Answer all parts!

15. Suppose a firm faces the following production function: Q = VK * VL (with MPL = VK 2 * VL and M PK = VI 2 * VK The wage rate is w = $50 and the rental rate is r = $200. Show your work for credit. Round to the nearest hundredth. (a) (6 points) Find the cost-minimizing L* and K* for Q = 100. (b) (6 points) Find the cost-minimizing L* and K* for Q = 200. (c) (6 points) Find the cost-minimizing [* and K* for Q = 300. (d) (4 points) Find the short-run equilibrium for Q = 200 by holding capital constant equal to the K* you found in question item (a). (e) (4 points) Find the short-run equilibrium for Q = 300 by holding capital constant equal to the K* you found in question item (a). (f) (2 points) Find the long run total cost of producing Q = 100. K - 50 (g) (2 points) Find the long run total cost of producing Q = 200. (h) (2 points) Find the long run total cost of producing Q = 300. @ 250 1? (i) (2 points) Find the short run total cost of producing Q = 200. 200 = (j) (2 points) Find the short run total cost of producing Q = 300. 40 090 150 (k) (4 points) What economies of scale does the firm exhibit between Q = 100 and Q = 300? 1 300 (1) (4 points) What returns to scale does the firm exhibit between Q = 100 and Q = 300? (m) (2 points) Find the long run average total cost of producing Q = 100. (n) (2 points) Find the long run average total cost of producing Q = 200. (o) (2 points) Find the long run average total cost of producing Q = 300. (p) (2 points) Find the short run average total cost of producing Q = 100. (q) (2 points) Find the short run average total cost of producing Q = 200. (r) (2 points) Find the short run average total cost of producing Q = 300. (s) (16 points) Plot the long run equilibria you found in (a)-(c). (t) EC (up to 4 points) Plot the short run equilibria points you found in (d) and (e) (no isocosts needed)