平狄克《微观经济学》课后答案 11-12

1、PAGE 1212111121212Figure 11.3121 221 In Example 11.1 we saw how producers of processed foods and related consumer goods use coupons as a means of price discrimination. Although coupons are widely used in the United States, that is not the case in other countries. In Germany, the use of coupons is pr

2、ohibited by law.a. Does prohibiting the use of coupons in Germany make German consumers better off or worse off?In general, we cannot tell whether consumers will be better off or worse off. Total consumer surplus can increase or decrease with price discrimination, depending on the number of differen

3、t prices charged and the distribution of consumer demand. Note, for example, that the use of coupons can increase the market size and therefore increase the total surplus of the market. Depending on the relative demand curves of the consumer groups and the producers marginal cost curve, the increase

4、 in total surplus can be big enough to increase both producer surplus and consumer surplus. Consider the simple example depicted in Figure 11.3.a:Figure 11.3.aIn this case there are two consumer groups with two different demand curves. Assuming marginal cost is zero, without price discrimination, co

5、nsumer group 2 is left out of the market and thus has no consumer surplus. With price discrimination, consumer 2 is included in the market and collects some consumer surplus. At the same time, consumer 1 pays the same price under discrimination in this example, and therefore enjoys the same consumer

6、 surplus. The use of coupons (price discrimination) thus increases total consumer surplus in this example.Furthermore, although the net change in consumer surplus is ambiguous in general, there is a transfer of consumer surplus from price-insensitive to price-sensitive consumers. Thus, price-sensiti

7、ve consumers will benefit from coupons, even though on net consumers as a whole can be worse off.b. Does prohibiting the use of coupons make German producers better off or worse off?Prohibiting the use of coupons will make the German producers worse off, or at least not better off. If firms can succ

8、essfully price discriminate (i.e. they can prevent resale, there are barriers to entry, etc.), price discrimination can never make a firm worse off.EEUUEUEUEUEEUUEUEEU EEUUEU1111222212 112212MC CM 12121212ABAA BBAA BBAABBABFigure 11.6.cNYNYLALANYLANYNYLALANYNY LALANYNYLALA NYLATTNYNYLALANYLATNYLANYL

9、AAAB AB ABAB AB1121212121212BFigure 11.12A cable TV company offers, in addition to its basic service, two products: a Sports Channel (Product 1) and a Movie Channel (Product 2). Subscribers to the basic service can subscribe to these additional services individually at the monthly prices P1 and P2 r

10、espectively, or they can buy the two as a bundle for the price PB, where PB P1 + P2. (Subscribers can also forego the additional services and simply buy the basic service.) The companys marginal cost for these additional services is zero. Through market research, the cable company has estimated the

11、reservation prices for these two services for a representative group of consumers in the companys service area. These reservation prices are plotted (as xs) in figure 11.21, as are the prices P1, P2, and PB that the cable company is currently charging. The graph is divided into regions, I, II, III,

12、and IV.Figure 11.21a.Which products, if any, will be purchased by the consumers in region I? In region II? In region III? In region IV? Explain briefly.Product 1 = sports channel. Product 2 = movie channel.RegionPurchaseReservation PricesInothingr1 p1, r2 p2, r1 + r2 P1, r2 P2, r1 PB - P2, r2 PB - P

13、1, r1 + r2 PBTo see why consumers in regions II and III do not buy the bundle, reason as follows: For region II, r1 P1, so the consumer will buy product 1. If she bought the bundle, she would pay an additional PB - P1. Since her reservation price for product 2 is less than PB - P1, she will choose o

14、nly to buy product 1. Similar reasoning applies to region III.Consumers in region I purchase nothing because the sum of their reservation values are less than the bundling price and each reservation value is lower than the respective price.In region IV the sum of the reservation values for the consu

15、mers are higher than the bundle price, so these consumers would rather purchase the bundle than nothing. To see why the consumers in this region cannot do better than purchase either of the products separately, reason as follows: since r1 PB - P2 the consumer is better off purchasing both products t

16、han just product 2, likewise since r2 PB - P1, the consumer is better off purchasing both products rather than just product 1.b.Note that the reservation prices for the Sports Channel and the Movie Channel, as drawn in the figure, are negatively correlated. Why would you, or would you not, expect co

17、nsumers reservation prices for cable TV channels to be negatively correlated?Prices may be negatively correlated if peoples tastes differ in the following way: the more avidly a person likes sports, the less he or she will care for movies, and vice versa. Reservation prices would not be negatively c

18、orrelated if people who were willing to pay a lot of money to watch sports were also willing to pay a lot of money to watch movies.c.The companys vice president has said: “Because the marginal cost of providing an additional channel is zero, mixed bundling offers no advantage over pure bundling. Our

19、 profits would be just as high if we offered the Sports Channel and the Movie Channel together as a bundle, and only as a bundle.” Do you agree or disagree? Explain why.It depends. By offering only the bundled product, the company would lose customers below the bundle price in regions II and III. At

20、 the same time, those consumers above the bundling price line in these regions would only buy one service, rather than the bundled service. The net effect on revenues is indeterminate. The exact solution depends on the distribution of consumers in those regions.d.Suppose the cable company continues

21、to use mixed bundling as a way of selling these two services. Based on the distribution of reservation prices shown in figure 11.21, should the cable company alter any of the prices it is now charging? If so, how?The cable company could raise PB, P1, and P2 slightly without losing any customers. Alt

22、ernatively, it could raise prices even past the point of losing customers as long as the additional revenue from the remaining customers made up for the revenue loss from the lost customers.1211122212T122222112 11 1121212Figure 12.2.b1121121212121212112111212212iiii12iiTTTTTT12111121111121212T12Two

23、firms compete in selling identical widgets. They choose their output levels Q1 and Q2 simultaneously and face the demand curveP = 30 - Q,where Q = Q1 + Q2. Until recently, both firms had zero marginal costs. Recent environmental regulations have increased Firm 2s marginal cost to $15. Firm 1s margin

24、al cost remains constant at zero. True or false: as a result, the market price will rise to the monopoly level.True.If only one firm were in this market, it would charge a price of $15 a unit. Marginal revenue for this monopolist would be MR = 30 - 2Q,Profit maximization implies MR = MC, or30 - 2Q =

25、 0, Q = 15, (using the demand curve) P = 15.The current situation is a Cournot game where firm 1s marginal costs are zero and firm 2s marginal costs are 15. We need to find the best response functions:Firm 1s revenue isPq1 = (30 - q1 -q2) q1 = 30q1 - - q1q2and its marginal revenue is given by:MR1 =

26、30 - 2q1 - q2Profit maximization implies MR1 = MC1 or30 - 2q1 - q2 = 0 q1 = 15 - (1/2) q2which is firm 1s best response function.Firm 2s revenue isP q2 = (30 - q1 - q2) q2 = 30q2 - q1q2 - ,and its marginal revenue is given by:MR2 = 30 - q1 - 2q2Profit maximization implies MR2 = MC2, or30 - q1 - 2q2

27、= 15 q2 = (15/2) - (1/2) q1which is firm 2s best response function.Cournot equilibrium occurs at the intersection of best response functions. Substituting for q1 in the response function for fq2 = (15/2) - (1/2) 15 - (1/2) q2 ,Thus q2 = 0, q1 = 15, andP = 30 - q1 + q2 = 15, which is the monopoly pri

28、ce.1122121211121221211112121212121111T12TT1212111211111212212112T12T12121121221121112122T12T12 21121111222122122EDEDEDEEEEEEDDEDIEDDEEEDTEDTTwo firms produce luxury sheepskin auto seat covers, Western Where (WW) and B.B.B. Sheep (BBBS). Each firm has a cost function given by:C (q) = 20q + q2The mark

29、et demand for these seat covers is represented by the inverse demand equation:P = 200 - 2Q,where Q = q1 + q2 , total output.a.If each firm acts to maximize its profits, taking its rivals output as given (i.e., the firms behave as Cournot oligopolists), what will be the equilibrium quantities selecte

30、d by each firm? What is total output, and what is the market price? What are the profits for each firm?We are given each firms cost function C(q) = 20q + q2 and the market demand function P = 200 - 2Q where total output Q is the sum of each firms output q1 and q2.We find the best response functions

31、for both firms:WWs revenue is R1 = P q1 = (200 - 2(q1 + q2) q1 = 200q1 - 2q12 - 2q1q2.Its marginal revenue and cost functions are:MR1 = 200 - 4q1 - 2q2MC1 = 20 + 2q1Profit maximization implies:MR1 = MC1 or 200 - 4q1 - 2q2 = 20 + 2q1 which yields the best response function:q1 = 30 - (1/3)q2.By symmet

32、ry, BBBSs best response function will be:q2 = 30 - (1/3)q1.Cournot equilibrium occurs at the intersection of these two best response functions, given by:q1 = q2 = 22.5.Thus,Q = q1 + q2 = 45P = 200 - 2(45) = $110.Profit for both firms will be equal and given by:R - C = (110) (22.5) - (20(22.5) + 22.5

33、2) = $1518.75b.It occurs to the managers of WW and BBBS that they could do a lot better by colluding. If the two firms collude, what would be the profit-maximizing choice of output? What is the industry price? What is the output and the profit for each firm in this case?If firms can collude, they sh

34、ould each produce half the quantity that maximizes total industry profits (i.e. half the monopoly profits).Joint Profits will be (200-2Q)Q - 2(20(Q/2) + (Q/2)2) = 180Q - 2.5Q2 and will be maximized at Q = 36.Thus, we will have q1 = q2 = 36 / 2 = 18 and P = 200 - 2(36) = $128Profit for each firm will

35、 be 18(128) - (20(18) + 182) = $1,620c.The managers of these firms realize that explicit agreements to collude are illegal. Each firm must decide on its own whether to produce the Cournot quantity or the cartel quantity. to aid in making the decision, the manager of WW constructs a payoff matrix lik

36、e the real one below. Fill in each box with the (profit of WW, profit of BBBS). Given this payoff matrix, what output strategy is each firm likely to pursue?If WW produces the Cournot level of output (22.5) and BBBS produces the collusive level (18), then:Q = q1 + q2 = 22.5 + 18 = 40.5P = 200 -2(40.

37、5) = $119.Profit for WW = 22.5(119) - (20(22.5) + 22.52) = $1721.25.Profit for BBBS = 18(119) - (20(18) + 182) = $1458.Both firms producing at the Cournot output levels will be the only Nash Equilibrium in this industry, given the following payoff matrix. (note: not only is this a Nash Equilibrium,

38、but it is an equilibrium in dominant strategies.)Profit Payoff MatrixBBBS(WW profit, BBBS profit)ProduceCournot qProduceCartel q WWProduceCournot q1518, 15181721, 1458ProduceCartel q 1458, 17211620, 1620d.Suppose WW can set its output level before BBBS does. How much will WW choose to produce in this case? How much