A firm produces output according to a production function: Q = F(K,L) = min {2K,

Question

A firm produces output according to a production function: Q = F(K,L) = min {2K,4L}. a. How much output is produced when K = 2 and L = 3? b. If the wage rate is $30 per hour and the rental rate on capital is $10 per hour, what is the cost-minimizing input mix for producing 4 units of output? Capital: Labor: c. How does your answer to part b change if the wage rate decreases to $10 per hour but the rental rate on capital remains at $20 per hour? Capital increases and labor decreases. Capital and labor increase. Capital decreases and labor increases. It does not change.

Explanation / Answer

A firm produces output according to a production function Q=F(K,L)=min {2K,4L}
A. How much output is produced when K=2 and L=3?

Q=min (4, 12) = 4

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B. If the wage rate is $30 per hour and the rental rate on capital is $10 per hour, what is the cost-minimizing input mix for producing 4 units of output

In equilibrium 2k =4L or K = 2L

So Q = 2K = 4L in equilibrium. To get Q= 4 we need K= 2 and L= 4

Total cost = 4*30 +2*10 = 80

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C.How does your answer to part b change if the wage rate decreases to $10 per hour but the rental rate on capital remains at $10 per hour?

The answer does not change as these inputs are perfect complements and there is zero substitution between them. Changes in input prices do not matter if Q is predetermined only the total cost will change to 40+20 = 60
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