Problem Set 9 Due Lecture 11 in class on paper. See charts for all subsections of this question at the end of the problem set.

Transcription

1 Intermediate Microeconomics Fall GLS Chapter 9, Question 3 2. GLS Chapter 9, Question 13 Problem Set 9 Due Lecture 11 in class on paper See charts all subsections of this question at the end of the problem set. (a) Calculate the profit-maximizing price and quantity of fairy dust. Calculate the seller s profit. The monopolist finds the profit maximizing Q by setting. We can use the mula given in the notes to find MR = 1 2Q. Setting, we can solve 1 2Q = 2 8 = 2Q Q = 4 means plug in the Q you just found into the demand curve: P = 1 Q = 1 4 = 6. Find the profit by subtracting total cost from total revenue. Note that because marginal cost is constant, AT C = MC, so we can write: = 6(4) 2(4) = 4(4) = 1, 6 (b) Suppose the new inverse demand curve is P = 2 2Q. Find the new profit-maximizing Q and P. Follow the steps as in (a). We can use the mula given in the notes to find MR = 2 4Q. 1

2 Setting, we can solve 2 4Q = 2 18 = 4Q Q = 45 means plug in the Q you just found into the demand curve: P = 2 2Q = 2 2(45) = 11. Find the profit by subtracting total cost from total revenue. = 11(45) 2(45) = 9(45) = 4, 5 (c) Suppose that the new inverse demand curve is P = 1.5Q. Find the new profitmaximizing P and Q. Follow the steps as in (a). We can use the mula given in the notes to find MR = 1 Q. Setting, we can solve 1 Q = 2 8 = Q Q = 8 means plug in the Q you just found into the demand curve: P = 1.5Q = 1.5(8) = 6. 2

3 Find the profit by subtracting total cost from total revenue. = 6(8) 2(8) = 4(8) = 3, 2 Find the new profit- (d) Suppose that the new inverse demand curve is P = 15 Q. maximizing P and Q. Follow the steps as in (a). We can use the mula given in the notes to find MR = 15 2Q. Setting, we can solve 15 2Q = 2 13 = 2Q Q = 65 means plug in the Q you just found into the demand curve: P = 15 Q = = 85. Find the profit by subtracting total cost from total revenue. = 85(65) 2(65) = 65(65) = 4, 225 (e) When demand increases, profits monopolistic suppliers always increase. Individually, P and Q both don t need to increase, but total profits do increase. 3. GLS Chapter 9, Question 18 (a) Is the firm a natural monopoly? Yes, over the range that consumers demand, average total cost (AT C) is always declining. (b) Will the firm earn a profit if not subject to regulation? 3

4 Left to its own devices, the firm will set Q such that. This yields production at Q = 5. Looking at the chart, we can see profits in the rectangle from to 5 on the x axis, and from to where Q = 5 intersects with demand, which is the maximum price the firm can charge at this quantity. The firm s costs at Q = 5 are the rectangle of width 5, and height where Q = 5 intersects the LAT C curve. The revenue rectangle is bigger than the cost rectangle. Theree, the firm makes positive profits. (c) If the government requires firms to charge no more than MC, what are P and Q? Is there a problem with this scheme? If the firm can charge no more than marginal cost, it would choose to produce Q = 1 and P = 1. However, at this level of production, the firm cannot cover its costs, since LAT C are far above LMC at Q = 1. The firm would exit the market. (d) Suppose the firm is not allowed to charge more than LAT C. What are P and Q? What is the problem with this scheme? If the firm charges LAT C, it will produce Q = 7, and sell at P = 25. This still yields a deadweight loss but it might be the best that the regulator can do. (e) Compare the DW L under each regime. In (c) there is no deadweight loss the firm produces Q such that P = MC. Of course, this firm will go out of business. 4

5 Part (b) poly. Price 1: Monopoly. ($/unit) Price ($/unit) Market Power and Monopoly Chapter Market Power and Monopoly Chapter P* DWL P* DWLLMC LATC LMC LATC MR D MR D 5 7 1, 5 7 1, r the government regulation, P = LMC. There is no deadweight loss. 2: r the Under government the government Part regulation, (d) regulation, P = LATC. P = LMC. There is no deadweight loss. 3: Under the government regulation, P = LATC. Price ($/unit) Price ($/unit) DWL DWLLMC LATC LMC LATC MR D MR D 5 7 1, 5 7 1, re vying to receive the pay-per-view broadcast rights to the World Series of Yahtzee. Each he orks inverse are vying demand to receive watching the pay-per-view this nail-biter broadcast of an rights event is to given the World by P Series = 1 of Yahtzee..1Q. Each e that the broadcast the inverse at demand a constant marginal watching cost this of nail-biter $1 per viewer. of an event is given by P = 1.1Q. provide deadweight the broadcast loss of monopoly at a constant in the market marginal cost the of televised $1 per viewer. Yahtzee tournament. late tournament the deadweight Yahtzee s loss governing of monopoly body in plans the market to select one the televised at Yahtzee its discretion tournament. to air se nt. that How tournament much will each Yahtzee s governing be willing body to plans spend to lobbying select one the broadcast at its rights? discretion to air, urnament. in this situation, How much the losses will each to society are be much willing greater to spend than lobbying just the deadweight the broadcast losses of rights? in why, in this situation, the losses to society are much greater than just the deadweight losses of poly. tion n rice nit) MR DWL MR D DWL MCD

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