B2: COSTS and PROFITS with ......20 points. (a) Suppose we have the following production function: Q=K¹1/2L1/2 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. COBB-DOUGLAS...................... (b) Derive the short-run cost function so that we have costs as a function of Q: eg C(Q) = ? Show your work/reasoning. (c) Show that average costs first fall then rise with greater output. You can do this in a table or mathematically. Why does AC fall then rise? (d) What do we mean by a shut-down price? How is the shut-down price related to average variable costs? Explain. (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. (g) Find optimal output. You can do this in a table or mathematically. Should the firm shut-down? Explain.
