33北大微观经济学全套课件 第03章选择理论

1(preferences)(choicebundle)31ABCABC()ABC??23-1XYX=(X1X2Xn)Y=(Y1Y2Yn)(1)XYXYXY(2)XfYXY(3)XYXYXY3-2(comprehensiverange)XYXYXY3-3(Dictionaryrange)XYXY??323-21(COmpletenessAssumption)XYXYXYXY2(ReflexivityAssumption)XXXXXXXXXX3(TransivityAssumption)XYZXYYZXZXYZXYYZXZABXYYZ1()AXZ,BZXAZBXYAZBX1(B2X)XBY1(BXY)YBZ1(BYZ)ZBXBAB4(NonsatiationAssumption)(MonotonityAssumption)X=(X1X2Xn)Y=(Y1Y2Yn)Xi=Yi,XiYii=1.2nijXYXiYiXYfABXYjXjYj1()AXYBXYAYBXAYX1(YX)fpa,b,c,d,e,f,ffafffbfdffdeffdfcabcb()341()?2(34)(26)35AB1()?1(34)(43)35ABACABCA353-4(Indifferencecurve)35Uo()()()()3611Q1Q2Q1Q237ABA(Q,)B(,Q),A1AQ2BQ1B2QQQ,BfA,A,BBABQ2A2B1A123-8U1U2ABCQQCB()CQ2BQ2C1B1ABABACACABCBC39341Q1Q2311Q22312313()CBA331(Perfectsubstitutes)101110()()314(110)10432(PerfectComplements)1121315112233D(21)A1OAOA?133(utility)NBA(TotalUtility)234(UtilityFunction)nXii=lnUU(X11X2,Xn)316X1UmX1()135(MarginalUtility)2553052(ThelawofDiminishingMarginalUtility)3U=U(X)()MU=U/XXMU=dU/dXXMUdMU/dx0dU/dx0224(1)3-1700012345610753101017222526263-17(2)000UU(X)dU/dX=OdU/dX0MU=dU/dX=031822(3)()==dMV/dXO==dU/dXO==22XonX=X(X1X2Xn)U=U(X1X2Xn)()1MUi=∂(i=1,2n)iiXU∂/iMUi0V=U(xi)MUi=(I=1,2….n)iXU∂∂/02∂∂=∂∂iiixUXMUi202∂∂∂jiXXU0)(2≠∂∂∂jiXXUjiijjijixMUxMUxxU∂∂=∂∂=∂∂∂2jixxU∂∂∂20=jixMU∂∂00∂∂xiMUi,jijixxU∂∂∂2jixxU∂∂∂20(ij)jixxU∂∂∂20=jixMU∂∂0ixU∂∂20iiijixxU∂∂∂2()jixxU∂∂∂2=0(ij)jixxU∂∂∂2=0=0=∂∂jixMU02=∂∂ixU1UU(X1X2)UU0constU0U(X1X2)X2X2(X1)U0319319U1U0U2Ux1x2100x2100/x1(x0)236x1x2x1x2(MarginalRateofSubstitution)MRS1,2=-x2x1x1,x2MRS1,2=-dx2dx1x1x2dx2dx1x2=x2(x1)3-20MRS1,2=-dx2dx1tga3?321x1ABx2x1CDx2x1EFx2ABCDEF1x1x2U0U(x1x)MRS1,2=-212dxdxd(MRS1,2)dx1=-ddx1(12dxdx)=-2122dxxd0x1x23-22ABCDEF122dxxd0122dxxd04nx=x(x1x2xn)U0U(x1,x2……xn)i,jMRSij)(jixxji≠∂∂−U0=U(x1x2……xn)MRSij=-dx2dx10)(22∂∂−=∂∂ijiijxxxMRS33nX=X(X1X2Xn)iXiPiMniPiXi∑=niiixP1∑=niiixP1=M(A)(BudgetConstraint)(A)(BudgetFunction)P1X1+P2X2=Mx1x23-23ABMn∑M=niiixP1(FeasibleSet)p1x1+pxM323px1+pxMAB22122p1x1+pxM222112ppdxdx−=12112ppdxdx−=3-24AB00ABOABABOA1B21222112P1P2|12dxdx|=|21PP|P1PX1BX1XX1OBBPP3252222X1AP1P32612?(1)PP12327A1B1327ABP1P222(2)P1P2328A1B1328ABP1P22(3)329329XX1E2PX1+PXMP1dx1x1dP1Pdx+x1dp0Ex1xdx10dx0x1dp1xpd0122222222212xx21dpdpEE08020405161?08x1+04x160.2x1+0.5x1022OABBCEFBDGH(MultipleConstraint)(NonlinearBudgetConstraint)X2X15555331ABBCCD331332ABUlU2U3U3ABU1ABCDCDU1??CXlX(ABC)DX2X1(ABD)EU2ABX1X22P1P2MUU(x1x2)X1X2X*1X*2MaxU=U(x1x2)s.t(subjectto)P1X1+P2X2=M(1)P1X1+P2X2=M=X2=M-P1X1P2U=U(X1,M-P1X1P2)X10X1=X1X2=X**2212dXUd02L=U(X1X2)+(M-P1X1-P2X2)FristOrderConditionF.O.C0111=−∂∂=∂∂PXUXLλX1=X*1X2=X*20222=−∂∂=∂∂PXUXLλSecondOrderCondition0212222121212212PPPXUXXUPXXUXU−−−∂∂∂∂∂−∂∂∂∂∂*1X*2X39(consumerEquilibrium)312UU(x1x2)21222211//0XUXUdXdXdXXUdXXUdU∂∂∂∂−===∂∂+∂∂=(A)11PXUλ=∂∂=2121//PPXUXU=∂∂∂∂(B)22PXUλ=∂∂P1X1+P2X2=MP1dX1+P2dX20dx2/dx1=P1P2(C)(A)(B)(C)3B212121//MUMUXUXUPP=∂∂∂∂=2211PMUPMU=,4dU/dMM=P1X1+P2X2=dM=P1dx1P2dx2=dUdM=2211211dXPdXPdXXUdXXU+∂∂+∂∂=U=U(X1,X2)=dU=1XU∂∂dX1+2XU∂∂dX2dUdM=22112211)()(dXPdXPdXMUdXMU++BMU1=P1MU2=P2dUdM=λλλ=++22112211dXPdXPdXPdXP5MRS1,2P1P2=MU1MU2MRS1,2=dX2dX11333E42U22334EACABMRS12P1P25X2nX=X(X1,X2……Xn)P=P(P1,P2,……Pn)M,U=U(x1x2……xn)1MaxU=U(x1x2……xn)s.tM=∑i=1,2……n=niiixP1L=U(x1,x2……xn)(M)∑=niiixP10111=−∂∂=∂∂PxUxLλx1=x*10222=−∂∂=∂∂PxUxLλ=*22xx=0=−∂∂=∂∂nnnPxUxLλ……0=−=∂∂∑iixPMLλxn=x*nn+1n+1x1x2xnx*1,x*2……x*,X=X*(x1,x*……x)n**2*nX*1n1n0..............................321222222212222322222212112312212212nnnnnnnPPPPPxUxxUxxUxxUPxxUxxUxUxxUPxxUxxUxxUxU−−−−−∂∂∂∂∂∂∂∂∂∂∂−∂∂∂∂∂∂∂∂∂∂∂−∂∂∂∂∂∂∂∂∂∂∂211PxUλ=∂∂λ=11PMU22PxUλ=∂∂λ=22PMU=11PMU=22PMU=……=nnPMU=λ=dMdU…………nnPxUλ=∂∂λ=nnPMUn(Gossen'sSecondLaw)n+l()302∂∂∂jixxU0fjixMU∂∂,0fiixMU∂∂,i,j02∂∂∂jixxU0pjixMU∂∂0piixMU∂∂,i,j02=∂∂∂jixxU0=∂∂jixMU0=∂∂iixMU,i,j4.U=U(x1,x2……xn)P=P(P1,P2,……Pn)U,P11dxxU∂∂22dxxU∂∂……nndxxU∂∂=0i,jiidxxU∂∂+jjdxxU∂∂=0=MRS=ijijijijPPMUMUxUxU==∂∂∂∂//