(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).

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter11: Profit Maximization

Section: Chapter Questions

Problem 11.9P

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