Problem 3. Consider a firm with production function y = f(K,L) = K 1/2 L 1/2. The price of capital is pк=10 and the price of labor is p₁=40. Suppose the firm wants to produce y=50 units of output. (This is the same setup as Notes #15, slides 3-4, with both exponents in the production function equal to ½ instead of ¼.) a) What is the firm's cost minimizing amount of labor, L*? b) What is the firm's cost minimizing amount of capital, K*? c) What is the firm's cost of producing 50 units, C(50)? Now suppose the firm wants to double output to y=100. d) In the short run, capital is fixed at the level K* you found in part b). What is the short run cost minimizing amount of labor, L*SR? e) What is the firm's short run cost of doubling production, CSR (100)? f) What is the firm's long run cost of doubling production, C(100)? g) How would you describe this firm's returns to scale in the short vs long run?

Fig: 1