FOC: on c(z) θ 1 θ−1 −1 θ−1 θ j −1 θ j p(z) = λ c (z) θ dz c (z) θ θ−1 0 θ−1 1 1 θ−1 θ−1 −1 p(z) = λ cj (z) θ dz cj (z) θ
0
using
1
cj (z)
θ−1 θ
dz
0
θ θ−1
= C j , we get
p(z) = λcj (z)
−1 θ
equation (1) for good z p(z ) = λcj (z )
j θ1 C
(1)
(2)
−1 θ
so that equations (1) and (2) yield
Cj
1θ
−1
1
p(z) cj (z) θ cj (z ) θ = = −1 1 p(z ) cj (z) θ cj (z ) θ θ p(z) j j c (z ) = c (z) p(z ) FOC: on C j P =λ Using (3), (1) then implies 1 −1 p(z) = P cj (z) θ C j θ j θ1 p(z) C = j P c (z) p(z) −θ j c(z) = C P
Demand for good z (static problem for the consumer) depends on • overall consumption • relative price avec elasticity of substitution θ 1
Mar 18, 1998 - This work has been partly supported by the ALAPEDES project of the ..... invariant measure p. This measure is explicitly computable : px = kθ x1.
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