1. Suppose that an individual's direct utility function is represented implicitly by: u = ΣΦ, log x-2 Φ i=1,2 where i = α + Bu 1+u Yi, Oi, and Bi are parameters with Σ a; = B₁ = 1. a) Derive the Hicksian demand and expenditure functions. b) Prove the homogeneity property. c) Use the Shephard's lemma to derive the Hicksian demand functions.
1. Suppose that an individual's direct utility function is represented implicitly by: u = ΣΦ, log x-2 Φ i=1,2 where i = α + Bu 1+u Yi, Oi, and Bi are parameters with Σ a; = B₁ = 1. a) Derive the Hicksian demand and expenditure functions. b) Prove the homogeneity property. c) Use the Shephard's lemma to derive the Hicksian demand functions.
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.11P
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Transcribed Image Text:1. Suppose that an individual's direct utility function is represented implicitly by:
u = ΣΦ, log
x-2
Φ
i=1,2
where i
=
α + Bu
1+u
Yi, Oi, and Bi are parameters with Σ a; = B₁ = 1.
a) Derive the Hicksian demand and expenditure functions.
b) Prove the homogeneity property.
c) Use the Shephard's lemma to derive the Hicksian demand functions.
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