A firm’s production function is q = f(K, L) = 7 ∙ K^(1/2) L^(1/3) . Capital is only available via a long term contract for K = 100 units of capital at a fixed rental rate r. The manager must decide whether or not to enter into such a contract. The firm can sell its output at the price p = $84 and pays w = $40 for each unit of labor employed.

a) Suppose r = $250, calculate the profit maximizing use of inputs and the profit maximizing output level. If all these prices stay fixed, is it profitable for this firm to enter into the contract? (Recall that K is fixed at 100 units if the contract is signed. If the contract is not signed you will not operate, i.e. K=0.)

b) At the use of inputs calculated in part (2a), determine if the rate at which the firm can trade inputs, TRSL,K(K, L) is equal to the rate at which the market can trade inputs − r w. If they are not equal, explain why if this action is profit maximizing?

c) Now suppose r = $300, will this change your answer to part (2a)? Why?