Econ Problem Set Essay Example for Free

Econ Problem Set Essay 1) Describe the effects on output and welfare if the government regulates a monopoly so that it may not charge a price above p, which lies between the unregulated monopoly price and the optimally regulate price (determined by the intersection of the firm’s marginal cost and the market demand curve). As usual, the monopoly determines its optimal output on the basis of MR = MC. Here, however, it cannot charge a price in excess of p*. So, for any output less than Q(p*) (where Q(p) is the demand function) its marginal revenue is p*. On the graph below that gives: pm p* MR MC Demand q m q * 2) The inverse demand curve a monopoly faces is p=10Q-1/2. The firm’s cost curve is c(Q) = 10 + 5Q. Find the profit maximizing price and quantity, and economic profit for the monopoly. Revenue = pQ = Q(10Q-1/2) = 10Q1/2 MR = 5Q-1/2 MC = 5 Profit maximization implies MR = MC, so 5Q-1/2 = 5, or Q* = 1; p* = 10. Economic Profit = Revenue – Cost = Q Ãâ€" p – c(Q) = 1(10) – (10 + 5Q) Economic Profit = 10 – 15 = -5. So, the monopoly will not produce at all, and will have a profit of zero. 3) The inverse demand curve a monopoly faces is p = 100 – Q. Find the profit maximizing price and quantity, and economic profit if: a) The total cost curve is c(Q) = 10 + 5Q. p = 100 – Q, R = p Ãâ€" Q = (100 – Q) Ãâ€" Q, so MR = 100 – 2Q. C(Q) = 10 + 5Q, therefore MC = 5. The profit-maximizing rule is MR = MC. 100 – 2Q = 5 ⇒ Q* = 47.5, p* = 100 – Q* = 52.5 So the profit-maximizing quantity is 47.5 units. The firm will charge $52.5 per unit. Economic Profit = Revenue – Cost = Q Ãâ€" p – c(Q) = Q(100 – Q) – (10 + 5Q) Economic Profit = 47.5(52.5) – (10 + 5(47.5)) = $2,246.25 b) The total cost curve is c(Q) = 100 + 5Q. How is this similar/different from that found in part a? The optimal price and quantity are the same, because the marginal cost doesn’t change. The marginal cost is constant at $5 as before. By setting MR = MC, the firm will have the same profit-maximizing solution. The only thing that changes is economic profit. Economic profit here is $90 less than in the previous problem (because of the difference in fixed costs). So, Economic Profit = $2,246.25 – 90 = $2,156.25. c) If the total cost curve is given by c(Q) = 16 + Q2. C(Q) = 16 + Q2, therefore MC = 2Q. The profit-maximizing rule is MR = MC. 100 – 2Q = 2Q ⇒ Q* = 25, p* = 100 – Q* = 75 So the profit-maximizing quantity is 25 units. The firm will charge $75 per unit. Economic Profit = Revenue – Cost = Q Ãâ€" p – c(Q) = 25(75) – (16 + Q2) = $1234. d) If the (total) cost curve is given by c(Q) = 16 + 4Q2, find the monopolist’s profit-maximizing quantity and price. How much economic profit will the monopolist earn? C(Q) = 16 + 4Q2, therefore MC = 8Q. The profit-maximizing rule is MR = MC. 100 – 2Q = 8Q ⇒ Q* = 10, p* = 100 – Q* = 90 So the profit-maximizing quantity is 10 units. The firm will charge $90 per unit. Economic Profit = Revenue – Cost = Q Ãâ€" p – c(Q) = 10(90) – (16 + 4Q2) = $484. e) Suppose (again) that the total cost curve is given by c(Q) = 16 + Q2 and the monopolist has access to a foreign market in which it can sell whatever quantity it chooses at a constant price of 60. How much will it sell in the foreign market? What will its new quantity and price be in the original market? It will sell on the foreign market up to the point where its marginal cost = 60. Since Marginal Cost = 2Q that means total production is 2QT = 60 or QT = 30. Domestic sales are now based on the marginal cost of $60 per unit, so The profit-maximizing rule is MR = MC. 100 – 2Q = 60 ⇒ QD = 20, pD = 100 – QD = 80 It will sell the remainder on the foreign market: QF = 30 – 20 = 10 units. f) Finally suppose the monopolist has a long-run constant marginal cost curve of MC = 20. Find the monopolist’s profit-maximizing quantity and price. Find the efficiency loss from this monopoly. MR = 100 – 2Q. The profit-maximizing rule is MR = MC. 100 – 2Q = 20 ⇒ Q* = 40, p* = 100 – Q* = 60 So the profit-maximizing quantity is 40 units. The firm will charge $60 per unit. Efficient production and price are: pe = 20; Qe = 80. Then Dead-Weight-Loss =  ½ (60 – 20) (80 – 40) = $800. 4) A monopoly sells its good in the United States, where the elasticity of demand is –2, and in Japan, where the elasticity of demand is –5. Its marginal cost is $10. a) At what price does the monopoly sell its good in each country if resales are impossible? The price-discriminating monopoly maximizes its profit by operating where its marginal revenue for each country equals the firm’s marginal cost. Hence, the marginal revenues for the two countries are equal; MRUS = MC = MRJ. MRUS = PUS (1 + 1/ÃŽ µUS) = MC. PUS (1 – 1/2) = 10. Therefore, PUS =20. MRJ = PJ (1 + 1/ÃŽ µJ) = MC. PJ (1 1/5) = 10. Therefore, PJ =12.5. b) What happens to the prices that the monopoly charges in the two countries if retailers can buy the good in Japan and ship it to the United States at a cost of (a) $10 or (b) $0 per unit? If retailers can buy the good in Japan and ship it to the United States at a cost of $10, then it can sell the good in the United States at the price of $22.50. Since it is not profitable, it never happens and nothing changes. However, if the shipping cost is zero, retailers can buy the good in Japan for $12.50 and sell it in the United States for $19 for a profit and undercut the monopolist. This means the monopoly cannot price-discriminate any more. As a result, there will be a single common price which will be somewhere between $12.5 and $ 20. 5) A monopoly sells in two countries, and resales between the countries are impossible. The demand curves in the two countries are p1=100 – Q1, p2=120 – 2Q2. The monopoly’s marginal cost is m = 30. Solve for the equilibrium price in each country. The price-discriminating monopoly maximizes its profit by operating where its marginal revenue for each country equals the firm’s marginal cost. Hence, the marginal revenues for the two countries are equal; MR1 = MC = MR2. P1 = 100 – Q1 MR1 = 100 – 2Q1, MC = 30 Since MR1 = MC, Q1*=35. Therefore, P1* = 65. P2 = 120 – 2Q2 MR2 = 120 – 4Q2, MC = 30. Similarly, MR2 = MC. Therefore, MQ2*=22.5 and P1* = 75.