Y6

Suppose that a firm's production function is given by: Q=L0.5K0.5. Suppose that the wage firms must pay for their workers is $90 per worker and the rental rate they must pay for their capital is $10 per unit.

a. Calculate the firm's SR production function if the firm uses 36 units of capital.

b. Calculate the firm's SR total cost function (must be as a function of Q).

c. Suppose the firm wants to produce 18 units of output, but it is the SR, so they cannot alter the amount of capital they use. How much labor will they need to produce these 18 units?

d. What is the short-run total cost of producing these 18 units.

e. Calculate the cost-minimizing combination of L and K if the firm wishes to produce 18 units of output when K is not fixed.

f. What is the total cost of producing 18 units in the long-run (when K is flexible). Compare your answer to part d.

g. Calculate the LR total cost function (must be a function of Q). Double check your answer against your answer to f for 18 units.