11) Firms 1 and 2 are duopolists that choose quantities in order to maximize profits. Further suppose that Firm 1's best response function is q1 = 80 - 0.50q2. while Firm2's best response function is q2 = 60 - 0.40q1. The Nash-Cournot equilibrium quantities are: q1 = _____ units for firm 1 and q2 =_____ units form firm 2.

A) 62.5; 62.5

B) 35; 62.5

C) 35; 35

D) 62.5; 35

E) None of the above

12) If a firm operating in a perfectly competitive industry maximizes short-run profits by producing some quantity of output q* > 0, which of the following must be true at that level of output? A) p > MC B) MR > MC C) p ? AVC D) All of the above E) B and C only 13) Suppose there are N firms in a perfectly competitive industry. Each firm is producing output Q using production function Q=K^0.40 X L^0.60. Which of the following statements must be true about the long-run competitive equilibrium?

A) p = AC = MC

B) profit = 0

C) w > r

D) All of the above.

E) A and B only

14) Suppose that for each firm in the perfectly competitive market for potatoes, long-run average cost is minimized at $0.20 per pound when 500 pounds are grown. The market demand function for potatoes is Q = 10,000/p. If the long-run supply curve is horizontal, then in the long run equilibrium the total expenditure by all consumers on potatoes will be ______ and there will be _______ firms in the industry.

A) $50,000, 20

B) $10,000, 20

C) $10,000, 100

D) $50,000, 100

E) None of the above

15) Consider an industry populated by identical firms, facing constant input prices, and having all the other characteristics of a perfectly competitive market. Which of the following statements describes the new long-run market equilibrium resulting from a shift in demand?

A) a shift in demand has no effect on the long-run average cost and so there is no change in equilibrium price and quantity.

B) a shift in demand will change the equilibrium price and quantity.

C) a shift in demand has no effect on the long-run average cost, resulting in change in equilibrium quantity but not price.

D) a shift in demand has no effect on the long-run average cost, resulting in change in equilibrium price but not quantity.

E) a shift in demand is not possible

II. (50 points) Suppose that a firm has a Leontief production function given by y = min {Z/2, A/4), and that the rental rates for labor and capital are given by w=l and v=4. Suppose also that K is fixed at 200 in the short run. (1) Write down the short-run cost minimization problem of the firm. (2) Find the conditional factor demand function for labor and calculate the firm's short-run cost function. (3) Calculate the firm's average fixed, average variable, average and marginal cost functions. (4) Draw the graph of all short-run cost curves. (5) Now suppose the firm can choose the level of capital stock K in the long run. Write down the firm's long-run cost minimization problem. (6) Find conditional factor demand functions for both inputs and calculate the firm's long-run cost function. (7) Calculate the firm's long run average and marginal cost functions. (8) Draw the graph of all long run cost curves. (9) Explain graphically the relationships between long-run and short-run cost curves for the production function given above. (10) Explain the relationships between production functions and cost functions for this problem.3. A firm uses the production function f(X1, 22) = 21 72 . 1/4 1/4 Assume that the prices of the inputs are given by w1 = 16 and w2 = 1. (a) Is the production function exhibit decreasing, constant, or increasing returns to scale? What does this mean for the slope of the LRATC curve? (b) Find c(y), the firm's long-run total cost function. Hint: the firm will choose inputs to minimize it's costs. (c) Find expressions for the LRATC and LRMC curves associated with the function found in part (b). (d) Now suppose the quantity of input 2 is fixed in the short run. Find Cs(y, 72), the firm's short-run total cost function if input 2 is fixed at some arbi- trary level 2. (e) Use your answer from part (d) to find SRATC and SRMC when T2 = 16