(a) Let ƒ : R¹→ R+ be a a firm's differentiable production function satisfying the usual assumptions. Suppose that x = R2 is a vector of inputs and that w € Rª are the factor prices. Let p ≤ R+ denote the output price. The profit of the firm is given by: π(p, w) : Derive and explain Shephard's = max [pf(x) — wx] . - x lemma: ƏT δω; = −x₂ (p, w).
(a) Let ƒ : R¹→ R+ be a a firm's differentiable production function satisfying the usual assumptions. Suppose that x = R2 is a vector of inputs and that w € Rª are the factor prices. Let p ≤ R+ denote the output price. The profit of the firm is given by: π(p, w) : Derive and explain Shephard's = max [pf(x) — wx] . - x lemma: ƏT δω; = −x₂ (p, w).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
![2. (a) Let f: R2→ R+ be a a firm's differentiable production function satisfying the
usual assumptions. Suppose that x € Rª is a vector of inputs and that w € Rª
are the factor prices. Let p E R+ denote the output price. The profit of the firm
is given by:
π (p, w): = max [pf(x) - wx] .
X
Derive and explain Shephard's
lemma:
Əπ
δω;
=
= − x₂ (p, w).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0a473134-4aa4-4f60-87c3-8811ff3a4fb2%2F3fac98ae-7a78-45d1-8755-7094ca38d9ad%2Fy52ywrl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. (a) Let f: R2→ R+ be a a firm's differentiable production function satisfying the
usual assumptions. Suppose that x € Rª is a vector of inputs and that w € Rª
are the factor prices. Let p E R+ denote the output price. The profit of the firm
is given by:
π (p, w): = max [pf(x) - wx] .
X
Derive and explain Shephard's
lemma:
Əπ
δω;
=
= − x₂ (p, w).
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