1. Consider the production function: f (L,K) =L^aK^a . Let w and r denote the price of labor and capital, and let p denote the price of the output good. Assume that we are in the long-run time horizon.

(a) Does the firm exhibit decreasing, constant, or increasing returns to scale? Does it depend on a?

(b) Find the cost minimizing input bundle and the cost function (as a function of w, r, and q).

(c) Is marginal cost increasing, constant, or decreasing in output level? Does it depend on a?

(d) Find the profit maximizing output level when a < 1/2 . What happens when a = 1/2 or a > 1/2 ?