6. Suppose y = f(x) is a production function determining output y as a function of the vector x of nonnegative factor inputs, with f(0) = 0. Show that: (a) If f is concave, then f(x) ≤0 (so each marginal product f(x) is decreasing). (b) If f is concave, then f(x)/λ is decreasing as a function of λ. (c) If f is homogeneous of degree 1 (constant returns to scale), then f is not strictly concave.

6. Suppose y = f(x) is a production function determining output y as a function of the vector x of nonnegative factor inputs, with f(0) = 0. Show that: (a) If f is concave, then f(x) ≤0 (so each marginal product f(x) is decreasing). (b) If f is concave, then f(x)/λ is decreasing as a function of λ. (c) If f is homogeneous of degree 1 (constant returns to scale), then f is not strictly concave.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.7P

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