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b) Suppose a business faces a production function which is of the Cobb-Douglas form: Q(L,K) = AL“ K® where Q represents total product, L represents labour units, K represents capital units, A is some fixed constant representing technology and a and B are fixed parameters. Show that if a + B> 1 there is increasing returns to scale. Also show that the output elasticities with respect to labour and capital are constants and equal to a and B, respectively.

b) Suppose a business faces a production function which is of the Cobb-Douglas form: Q(L,K) = AL“ K® where Q represents total product, L represents labour units, K represents capital units, A is some fixed constant representing technology and a and B are fixed parameters. Show that if a + B> 1 there is increasing returns to scale. Also show that the output elasticities with respect to labour and capital are constants and equal to a and B, respectively.

Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.10P
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b) Suppose a business faces a production function which is of the Cobb-Douglas form: Q(L,K) = AL“ Kß where Q represents total product, L represents labour units, K represents capital units, A is some fixed constant representing technology and a and B are fixed parameters. Show that if a + B> 1 there is increasing returns to scale. Also show that the output elasticities with respect to labour and capital are constants and equal to a and B, respectively.
Transcribed Image Text:b) Suppose a business faces a production function which is of the Cobb-Douglas form: Q(L,K) = AL“ Kß where Q represents total product, L represents labour units, K represents capital units, A is some fixed constant representing technology and a and B are fixed parameters. Show that if a + B> 1 there is increasing returns to scale. Also show that the output elasticities with respect to labour and capital are constants and equal to a and B, respectively.
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