A firm producing hockey sticks has a production function given by

q = 2 √K ∙ L

In the short run, the firm’s amount of capital equipment is fixed at K = 100. The rental rate for K is v = $1, and the wage rate for L is w = $4.

a. Calculate the firm’s short-run total cost function. Calculate the short-run average cost function.

b. The firm’s short-run marginal cost function is given by SMC = q/50. What are the STC, SAC, and SMC for the firm if it produces 25 hockey sticks? Fifty hockey sticks? One hundred hockey sticks? Two hundred hockey sticks?

c. Graph the SAC and the SMC curves for the firm. Indicate the points found in part b.

d. Where does the SMC curve intersect the SAC curve? Explain why the SMC curve will always intersect the SAC at its lowest point.