微观经济学1920.docx
《微观经济学1920.docx》由会员分享，可在线阅读，更多相关《微观经济学1920.docx（17页珍藏版）》请在冰豆网上搜索。
微观经济学1920
19EXCHANGE
Partialequilibriumanalysis:
howdemandandsupplywereaffectedbythepriceoftheparticulargoodwewereexamining.
Generalequilibriumanalysis:
howdemandandsupplyconditionsinteractinseveralmarketstodeterminethepricesofmanygoods.
Thestructureofthemodel:
Competitivemarket.
Twogoodsandtwoconsumers.
Intwostages.
TheEdgeworthBox
Twopeople:
AandB.
Twogoods:
1and2.
A’sconsumptionbundle:
XA=（x1A,x2A）
B’sconsumptionbundle:
XB=（x1B,x2B）.
Anallocation:
（XA,XB）.
Theinitialendowmentallocation,（w1A,w2A）and（w1B,w2B）.
Afeasibleallocation（XA,XB）:
x1A+x1B=w1A+w1B
x2A+x2B=w2A+w2B
Makearectangle:
Height:
w2A+w2B
Width:
w1A+w1B
DepictA’sandB’sindifferencecurves
----Edgeworthbox
XB1OB
XA2WXB2
OAXA1
Trade
Anytradefromendowmentcanbeinthebox.
XB1OB
M
XA2WXB2
OAXA1
TherearesometradesmakeAandBbothbetteroff:
M.
Equilibrium:
thestatenobodywouldlikechange.
MRSA12=MRSB12
----Paretoefficientallocation.
OB
OA
Contractcurve:
thesetofallParetoefficientpoints.
MarketTrade
Marketprice:
（p1,p2）
ConsumerA’sproblem:
Maxu（xA1,xA2）
s.t.p1xA1+p2xA2p1wA1+p2wA2
Theconditionsforhisbestchoice
MRS12A=–
p1xA1+p2xA2=p1wA1+p2wA2
Thesolution:
[xA1（p1,p2）,xA2（p1,p2）]
Thenetdemandor“excessdemand”ofA:
eA1=xA1–wA1
eA2=xA2–wA2
ConsumerB’sproblem:
Maxu（xB1,xB2）
s.t.p1xB1+p2xB2p1wB1+p2wB2
theconditionsforhisbestchoice
MRS12B=-
p1xB1+p2xB2=p1wB1+p2wB2
Thenetdemandor“excessdemand”ofB:
eB1=xB1–wB1
eB2=xB2–wB2
eB1OB
XA2WXB2
OAeA1
Amarketequilibrium:
（p1,p2）suchthat
eA1+eB1=0
eA2+eA2=0
eB1OB
XA2WXB2
OAeA1
Wehave6equationsfor6variables:
MRS12A=MRS12B=-
p1xA1+p2xA2=p1wA1+p2wA2
p1xB1+p2xB2=p1wB1+p2wB2
xA1+xB1=wA1+wB1
xA2+xB2=wA2+wB2
Theaggregateexcessdemands
Anequilibrium:
Walras’Law
Byconsumer’sbudget,
or
ThevalueofagentA’snetdemandiszero（forany（p1,p2））.
ThesimilarequationforagentB:
Addthemup
or
Walras’law:
thevalueofaggregateexcessdemandisidenticallyzeroforallpossiblechoicesofprices.
----only5equationsareindependent.
RelativePrices
It’sreasonablethatpricesofallgoodsarerelativeinequilibrium.
Generalizedmodel:
intheeconomywithnconsumersandmgoods
Howmanyarethereequationsforequilibrium?
Howmanynumberstobedecided?
Inak-goodandn-persongeneralequilibriummodel,therearenk+k=（n+1）kvariables.Walras’lawimpliesthatthereareonly（n+1）k–1independentequations
EquilibriumandEfficiency
IsthemarketequilibriumParetoefficient?
Ifnot,thereissomeotherfeasibleallocationsuchthat
and
Byhypothesisofmarketequilibrium:
Nowaddthem
Substitutefromequations（19.1）and（19.2）toget
FirstTheoremofWelfareEconomics:
allmarketequilibriaareParetoefficient.
EfficiencyandEquilibrium
GivenaParetoefficientallocation,canwefindpricessuchthatitisamarketequilibrium?
OB
OA
SecondTheoremofWelfareEconomics:
ifallagentshaveconvexpreferences,thentherewillalwaysbeasetofpricessuchthatParetoefficientallocationisamarketequilibriumforanappropriateassignmentofendowments.
20PRODUCTION
TheRobinsonCrusoeEconomy
RobinsonCrusoeeconomy:
economicmodelwithoneconsumer,onefirm,andtwogoods.
RobinsonCrusoeplaysadualrole:
bothaconsumerandaproducer.
Twogoods:
coconutsandleisure.
Preferencesforcoconutsandleisure:
C,T
U=u（C,T）
c
T
productionfunction：
usingtimeLtocollectcoconuts
c
L
UtilityintermsofCandL:
U=u（C,L0–L）
c
24L
Robinson’schoice:
consumingleisure,orgatheringcoconuts.
Themostpreferredcombination:
theslopeoftheindifferencecurvemustequaltheslopeoftheproductionfunction.
ΔC/ΔT=-MRS=MP=ΔC/ΔL
Crusoe,Inc.
Robinsondivideshimselfintotworoles:
producerandconsumer.
Thefirm:
howmuchlabortohireandhowmanycoconutstoproduce.
Consumer:
collectincomeasworkerandprofitsasshareholder;purchasethefirm’soutput.
Setthepriceofcoconutsatonedollarapiece.
TheFirm
Thefirm’sprofit
=PC–wL
Theisoprofitlines:
C=（+wL）/P
Theverticalinterceptoftheisoprofitlinemeasuresthemaximallevelofprofits:
.
It’sthestockdividendtosoleshareholder,Robinson.
c
L
Thefirm’sprogram
Max=PC–wL
s.t.C=f（L）
max=Pf（L）–wL
Thefirst-ordercondition
MP=w/P
Tangencycondition:
themarginalproductoflabormustequalw.
FromtheviewpointofRobinson,theconsumer.
Robinsonreceiveshis
升级会员 