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 {3K,3L}.

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




b. If the wage rate is $40 per hour and the rental rate on capital is $30 per hour, what is the cost-minimizing input mix for producing 6 units of output?

Capital: ?
Labor: ?


c. How does your answer to part b change if the wage rate decreases to $30 per hour but the rental rate on capital remains at $20 per hour?

A. It does not change. B. Capital and labor increase. C. Capital increases and labor decreases. D. Capital decreases and labor increases.

Explanation / Answer

a) A firm produces output according to a production function Q=F(K,L)=min {3K,3L}
A. How much output is produced when K=2 and L=3?
Q=min (6, 9) = 6 units

b) cost-minimizing input mix for producing 6 units of output is K = 2 and L = 2

Capital: 2 units
Labor: 2 units

c) since K and l are perfect complements n the production process, the cost minimizing levels of K and L do not depend on the rental rate of K and L. therefore

A. It does not change.

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