7 A profit maximizing firm produces outputusing capital, K, and labour, L, in thefollowing production technology:Y = 2*K^0.5*L^0.5The cost function of the firm is:C = w*L+ r*Kwhere r=1.8.You are told that the firm employs L = 22workers.Find the optimal capital stock, K*.

We have given the cobb Douglas production with L=22.

A profit maximizing firm produces output using capital, K, and labour, L, in the following production technology: Y = 2*K^O.5*L^0.5 The cost function of the firm is: C = w*L+ r*K where r=1.8. You are told that the firm employs L = 22 workers. Find the optimal capital stock, K*.

A profit maximizing firm produces output using capital, K, and labour, L, in the following production technology: Y = 2K^O.5L^0.5 The cost function of the firm is: C = wL+ rK where r=1.8. You are told that the firm employs L = 22 workers. Find the optimal capital stock, K*.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter10: Cost Functions

Section: Chapter Questions

Problem 10.7P

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Question

A profit maximizing firm produces output
using capital, K, and labour, L, in the
following production technology:
Y = 2*K^0.5*L^0.5
The cost function of the firm is:
C = w*L+ r*K
where r=1.8.
You are told that the firm employs L = 22
workers.
Find the optimal capital stock, K*.

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