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.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c043421-2d38-4023-bfad-9b2d578eeebf%2F4e4c93a3-6777-47a6-a1e7-6aca49d63abf%2Fyogjh2w_processed.jpeg&w=3840&q=75)
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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