3. A price-taking profit-maximizing firm uses capital (K) and labor (L) to produce output according to the production function Q = K312. (a) Provide an expression for the marginal rate of technical substitution between labor and capital. (5 points) (b) Does the firm's technology exhibit decreasing MRTSL,K? A yes or no answer will suffice; no justification needed. (5 points) (c) Suppose the market price is p, the rental rate of capital is r, and the wage rate is w. Setup the firm's long-run profit-maximization problem. (5 points) (d) Suppose r = w. If the firm's profit-maximizing choice of capital is K* = 3, what must be the firm's profit-maximizing choice of labor? (10 points)