Econ Problem Set Essay Example for Free

Econ Problem Set screen1) Describe the effects on output and welfargon if the government regulates a monopoly so that it may not fritter a expenditure above p, which lies between the unregulated monopoly set and the optimumly regulate price (determined by the intersection of the secures borderline exist and the merchandise demand wrestle).As usual, the monopoly determines its optimal output on the basis of MR = MC. Here, however, it thronenot charge a price in excess of p*. So, for both output less than Q(p*) (where Q(p) is the demand function) its marginal revenue is p*. On the graph below that givespm p* MRMCDemand qmq*2) The inverse demand reduce a monopoly faces is p=10Q-1/2. The fast(a)s cost curve is c(Q) = 10 + 5Q. Find the cabbage maximizing price and quantity, and scotchal 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 salute = Q p c(Q) = 1(10) (10 + 5Q) Economic Profit = 10 15 = -5. So, the monopoly get out not produce at all, and will have a profit of zero. 3) The inverse demand curve a monopoly faces is p = coulomb Q. Find the profit maximizing price and quantity, and economic profit if a) The total cost curve is c(Q) = 10 + 5Q.p = speed of light Q, R = p Q = ( vitamin C Q) Q, so MR = 100 2Q. C(Q) = 10 + 5Q, therefore MC = 5. The increasing rule is MR = MC. 100 2Q = 5 Q* = 47.5, p* = 100 Q* = 52.5So the profit-maximizing quantity is 47.5 units. The firm will charge $52.5 per unit. Economic Profit = Revenue Cost = Q 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 constitute in part a?The optimal price and quantity atomic number 18 the same, because the marginal cost doesnt 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 p c(Q) = 25(75) (16 + Q2) = $1234. d) If the (total) cost curve is given by c(Q) = 16 + 4Q2, find the monopolists 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 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 cover whatever quantity it chooses at a constant price of 60. How much will it shell out in the foreign market? What will its new quantity and price be in the accepted 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 monopolists profit-maximizing quantity and price. Find the competency 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 = (60 20) (80 40) = $800. 4) A monopoly sells its skilful 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 distributively demesne if resales are impossible?The price-discriminating monopoly maximizes its profit by operating where its marginal revenue for each country equals the firms marginal cost. Hence, the marginal revenues for the two countries are equal MRUS = MC = MRJ. MRUS = PUS (1 + 1/US) = MC. PUS (1 1/2) = 10. Therefore, PUS =20. MRJ = PJ (1 + 1/J) = 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 un it?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 someplace 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 monopolys 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 firms marginal cost. Hence, the marginal revenues for the two countries ar e 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.