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1. Consider the Cobb-Douglas production funetion f(K,L) = cK"L*, where a, b, and e are constants greater than 0. (a) Show that if a + b>1 then f() will be increasing returns to scale. (b) Show that if a + b =1 then f(-) will be constant returns to scale. (c) Show that if a +b<1 then f(-) will be decreasing returns to scale.

1. Consider the Cobb-Douglas production funetion f(K,L) = cK"L*, where a, b, and e are constants greater than 0. (a) Show that if a + b>1 then f() will be increasing returns to scale. (b) Show that if a + b =1 then f(-) will be constant returns to scale. (c) Show that if a +b<1 then f(-) will be decreasing returns to scale.

Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.7P
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1. Consider the Cobb-Douglas production function f(K,L) = CKªL*, where a, b, and e are constants greater than 0. (a) Show that if a + b >1 then f(-) will be increasing returns to seale. (b) Show that if a + b = 1 then f(-) will be constant returns to scale. (c) Show that if a + b<1 then f(-) will be decreasing returns to scale. Now, let f() be a general production function (i.e., not necessarily a Cobb- Douglas one). (d) Suppose f(-) always exhibits increasing returns to scale. Show that there is no solution to the firm's profit maximization problem (You can assume the firm is a price-taking firm
Transcribed Image Text:1. Consider the Cobb-Douglas production function f(K,L) = CKªL*, where a, b, and e are constants greater than 0. (a) Show that if a + b >1 then f(-) will be increasing returns to seale. (b) Show that if a + b = 1 then f(-) will be constant returns to scale. (c) Show that if a + b<1 then f(-) will be decreasing returns to scale. Now, let f() be a general production function (i.e., not necessarily a Cobb- Douglas one). (d) Suppose f(-) always exhibits increasing returns to scale. Show that there is no solution to the firm's profit maximization problem (You can assume the firm is a price-taking firm
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