Answered: inction: Consider the 'Cobb-Douglas'… | bartleby

Microeconomic Theory

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.4P

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2

Consider the 'Cobb-Douglas' production
function:
2. Consider the 'Cobb-Douglas' production function:
1-a
f(ke, ne) = k;"n}"
where a is an exogenous parameter that determines the share of output produced by each
factor of production. Assume that capital and labor inputs, k and nų, must be positive
and that 0<a < 1.
Mathematically show the following:
(a) An increase in k will increase the marginal product of labor.
(b) An increase in nų will increase the marginal product of capital.

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