Question

7. Suppose a firm's production function is Q-min(L,K). (This means the level of O produced is the smaller of L and K) a. Graph some isoquants for this firm. b. Let w = 2, r= 1, and suppose the firm's expenditures are C-12. What are the firm's demands for L and K? What is the share of labor in the cost of output? c. Now let w rise to 3. What are the firm's new demands for L and K? d. Now suppose instead that the production function is Q = min(L,2K), Draw some isoquants for this firm. e. Again, let w 2 and r 1, and suppose the firm's expenditures are C 12. What are the firm's demands for L and K? What is the share of labor in the cost of output? f. Now let w rise to 3. What are the firm's new demands for L and K? g. Why does labor demand fall more in part f than in part c? (Hint: Use one of Marshall's Laws.)

Answer 1

a) Q = min (L, K) b) From the production function, we can say L = K & L = K = Q C = wL + rK 12 = 2Q + 1Q = 3Q Q = 12/3 = 4 Therefore L = K = 4 are the demands c) 12 = 3L + 1 K 12 = 3Q + Q Q = 12/3 = 3 Therefore L = k = 3 are the new demands d) Q = min (L, 2K) = > L = 2K K = L/2