Problem 2. Consider two firms that produce a single output good, y, using two inputs: Capital, K, and labor, L. The prices of each unit of capital and labor are r and w, respectively. The output good y sells for $p per unit. Firm A's production function is y = fA(K,L) = K1/4 L 1/4. The profit function is thus: 1 1 πд(K, L) = pKĀLĀ – rK - WL Note that this is the same Cobb-Douglas production function from lecture, so you can either do the calculus yourself (suggested, at least once) or use the results from Slides 12-14 of Notes #14. a) Find the profit maximizing levels of K and L as functions of r, w, and p. b) Suppose that r=w=$1 and p=$4. What is the profit maximizing level of output, y? Suppose that the input prices both rise to r=w=$2. c) What is Firm A's new profit maximizing level of L? d) Suppose that capital (K) is fixed in the short run, so the firm is stuck using the level of K you found in part b). What is the optimal short run level of L? Firm B's production function is y = f(K,L) = [K + 2L] 1/2. Again suppose r=w=$1 and p=$4. e) What are Firm B's profit maximizing levels of K and L? f) If wincreases to $2 but r remains at $1, what are firm B's optimal levels of K and L?

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Problem 2. Consider two firms that produce a single output good, y, using two inputs: Capital, K, and labor, L. The prices of each unit of capital and labor are r and w, respectively. The output good y sells for $p per unit. Firm A's production function is y = fA(K,L) = K1/4 L 1/4. The profit function is thus: 1 1 πд(K