范里安现代观点课件(2)南开大学中级微观经济学

范里安现代观点课件(2)南开大学中级微观经济学第一页，共76页。ConsumptionChoiceSetsAconsumptionchoicesetisthecollectionofallconsumptionchoicesavailabletotheconsumer.Whatconstrainsconsumptionchoice?Budgetary,timeandotherresourcelimitations.第二页，共76页。BudgetConstraintsAconsumptionbundlecontainingx1unitsofcommodity1,x2unitsofcommodity2andsoonuptoxnunitsofcommoditynisdenotedbythevector(x1,x2,…,xn).Commoditypricesarep1,p2,…,pn.第三页，共76页。BudgetConstraintsQ:Whenisaconsumptionbundle

(x1,…,xn)affordableatgivenpricesp1,…,pn?第四页，共76页。BudgetConstraintsQ:Whenisabundle(x1,…,xn)affordableatpricesp1,…,pn?A:When

p1x1+…+pnxn

£

m

wheremistheconsumer’s(disposable)income.第五页，共76页。BudgetConstraintsThebundlesthatareonlyjustaffordableformtheconsumer’sbudgetconstraint.Thisistheset

{(x1,…,xn)|x1³0,…,xn

³0and

p1x1+…+pnxn

=

m}.

第六页，共76页。BudgetConstraintsTheconsumer’sbudgetsetisthesetofallaffordablebundles;

B(p1,…,pn,m)=

{(x1,…,xn)|x1

³0,…,xn

³0and

p1x1+…+pnxn

£

m}Thebudgetconstraintistheupperboundaryofthebudgetset.第七页，共76页。BudgetSetandConstraintforTwoCommoditiesx2x1Budgetconstraintisp1x1+p2x2=m.m/p1m/p2第八页，共76页。BudgetSetandConstraintforTwoCommoditiesx2x1Budgetconstraintisp1x1+p2x2=m.m/p2m/p1第九页，共76页。BudgetSetandConstraintforTwoCommoditiesx2x1Budgetconstraintisp1x1+p2x2=m.m/p1Justaffordablem/p2第十页，共76页。BudgetSetandConstraintforTwoCommoditiesx2x1Budgetconstraintisp1x1+p2x2=m.m/p1JustaffordableNotaffordablem/p2第十一页，共76页。BudgetSetandConstraintforTwoCommoditiesx2x1Budgetconstraintisp1x1+p2x2=m.m/p1AffordableJustaffordableNotaffordablem/p2第十二页，共76页。BudgetSetandConstraintforTwoCommoditiesx2x1Budgetconstraintisp1x1+p2x2=m.m/p1BudgetSetthecollection

ofallaffordablebundles.m/p2第十三页，共76页。BudgetSetandConstraintforTwoCommoditiesx2x1p1x1+p2x2=misx2=-(p1/p2)x1+m/p2soslopeis-p1/p2.m/p1BudgetSetm/p2第十四页，共76页。BudgetConstraintsIfn=3whatdothebudgetconstraintandthebudgetsetlooklike?第十五页，共76页。BudgetConstraintforThreeCommoditiesx2x1x3m/p2m/p1m/p3p1x1+p2x2+p3x3=m第十六页，共76页。BudgetSetforThreeCommoditiesx2x1x3m/p2m/p1m/p3{(x1,x2,x3)|x1

³0,x2³0,x3

³

0andp1x1+p2x2+p3x3

£

m}第十七页，共76页。BudgetConstraintsForn=2andx1onthehorizontalaxis,theconstraint’sslopeis-p1/p2.Whatdoesitmean?

第十八页，共76页。BudgetConstraintsForn=2andx1onthehorizontalaxis,theconstraint’sslopeis-p1/p2.Whatdoesitmean?

Increasingx1by1mustreducex2byp1/p2.第十九页，共76页。BudgetConstraintsx2x1Slopeis-p1/p2+1-p1/p2第二十页，共76页。BudgetConstraintsx2x1+1-p1/p2Opp.costofanextraunitof

commodity1isp1/p2units

foregoneofcommodity2.第二十一页，共76页。BudgetConstraintsx2x1Opp.costofanextraunitof

commodity1isp1/p2units

foregoneofcommodity2.And

theopp.costofanextra

unitofcommodity2is

p2/p1unitsforegone

ofcommodity1.-p2/p1+1第二十二页，共76页。BudgetSets&Constraints;IncomeandPriceChangesThebudgetconstraintandbudgetsetdependuponpricesandincome.Whathappensaspricesorincomechange?第二十三页，共76页。Howdothebudgetsetandbudgetconstraintchangeasincomemincreases?Originalbudgetsetx2x1第二十四页，共76页。HigherincomegivesmorechoiceOriginalbudgetsetNewaffordableconsumption

choicesx2x1Originalandnewbudgetconstraintsareparallel(sameslope).第二十五页，共76页。Howdothebudgetsetandbudgetconstraintchangeasincomemdecreases?Originalbudgetsetx2x1第二十六页，共76页。Howdothebudgetsetandbudgetconstraintchangeasincomemdecreases?x2x1New,smallerbudgetsetConsumptionbundlesthatarenolongeraffordable.Oldandnewconstraintsareparallel.第二十七页，共76页。BudgetConstraints-IncomeChangesIncreasesinincomemshifttheconstraintoutwardinaparallelmanner,therebyenlargingthebudgetsetandimprovingchoice.第二十八页，共76页。BudgetConstraints-IncomeChangesIncreasesinincomemshifttheconstraintoutwardinaparallelmanner,therebyenlargingthebudgetsetandimprovingchoice.Decreasesinincomemshifttheconstraintinwardinaparallelmanner,therebyshrinkingthebudgetsetandreducingchoice.第二十九页，共76页。BudgetConstraints-IncomeChangesNooriginalchoiceislostandnewchoicesareaddedwhenincomeincreases,sohigherincomecannotmakeaconsumerworseoff.Anincomedecreasemay(typicallywill)maketheconsumerworseoff.第三十页，共76页。BudgetConstraints-PriceChangesWhathappensifjustonepricedecreases?Supposep1decreases.第三十一页，共76页。Howdothebudgetsetandbudgetconstraintchangeasp1

decreasesfromp1’top1”?Originalbudgetsetx2x1m/p2m/p1’m/p1”-p1’/p2第三十二页，共76页。Howdothebudgetsetandbudgetconstraintchangeasp1

decreasesfromp1’top1”?Originalbudgetsetx2x1m/p2m/p1’m/p1”Newaffordablechoices-p1’/p2第三十三页，共76页。Howdothebudgetsetandbudgetconstraintchangeasp1

decreasesfromp1’top1”?Originalbudgetsetx2x1m/p2m/p1’m/p1”NewaffordablechoicesBudgetconstraintpivots;slopeflattensfrom-p1’/p2to-p1”/p2-p1’/p2-p1”/p2第三十四页，共76页。BudgetConstraints-PriceChangesReducingthepriceofonecommoditypivotstheconstraintoutward.Nooldchoiceislostandnewchoicesareadded,soreducingonepricecannotmaketheconsumerworseoff.第三十五页，共76页。BudgetConstraints-PriceChangesSimilarly,increasingonepricepivotstheconstraintinwards,reduceschoiceandmay(typicallywill)maketheconsumerworseoff.第三十六页，共76页。UniformAdValoremSalesTaxesAnadvaloremsalestaxleviedatarateof5%increasesallpricesby5%,frompto(1+0.05)p=1.05p.Anadvaloremsalestaxleviedatarateoftincreasesallpricesbytpfrompto(1+t)p.Auniformsalestaxisapplieduniformlytoallcommodities.第三十七页，共76页。UniformAdValoremSalesTaxesAuniformsalestaxleviedatratetchangestheconstraintfrom

p1x1+p2x2=m

to

(1+t)p1x1+(1+t)p2x2=m第三十八页，共76页。UniformAdValoremSalesTaxesAuniformsalestaxleviedatratetchangestheconstraintfrom

p1x1+p2x2=m

to

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

i.e.

p1x1+p2x2=m/(1+t).第三十九页，共76页。UniformAdValoremSalesTaxesx2x1p1x1+p2x2=m第四十页，共76页。UniformAdValoremSalesTaxesx2x1p1x1+p2x2=mp1x1+p2x2=m/(1+t)第四十一页，共76页。UniformAdValoremSalesTaxesx2x1Equivalentincomeloss

is第四十二页，共76页。UniformAdValoremSalesTaxesx2x1Auniformadvalorem

salestaxleviedatratet

isequivalenttoanincome

taxleviedatrate第四十三页，共76页。TheFoodStampProgramFoodstampsarecouponsthatcanbelegallyexchangedonlyforfood.Howdoesacommodity-specificgiftsuchasafoodstampalterafamily’sbudgetconstraint?第四十四页，共76页。TheFoodStampProgramSupposem=$100,pF=$1andthepriceof“othergoods”ispG=$1.Thebudgetconstraintisthen

F+G=100.第四十五页，共76页。TheFoodStampProgramGF100100F+G=100;beforestamps.第四十六页，共76页。TheFoodStampProgramGF100100F+G=100:beforestamps.第四十七页，共76页。TheFoodStampProgramGF100100F+G=100:beforestamps.Budgetsetafter40food

stampsissued.14040第四十八页，共76页。TheFoodStampProgramGF100100F+G=100:beforestamps.Budgetsetafter40food

stampsissued.140Thefamily’sbudget

setisenlarged.40第四十九页，共76页。TheFoodStampProgramWhatiffoodstampscanbetradedonablackmarketfor$0.50each?第五十页，共76页。TheFoodStampProgramGF100100F+G=100:beforestamps.Budgetconstraintafter40

foodstampsissued.140120Budgetconstraintwith

blackmarkettrading.40第五十一页，共76页。TheFoodStampProgramGF100100F+G=100:beforestamps.Budgetconstraintafter40

foodstampsissued.140120Blackmarkettrading

makesthebudget

setlargeragain.40第五十二页，共76页。BudgetConstraints-RelativePrices“Numeraire”means“unitofaccount”.Supposepricesandincomearemeasuredindollars.Sayp1=$2,p2=$3,m=$12.Thentheconstraintis

2x1+3x2=12.第五十三页，共76页。BudgetConstraints-RelativePricesIfpricesandincomearemeasuredincents,thenp1=200,p2=300,m=1200andtheconstraintis

200x1+300x2=1200,

thesameas

2x1+3x2=12.Changingthenumerairechangesneitherthebudgetconstraintnorthebudgetset.第五十四页，共76页。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.第五十五页，共76页。BudgetConstraints-RelativePricesAnycommoditycanbechosenasthenumerairewithoutchangingthebudgetsetorthebudgetconstraint.第五十六页，共76页。BudgetConstraints-RelativePricesp1=2,p2=3andp3=6priceofcommodity2relativetocommodity1is3/2,priceofcommodity3relativetocommodity1is3.Relativepricesaretheratesofexchangeofcommodities2and3forunitsofcommodity1.第五十七页，共76页。ShapesofBudgetConstraintsQ:Whatmakesabudgetconstraintastraightline?A:Astraightlinehasaconstantslopeandtheconstraintis

p1x1+…+pnxn=m

soifpricesareconstantsthenaconstraintisastraightline.第五十八页，共76页。ShapesofBudgetConstraintsButwhatifpricesarenotconstants?E.g.bulkbuyingdiscounts,orpricepenaltiesforbuying“toomuch”.Thenconstraintswillbecurved.第五十九页，共76页。ShapesofBudgetConstraints-QuantityDiscountsSupposep2isconstantat$1butthatp1=$2for0£x1

£20andp1=$1forx1>20.第六十页，共76页。ShapesofBudgetConstraints-QuantityDiscountsSupposep2isconstantat$1butthatp1=$2for0£x1

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

-2,for0£x1

£20

-p1/p2=

-1,forx1>20

andtheconstraintis{第六十一页，共76页。ShapesofBudgetConstraintswithaQuantityDiscountm=$1005010020Slope=-2/1=-2

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

(p1=1,p2=1)80x2x1第六十二页，共76页。ShapesofBudgetConstraintswithaQuantityDiscountm=$1005010020Slope=-2/1=-2

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

(p1=1,p2=1)80x2x1第六十三页，共76页。ShapesofBudgetConstraintswithaQuantityDiscountm=$100501002080x2x1BudgetSetBudgetConstraint第六十四页，共76页。ShapesofBudgetConstraintswithaQuantityPenaltyx2x1BudgetSetBudgetConstraint第六十五页，共76页。ShapesofBudgetConstraints