倫敦經(jīng)濟(jì)學(xué)院高微講義-消費者理論-wenkub
2022-11-02 11:17:42 本頁面
【正文】 l?U1(x*) = p1 l?U2(x*) = p2 ... ... ... l?Un(x*) = pn u = U(x*) Lagrange multiplier ??????gcvg)]([1xUuxpniii??= ?=l? goods MRS = price ratio _____ __ = Ui(x) pi Uj(x) pj If both i and j are bought... C(p, u) := vector of goods prices Specified utility level min ? pi xi {U(x) ? u} The solution is the consumer’s cost function or expenditure function Example:CobbDouglas utility two goods ]12111 ??l? ??= xxp])1( 212 ???l ??= xxp12211 xxpp???=][ 1212211 ??l ????= xxuxpxp??? ?= 121 xxu1212)1(xppx???=Solve for conditional demands 121*1 ])1([ ??= ???ppux ???])1([21*2?=ppuxC(p, u) = *22*11 xpxp ?C(p, u)= ])1()1[( 1121 ???????? ??? ??ppu?Nondecreasing in every price. Increasing in at least one price ?Increasing in utility u. ?Concave in p ?Homogeneous of degree 1 in all prices p. ?Shephard39。s Lemma) ? ?? ?? ?x D MV MV Mii iM*,= = ?pppand so... The ordinary demand function for modity i Roy39。s run through the primal problem Again use the FOC At x* we find... The primal problem How to solve the problem ?Now that we know the constrain
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