3. A price-taking firm produces a single output, y, using capital (K ) and labor (L). The price of output is p, the per-unit price of capital is r = 1, and the per-unit price of labor is w = 1. The firm's production function is f( L, K) = L3 K3 (a) What are the returns to scale of this firm's production technology? Justify your answer mathematically. (6 points) (b) Solve for the marginal product of labor, the marginal product of capital, and the MRTSL,K. (6 points) (c) Setup the firm's (long-run) profit-maximization problem. (4 points) (d) Solve for the firm's (long-run) profit-maximizing choices of capital and labor (your answer should be given in terms of p). (8 points) (e) Solve for the firm's (long-run) supply function, y(p). (6 points)