A firm produces output according to a production function Q

A firm produces output according to a production function: Q = F(K,L) = min {3K,6L}.

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

b. If the wage rate is $55 per hour and the rental rate on capital is $45 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 $45 per hour but the rental rate on capital remains at $45 per hour?

- Capital decreases and labor increases

-Capital increases and labor decreases

-Capital and labor increase

-It does not change.

Solution

a.

Q = F(K,L) = min {3K,6L}

Q = F(2,3) = min {3*2,6*3} = min {6,18} = 6 units

b.

The cost-minimizing mix of Kand Lthat produceQ =6 is K =2,L =1 based on hit and trial method used in the Q equation.

c.

Since K and L are perfect complements in the production process, the cost-minimizing levels of K and L do not depend on the rental rates of K and L. Therefore, the cost-minimizing levels of K and L do not change with changes in the relative rental rates.