第一部分消费者行为理论(21-22)

11„1„2„3„4„5„6---„722„2.1„2.2„2.3„2.4„2.532.11„„ordinarygoodsandGiffengoods)2„„342.11„„normalgoodsandinferiorgoods2352.162.2(Slutskyequation)1n2„„„„11?xp∂=∂011?uuxp=∂=∂11?xmmp∂∂=∂∂72.2(Slutskyequation)„11?xp∂=∂121122121211221112221122max(,).(,,)(,)()0:00uxxstpxpxmLxxuxxmpxpxLupxxLuFOCpxxLmpxpxλλλλλ+==+−−∂∂⎧=−=⎪∂∂⎪∂∂⎪=−=⎨∂∂⎪⎪∂=−−=⎪∂⎩82.2(Slutskyequation)21*11211121111122122211112121110,0000dpdmdpxpxxuuppppxxuuppppxxppxppλλλ==≠⎧∂∂∂+−−=⎪∂∂∂⎪⎪∂∂∂⎪+−=⎨∂∂∂⎪⎪∂∂−−−=⎪∂∂⎪⎩92.2(Slutskyequation)111112122122211121131111100,xpuupxuuppxpppDxDxDpDDλλλ⎡⎤∂⎢⎥∂⎢⎥−⎡⎤⎡⎤⎢⎥∂⎢⎥⎢⎥−=⎢⎥⎢⎥⎢⎥∂⎢⎥⎢⎥⎢⎥−−⎣⎦⎣⎦⎢⎥∂⎢⎥∂⎢⎥⎣⎦∂=+∂102.2(Slutskyequation)1322121131331xDxDpDDDxDpDDλλλ∂=+∂∂=+∂112.2(Slutskyequation)1„011?uuxp=∂=∂1122012012112212111222012min.(,)(,,)((,))0:0(,)0pxpxstuxxuLxxpxpxuuxxLupxxLuFOCpxxLuuxxµµµµµ+==++−⎧∂∂=−=⎪∂∂⎪⎪∂∂=−=⎨∂∂⎪⎪∂=−=⎪∂⎩122.2(Slutskyequation)21*1121112111112212221111212110,01000dpdudpxpxxuuupppxxuuupppxxuuppµµµµµµ==≠⎧∂∂∂−−−+=⎪∂∂∂⎪⎪∂∂∂⎪−−−=⎨∂∂∂⎪⎪∂∂−−=⎪∂∂⎪⎩132.2(Slutskyequation)0111112122122211211111111000uuxpuuuxuuupuupxDDpDDµµµµµλµ=⎡⎤∂⎢⎥∂⎢⎥−−−−⎡⎤⎡⎤⎢⎥∂⎢⎥⎢⎥−−−=⎢⎥⎢⎥⎢⎥∂⎢⎥⎢⎥⎢⎥−−⎣⎦⎣⎦⎢⎥∂⎢⎥∂⎢⎥⎣⎦∂==∂142.2(Slutskyequation)001121131uuuuxDpDDpDλλµ==∂=∂∂=∂152.2(Slutskyequation)1„121122121211221112221122max(,).(,,)(,)()0:00uxxstpxpxmLxxuxxmpxpxLupxxLuFOCpxxLmpxpxλλλλλ+==+−−∂∂⎧=−=⎪∂∂⎪∂∂⎪=−=⎨∂∂⎪⎪∂=−−=⎪∂⎩11?xmmp∂∂=∂∂162.2(Slutskyequation)21*1211121122122212120,00010dpdpdmxmxxuupmmmxxuupmmmxxppmmλλ==≠∂∂∂⎧+−=⎪∂∂∂⎪∂∂∂⎪+−=⎨∂∂∂⎪∂∂⎪−−+=⎪∂∂⎩172.2(Slutskyequation)0111121221222123110010ppxmuupxuupmppmDxmDλ=∂⎡⎤⎢⎥∂−⎡⎤⎡⎤⎢⎥∂⎢⎥⎢⎥⎢⎥−=⎢⎥⎢⎥⎢⎥∂⎢⎥⎢⎥−−−⎢⎥⎣⎦⎣⎦∂⎢⎥⎢⎥∂⎣⎦∂=∂182.2(Slutskyequation)0032233ppppDxmDDmDµ==∂=∂∂=∂192.2(Slutskyequation)1„000013111111111311111111,uuppuuppxDxDpDDxDpDDxmDxxxxppmλλ====∂=+∂∂=∂∂=∂∂∂∂⇒=−∂∂∂202.2(Slutskyequation)1„nij,003iiijuuppjjjiijxxxxppmDDxDDλ==∂∂∂=−∂∂∂=+212.22****,()(,)(,(,)),,,:(,)(,)(,)(,)(,)(,)(,)(,)iijiiijjjiiijjjxpmuuxhpuxpepuppmmphpuxpmxpmepuppmpxpmhpuxpmepuppmp∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗≡==∂∂∂∂=+⋅∂∂∂∂∂∂∂∂=−⋅∂∂∂∂222.22(,)(,)(,)(,)(,(,))(,)(,)iiijjjiiijjjxpmhpuxpmxppmxpmhpvpmxpmxpmppm∗∗∗∗∗∗∗∂∂∂=−⋅∂∂∂∂∂∂=−⋅∂∂∂232.2311121121112221221222(,)(,)(,)2(,)(,)(,)(,)(,),,,,,(,)(,)(,)(,)(,),,ppmDxpmDhpuDxpmxnxpmxpmhpmhpmxpmppppmxpmxpxpmxpmhpmhpmxpmppppm=−⋅=∂∂∂∂⎛⎞⎛⎞∂⎛⎞⎜⎟⎜⎟⎜⎟∂∂∂∂∂⎜⎟⎜⎟=−⎜⎟⎜⎟⎜⎟∂∂∂∂∂⎜⎟⎜⎟⎜⎟⎜⎟∂∂∂∂∂⎝⎠⎝⎠⎝⎠()m242.231111111122221(,)(,)(,)(,),,(,)(,)(,)(,),,(,)(,),nnnnnnnxpmhpmxpmhpmppppxpmhpmxpmhpmppppxpmxpmpp∂∂∂∂⎛⎞⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⎜⎟∂∂∂∂⎜⎟⎜⎟∂∂∂∂⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⎜⎟∂∂∂∂=⎜⎟⎜⎟⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⎜⎟∂∂⎜⎟⋅⋅⋅⋅⋅⎜⎟∂∂⎝⎠(1211(,)(,)(,),(,(,)(,)(,),nnnnnxpmmxpmxpmxpmxpmhpmhpmmppnn⎛⎞∂⎛⎞⎜⎟⎜⎟∂⎜⎟⎜⎟⎜⎟∂⎜⎟⎜⎟⎜⎟−⋅⋅⋅⋅⋅∂⎜⎟⎜⎟⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⎜⎟⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⎜⎟⎜⎟⎜⎟∂∂∂⎜⎟⋅⋅⋅⋅⋅⎜⎟⎜⎟∂⎝⎠∂∂⎝⎠×252.2101111111212122221222211211220100(1)()000()uuxDpDuupDuupHppupDppλλλ=+∂=∂−⎡⎤⎢⎥⎡⎤=−=⎣⎦⎢⎥⎢⎥−−⎣⎦−⎡⎤=−=−−⎢⎥−⎣⎦262.22000001311112231311222212221111,0,0,(1):00:00ippippppippppxDxxmDxDupDupupupxxxmmxxxmm=+====∂−=∂−⎡⎤=−=−+⇒⎢⎥−⎣⎦∂∂⇒−∂∂∂∂⇒−∂∂272.23282.21003,;1,2iiijuuppjjjijixxxxppmDxDijijnDDλ==∂∂∂=−∂∂∂+∀≠=⋅⋅⋅⋅⋅00:0:0iuujiuujxijpxijp==∂∂∂∂292.2200,,,,ijjiijjijiuuuujijijiDDDDDDxxpphhppλλ===∴=∂∂=∂∂∂∂=∂∂Q302.2300(,)0,000,0ijiuujxpmijpxijp=∂∂=∂∂=