUniformAdValoremSalesTaxesx2x1p1x1+p2x2=mp1x1+p2x2=m/(1+t)UniformAdValoremSalesTaxesx2x1Equivalentincomeloss

isUniformAdValoremSalesTaxesx2x1Auniformadvalorem

salestaxleviedatratet

isequivalenttoanincome

taxleviedatrateTheFoodStampProgramFoodstampsarecouponsthatcanbelegallyexchangedonlyforfood.Howdoesacommodity-specificgiftsuchasafoodstampalterafamily’sbudgetconstraint?TheFoodStampProgramSupposem=$100,pF=$1andthepriceof“othergoods”ispG=$1.Thebudgetconstraintisthen

F+G=100.TheFoodStampProgramGF100100F+G=100;beforestamps.TheFoodStampProgramGF100100F+G=100:beforestamps.TheFoodStampProgramGF100100F+G=100:beforestamps.Budgetsetafter40food

stampsissued.14040TheFoodStampProgramGF100100F+G=100:beforestamps.Budgetsetafter40food

stampsissued.140Thefamily’sbudget

setisenlarged.40TheFoodStampProgramWhatiffoodstampscanbetradedonablackmarketfor$0.50each?TheFoodStampProgramGF100100F+G=100:beforestamps.Budgetconstraintafter40

foodstampsissued.140120Budgetconstraintwith

blackmarkettrading.40TheFoodStampProgramGF100100F+G=100:beforestamps.Budgetconstraintafter40

foodstampsissued.140120Blackmarkettrading

makesthebudget

setlargeragain.40BudgetConstraints-RelativePrices“Numeraire”means“unitofaccount”.Supposepricesandincomearemeasuredindollars.Sayp1=$2,p2=$3,m=$12.Thentheconstraintis

2x1+3x2=12.BudgetConstraints-RelativePricesIfpricesandincomearemeasuredincents,thenp1=200,p2=300,m=1200andtheconstraintis

200x1+300x2=1200,

thesameas

2x1+3x2=12.Changingthenumerairechangesneitherthebudgetconstraintnorthebudgetset.BudgetConstraints-RelativePricesTheconstraintforp1=2,p2=3,m=12

2x1+3x2=12

isalso1.x1+(3/2)x2=6,

theconstraintforp1=1,p2=3/2,m=6.Settingp1=1makescommodity1thenumeraireanddefinesallpricesrelativetop1;e.g.3/2isthepriceofcommodity2relativetothepriceofcommodity1.BudgetConstraints-RelativePricesAnycommoditycanbechosenasthenumerairewithoutchangingthebudgetsetorthebudgetconstraint.BudgetConstraints-RelativePricesp1=2,p2=3andp3=6

priceofcommodity2relativetocommodity1is3/2,priceofcommodity3relativetocommodity1is3.Relativepricesaretheratesofexchangeofcommodities2and3forunitsofcommodity1.ShapesofBudgetConstraintsQ:Whatmakesabudgetconstraintastraightline?A:Astraightlinehasaconstantslopeandtheconstraintis

p1x1+…+pnxn=m

soifpricesareconstantsthenaconstraintisastraightline.ShapesofBudgetConstraintsButwhatifpricesarenotconstants?E.g.bulkbuyingdiscounts,orpricepenaltiesforbuying“toomuch”.Thenconstraintswillbecurved.ShapesofBudgetConstraints-QuantityDiscountsSupposep2isconstantat$1butthatp1=$2for0￡x1

￡20andp1=$1forx1>20.ShapesofBudgetConstraints-QuantityDiscountsSupposep2isconstantat$1butthatp1=$2for0￡x1

￡20andp1=$1forx1>20.Thentheconstraint’sslopeis

-2,for0￡x1

￡20

-p1/p2=

-1,forx1>20

andtheconstraintis{ShapesofBudgetConstraintswithaQuantityDiscountm=$1005010020Slope=-2/1=-2

(p1=2,p2=1)Slope=-1/1=-1

(p1=1,p2=1)80x2x1ShapesofBudgetConstraintswithaQuantityDiscountm=$1005010020Slope=-2/1=-2

(p1=2,p2=1)Slope=-1/1=-1

(p1=1,p2=1)80x2x1ShapesofBudgetConstraintswithaQuantityDiscountm=$100501002080x2x1BudgetSetBudgetConstraintShapesofBudgetConstraintswithaQuantityPenaltyx2x1BudgetSetBudgetConstraintShapesofBudgetConstraints-OnePriceNegativeCommodity1isstinkygarbage.Youarepaid$2perunittoacceptit;i.e.p1=-$2.p2=$1.Income,otherthanfromacceptingcommodity1,ism=$10.Thentheconstraintis

-2x1+x2=10orx2=2x1+10.ShapesofBudgetConstraints-OnePriceNegative10Budgetconstraint’sslopeis-p1/p2=-(-2)/1=+2x2x1x2=2x1+10ShapesofBudgetConstraints-OnePriceNegative10x2x1

Budgetsetis

allbundlesfor

whichx1

30,

x2

30andx2

￡2x1+10.MoreGeneralChoiceSetsChoicesareusuallyconstrainedbymorethanabudget;e.g.timeconstraintsandotherresourcesconstraints.Abundleisavailableonlyifitmeetseveryconstraint.MoreGeneralChoiceSetsFoodOtherStuff10Atleast10unitsoffoodmustbeeatentosurviveMoreGeneralChoiceSetsFoodOtherStuff10BudgetSetChoiceisalsobudget

constrained.MoreGeneralChoiceSetsFoodOtherStuff10Choiceisfurtherrestrictedbyatimeconstraint.MoreGeneralChoiceSetsSowhatisthechoiceset?MoreGeneralChoiceSetsFoodOtherStuff10MoreGeneralChoiceSetsFoodOtherStuff10MoreGeneralChoiceSetsFoodOtherStuff10Thechoicesetistheintersectionofalloftheconstraintsets.ChapterThreePreferencesRationalityinEconomics

BehavioralPostulate:

Adecisionmakeralwayschoosesitsmostpreferredalternativefromitssetofavailablealternatives.Sotomodelchoicewemustmodeldecisionmakers’preferences.PreferenceRelationsComparingtwodifferentconsumptionbundles,xandy:strictpreference:xismorepreferredthanisy.weakpreference:xisasatleastaspreferredasisy.indifference:xisexactlyaspreferredasisy.PreferenceRelationsStrictpreference,weakpreferenceandindifferenceareallpreferencerelations.Particularly,theyareordinalrelations;i.e.theystateonlytheorderinwhichbundlesarepreferred.PreferenceRelations

denotesstrictpreference;

xymeansthatbundlexispreferredstrictlytobundley.ppPreferenceRelations

denotesstrictpreference;

xymeansbundlexispreferredstrictlytobundley.~denotesindifference;x~ymeansxandyareequallypreferred.ppPreferenceRelations

denotesstrictpreferenceso

xymeansthatbundlexispreferredstrictlytobundley.~denotesindifference;x~ymeansxandyareequallypreferred.denotesweakpreference;

xymeansxispreferredatleastasmuchasisy.

~f~fppPreferenceRelationsxyandyximplyx~y.~f~fPreferenceRelationsxyandyximplyx~y.xyand(notyx)implyxy.~f~f~f~fpAssumptionsaboutPreferenceRelationsCompleteness:Foranytwobundlesxandyitisalwayspossibletomakethestatementthateither

xy

or

yx.~f~fAssumptionsaboutPreferenceRelationsReflexivity:Anybundlexisalwaysatleastaspreferredasitself;i.e.

xx.~fAssumptionsaboutPreferenceRelationsTransitivity:If

xisatleastaspreferredasy,and

yisatleastaspreferredasz,then

xisatleastaspreferredasz;i.e.

xyandyzxz.~f~f~fIndifferenceCurvesTakeareferencebundlex’.Thesetofallbundlesequallypreferredtox’istheindifferencecurvecontainingx’;thesetofallbundlesy~x’.Sinceanindifference“curve”isnotalwaysacurveabetternamemightbeanindifference“set”.IndifferenceCurvesx2x1x”x”’x’~x”~x”’x’IndifferenceCurvesx2x1z

x

yppxyzIndifferenceCurvesx2x1xAllbundlesinI1arestrictlypreferredtoallinI2.yzAllbundlesinI2arestrictlypreferredto

allinI3.I1I2I3IndifferenceCurvesx2x1I(x’)xI(x)WP(x),thesetof

bundlesweaklypreferredtox.IndifferenceCurvesx2x1WP(x),thesetof

bundlesweaklypreferredtox.

WP(x)

includes

I(x).xI(x)IndifferenceCurvesx2x1SP(x),thesetof

bundlesstrictlypreferredtox,

doesnot

includeI(x).xI(x)IndifferenceCurvesCannotIntersect

x2x1xyzI1I2FromI1,x~y.FromI2,x~z.Thereforey~z.IndifferenceCurvesCannotIntersect

x2x1xyzI1I2FromI1,x~y.FromI2,x~z.Thereforey~z.ButfromI1andI2weseeyz,a

contradiction.pSlopesofIndifferenceCurvesWhenmoreofacommodityisalwayspreferred,thecommodityisagood.Ifeverycommodityisagoodthenindifferencecurvesarenegativelysloped.SlopesofIndifferenceCurvesBetterWorseGood2Good1Twogoods

anegativelyslopedindifferencecurve.SlopesofIndifferenceCurvesIflessofacommodityisalwayspreferredthenthecommodityisabad.SlopesofIndifferenceCurvesBetterWorseGood2Bad1Onegoodandone

badapositivelyslopedindifferencecurve.ExtremeCasesofIndifferenceCurves;PerfectSubstitutesIfaconsumeralwaysregardsunitsofcommodities1and2asequivalent,thenthecommoditiesareperfectsubstitutesandonlythetotalamountofthetwocommoditiesinbundlesdeterminestheirpreferencerank-order.ExtremeCasesofIndifferenceCurves;PerfectSubstitutesx2x1881515Slopesareconstantat-1.I2I1BundlesinI2allhaveatotal

of15unitsandarestrictlypreferredtoallbundlesin

I1,whichhaveatotalof

only8unitsinthem.ExtremeCasesofIndifferenceCurves;PerfectComplementsIfaconsumeralwaysconsumescommodities1and2infixedproportion(e.g.one-to-one),thenthecommoditiesareperfectcomplementsandonlythenumberofpairsofunitsofthetwocommoditiesdeterminesthepreferencerank-orderofbundles.ExtremeCasesofIndifferenceCurves;PerfectComplementsx2x1I145o5959Eachof(5,5),(5,9)and(9,5)contains

5pairssoeachisequallypreferred.

ExtremeCasesofIndifferenceCurves;PerfectComplementsx2x1I2I145o5959Sinceeachof(5,5),(5,9)and(9,5)contains5pairs,eachislesspreferredthanthebundle(9,9)

whichcontains9pairs.

PreferencesExhibitingSatiationAbundlestrictlypreferredtoanyotherisasatiationpointorablisspoint.Whatdoindifferencecurveslooklikeforpreferencesexhibitingsatiation?IndifferenceCurvesExhibitingSatiationx2x1Satiation

(bliss)

pointIndifferenceCurvesExhibitingSatiationx2x1BetterBetterBetterSatiation

(bliss)

pointIndifferenceCurvesExhibitingSatiationx2x1BetterBetterBetterSatiation

(bliss)

pointIndifferenceCurvesforDiscreteCommoditiesAcommodityisinfinitelydivisibleifitcanbeacquiredinanyquantity;e.g.waterorcheese.Acommodityisdiscreteifitcomesinunitlumpsof1,2,3,…andsoon;e.g.aircraft,shipsandrefrigerators.IndifferenceCurvesfo