北大微观经济学全套课件 第04章均衡的变动

133241332E1E2E3E4(IncomeConsumptionCurve)ICIC2X1XMX142(IncomeDemandCurve)IDIDX13X1X143X1X1316X2X2.x1X1=X1(M)U=U(X1X2)P1X1+P2X2=MMaxU=U(X1,X2)s.tM=P1X1+P2X2L=U(X1X2+λ(MP1X1P2X2)0111=−∂∂=∂∂PXUXLλ0222=−∂∂=∂∂PXUXLλ02211=−−=∂∂XPXPMLλX1X2),,(21*1*1MPPXX=),,(21*2*2MPPXX=x1x2X1=X1(M)X2=X2(M)X1=X1(M)42ID4-314-4X1AAIDNAEM=AXNXOXOMtgxXMXMdMdXXMdMdXMdMXdXAAAAAAAA111111111111.//====OM=AAXA1EM=A1AX11/11AAOXNXANNOEM=145AAOXNX11=EM=111111==AAAAOXAXOMOXXMdMdXAN0,0EM14-6AAOXNX11EM=11111111==AAAAAAOXNXOXAXOMNXXMdMdXNAX1X1AN********0,EM0,4-8249LMX1()Em1MP00Em1PQ014-2X1(NomlativeGoods)X1X1=X1(M)dX1dM0EM=dX1/X1dM/M024-10M0XlMoX14-1(InferiorGoods)X1X1=X1(M)dX1dM0EM=dX1/X1dM/M034-11142(LuxuriousGoods)X1X1=X1(M)dX1dM0EM=dX1/X1dM/M140143(NecessayGoods)X1X1=X1(M)dX1dM01EM=dX1/X1dM/M0EM0EM00EM1EM1EM0EM0EP0EM0EP0EPEP0144En=En(Engel'scoefficient)24-12A80402060(Lorenz'sCurve)42CAMOMB6060ONM0OM45ONM(Gini'sCoefficient)OMNSSg∆=g0g1nXX(X1X2Xn)PP(P1P2Pn)M1MaxU=U(X1,X2Xn)s.tPiXi=ML=U(X1,X2……Xn))(∑−PiXiMλ0=−∂∂=∂∂iiiPXUXLλi=1,2,…n01=−=∂∂∑−niiiXPMLλn1),,......,,(21**MPPPXXnii=i=1,2IXiXi(M)2iiiiMXMMXMMXXE∂∂=∂∂=//ME1iX01MEiXME0iX1P2PI413P332ElE2E3P(PriceconsumptionCurve)PCPC2XlX1P1X1(PriceDemandCurve)P1X1414X1=Xl(P1)P1X2?415X2X2(P1)415XlX1X1(P1)4-13414X1X1(P1)P1X2P1X2X2(P1)ON45OP1P1X2ABP1oX2X2(P1)X1X1(P1)X2X2(P1)UU(X1X2)P1X1P2X2MMaxUU(X1X2)s.tMP1X1+P2X2)(),(221121XPXPMXXUL−−+=λ0111=−∂∂=∂∂PXUXLλ0222=−∂∂=∂∂PXUXLλ0=2211−−=∂∂XPXPMLλX1X2),,(21*1*1MPPXX=),,(21*2*2MPPXX=P2MX1=X1(P1)X2=X2(P1)1*1X*2X),,(21MPP21()4-16P1PCBCP11P1,OHOK,∆2HK)(111PL)(212PLP=1OHHKOFGJOFFGOHHKOFGJFGOHHKOFFJPPXXEP///)(////1111+−=+−=−=∆∆=OHHKABBCOFFG==Q)//1(OHHKOFGJEp+−=∴(4-1)XIE416CKCKEPC416GJ0OFHKOH0(4-1)Ep1X1ECGJ=0(4-1)EP=1X1EKCJKGJ0OFHKOH01//0−OHHKOFGJ(?)(4-1)Ep1Xl418EKGJ0OFHKOH01//−OHHKOFGJ(?)(41)E0PX1X14194174184192()X1X24X2X2(P1)P1X20/12∂∂PXX1X2415417418419417∂,X1X2418∂X1X24190/12=∂PX0/12∂PXnX=X(X1,X2,……Xn)P=P(P1,P2,……,Pn)M.1MaxU=U(x1,x2,…xn)s.t∑==niiiMxP1)(),......,(121∑=−+=niiinXPMxxxULλ0=−∂∂=∂∂iiiPXUXLλ01=−=∂∂∑=niiiXPMLλn+1Xi)),,...,(21**MPPPXXnii=i=1,2……ni)(iiiPXX=iji)(jiiPXX=21M),niiPPPXX...(21=iiiiiiiiiXPPXPPXXEp∂∂−=∂∂−=//iEp1Xi0-1XiiEpiEp1XiiEp0Xi2XiXiP1,P2….Pn,MijjijjiiijXPPXPPXXEp∂∂=∂∂=//ijEp0XiXjijEp0XiXjijEp0XiXj(CompensationDemandFunctiOn)1U=U(x1,x2,…xn)P=(P1,P2……Pn)Mine=s.t∑=niiiXP1),....,(21nxxxU=UL=+∑=niiiXP1λ(),....,(21nxxxU−U),0=∂∂−=∂∂iiiXUPXLλ)nx,....,(21xxUUL−=∂∂λi1,2……nn+1),,......,(21**UPPPXXnii=i1,2,……n212(ConsumerSurplus)14204OLKHGFDACOOPABABPCS=(A)P(X)ABC(A)MarshallianConsumerSurplus.24-22OMXEX1ONMMUX1QKMKMHX1MNX1MHMN=NHEK3()423XXE1UMBXKLKLMBXUMK(Hicks’consumersurplus),(X1)(X2)X1?39(SubstitutionEffect)(1ncomeEffect)(TotalEffect)X1X1X2X1X2X1X1X2424MAE1U1;MBX1E2X1X1X2MBMBU1E3E3ElX1E1E3(E1E3)X1X1X2X2X1E1E3X1X111X21X31X11XX13X121X31X(TE)(SE)(IE)(TE=)(SE)+(IE=)21X11X31X11X21X31X(1)()(MNX2BLX1)425MNX2BLX1(2)XlXlXX2(HicksDemandFunction)429X1426MAElMBXE2MBElNLE3.XlXlX1XlX2(TE)(SE)(1E)11X21X21XX31XX3111(TE=)(SE=)+(IE=)1121XX−1131XX−3121XX−(1)()(2)x1x2(SlutskyDemandFunction)12(1)427X1MNX2BLX1MHX2BKX1(2)428X1MNX2BLX1MHX2BKX1(3)(4)()429()MDHDSD()HDSDMDEEE1424X1E3E1X1X10E2MBE2CBX1E2CDX1C0000E2DBX1E2DMXlD00002(1)E2CBX1X1(2)E2CDX1X1X1(3)E2DMX1X1X1(GiffenGoods)414-1E2SEIETECBDC+DM+3(RobenGiffen)?1003903010154530453020359923208431()(SlutskyEquation)(EugeneSlutsky)424TESEIETE=X1,1112XX∆=−SE=sXXX11131∆=−IE=mXXX13121∆=−msXXX111∆+∆=∆,1X1P∆111111PXPXPXms∆∆+∆∆=∆∆1M221111XPXPM+=QP1M1221212XPXPM+=PXPPXMMM∆−=−=−=∆11121112)((MP1)1XMP∆−=∆1MXXPXPXms∆∆−∆∆=∆∆11111111PX∆∆11211112211),(),(PPMPXMPX−−,X1P11P1211PXs∆∆112111112211),(),(PPMPXMPX−−P11P12=∆∆MXXm111211112211),(),(MMMPXMPX−−1X,MXm∆∆11P∆constPconstUMXXPXPX==∂∂−∂∂=∂∂)()(111111U=U(X1,X2),M=P1X1+P2X2MaxU=U(X1,X2)s.tM=P1X1+P2X2L=U(X1,X2)+)2211(XPXPM−−λ,3P1dP1=0dM0constPMXDDDDdMdX=∂∂−==−=)(131311D11/D,dU=002211=+=dxUdxUdU62121PPMUMU=2121PPUU=602111=+dxPdxP21)(011=+−dPXdM3constu1111)d(dPDDXλ=constu1111)(PXDD∂∂=λ775411PX∂∂=(11PX∂∂)X(constu1MX∂∂1)constP1P12X1X13