5. Let a firm's production function be given by f(l, k) = 1/41/4. Let the output price be p and the price of labor and capital be w and r, respectively.
(a) Does the production function exhibit decreasing, constant or increasing returns to scale?
(b) First consider one-step profit maximization. Write down the profit function of the firm and solve the maximization problem by checking the first order conditions.
(c) Now consider two-step maximization and show that you obtain the same optimal bundle of inputs.