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11. Suppose that a firm that uses 2 inputs has the production function f(x1, x₂) = = 12xx and faces the input prices (P₁, P2) and the output price 1. Show that f is concave for ₁> 0 and x₂ > 0, so that the firm's profit function , defined by (T1, 12) = f(x₁, x2) - P11 - P22, is concave.

11. Suppose that a firm that uses 2 inputs has the production function f(x1, x₂) = = 12xx and faces the input prices (P₁, P2) and the output price 1. Show that f is concave for ₁> 0 and x₂ > 0, so that the firm's profit function , defined by (T1, 12) = f(x₁, x2) - P11 - P22, is concave.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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11. Suppose that a firm that uses 2 inputs has the production function f(x₁, x₂) = 12x³x and faces the input prices (P₁, P₂) and the output price 1. Show that f is concave for £₁ > 0 and x₂ > 0, so that the firm's profit function , defined by (1, ₂) = f(x1, T2)-P₁1 - P22, is concave.
Transcribed Image Text:11. Suppose that a firm that uses 2 inputs has the production function f(x₁, x₂) = 12x³x and faces the input prices (P₁, P₂) and the output price 1. Show that f is concave for £₁ > 0 and x₂ > 0, so that the firm's profit function , defined by (1, ₂) = f(x1, T2)-P₁1 - P22, is concave.
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