Given a firm which uses 2 inputs, X1 and X2; to produce a good that is described by the production function: Q = f (X1 X2) = X11/2 X21/4   The firm sells its ouput at N$80 per units. Given cost of input 1, X1; is N$4; and the cost of input 2, X2; is N$2 Solve for the profit maximizing input mix, output, and profit.

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.12P
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Given a firm which uses 2 inputs, X1 and X2; to produce a good that is described by

the production function: Q = f (X1 X2) = X11/2 X21/4

 

The firm sells its ouput at N$80 per units. Given cost of input 1, X1; is N$4; and

the cost of input 2, X2; is N$2

Solve for the profit maximizing input mix, output, and profit.

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