Consider a representative firm that produces using capital (K) and labor (N), but that owns no capital

Consider a representative firm that produces using capital (K) and labor (N), but that owns no capital. The firm can hire workers in the labor market at a wage w and can rent capital market at a rental rate r (that is, the firm can rent K units of capital for which it would have to pay rK). The production function of the firm is given by zF (K, N) where: F (K, N) = KaN ß and a + ß < 1. (a) Does the technology exhibit constant returns to scale? If not does it exhibit increasing returns, decreasing returns, or neither? (b) Pose the profit maximization problem of the firm. (c) Suppose K is exogenously given. Find the firm’s optimal labor demand. (d) Suppose K is exogenously given. Find the firm’s optimal profits. (e) What happens to the optimal profits when ß = 1 - a?