A firm produces output according to a production function: Q = F ( K,L ) = min {

Question

A firm produces output according to a production function:

Q = F(K,L) = min {5K,5L}.

a. How much output is produced when K = 2 and L = 3?




b. If the wage rate is $60 per hour and the rental rate on capital is $35 per hour, what is the cost-minimizing input mix for producing 10 units of output?

Capital =
Labor =


c. How does your answer to part b change if the wage rate decreases to $35 per hour but the rental rate on capital remains at $35 per hour?

Capital decreases and labor increases. Capital and labor increase. Capital increases and labor decreases. It does not change.

Explanation / Answer

(a)Q = F(K,L) = min {5K,5L}.

for K=2 and L=3

Q =min(5*2 , 5*3 ) = min(10,15) = 10

so for fiven value Q = 5K (Ans)

(b)

cost = 60*L + 35*k

Q = min{ 5K. 5L) = 10

this only possible if K=2 and L=2

for above value of K and L cost will be minimum

capital =2

labour =2

(C)

it doesn't changes

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