Answer to Question #103814 in Microeconomics for adv micro 1.36

Question

1.36 Provide an alternative proof of Roy’s identity by completing the following steps:
(a) Using the definition of v, show that if p
0 and x0 = x(p0, y0), then v(p, p · x0) ≥ v(p0, p0 ·
x0) ∀p
0.
(b) Conclude that f(p) ≡ v(p, p · x0) is minimised on Rn
++ at p = p0.
(c) Assume f is differentiable at p0. What value must its gradient have at p0?
(d) Prove Roy’s identity using parts (a) to (c).

Answer 1

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