(2 points) (a) Suppose we have the following production function: Q = K1/2L1/2. Suppose K is fixed in the short-run at 16. Let r = $20 and w = $20. State the firm's short-run cost minimization problem given the fixed input. (4 points) (b) Derive the short-run cost function so that we have costs as a function of Q: eg C(Q) = ? Show your work/reasoning. (4 points) (c) Show that average costs first fall then rise with greater output. You can in a table or mathematically. Why does AC fall then rise? (3 points) (d) What do we mean by a shut-down price? How is the shut-down price related to average variable costs? Explain. (2 points) (e) What is the shut-down price if r = $20 and w = $20? Explain. (1 points) (f) Let P = $12. State the firm's profit maximizing problem. (4 points) (g) Find optimal output. You can in a table or mathematically. Should the firm shut-down? Explain.

needs to be mathematically answered