产业组织理论课后习题答案

1、Instructors Manual for Industrial Organization Theory and Applications by Oz Shy The MIT Press Cambridge, Massachusetts London, England Copyright c 19952004 Oz Shy. All rights reserved. The manual was typeset by the author using the L ATEX2 document preparation software by Leslie Lamport (a special

2、version of Donald Knuths TEX program) during the months from September 1995 to November 1995 while I was visiting the Economics Department of the University of Michigan. All the gures are also drawn in L ATEX using software called TEXcad developed by Georg Horn, which can be downloaded from various

3、mainframes. Version 1.0 Draft 20, (1995): Prepared for the rst printing of the rst edition bkman21.tex rst draft to be posted on the Web (2000/07/07) (parallel to the 5th Printing of the book) v.24 (2004/04/14): 6.1.d, 6.1.e This version: bkman24.tex2004/04/14 17:36 Contents To the Instructorv 2Basi

4、c Concepts in Noncooperative Game Theory1 3Technology, Production Cost, and Demand7 4Perfect Competition9 5The Monopoly11 6Markets for Homogeneous Products17 7Markets for Dierentiated Products25 8Concentration, Mergers, and Entry Barriers29 9Research and Development33 10The Economics of Compatibilit

5、y and Standards35 11Advertising37 12Quality, Durability, and Warranties39 13Pricing Tactics: Two-Part Tari and Peak-Load Pricing43 14Marketing Tactics: Bundling, Upgrading, and Dealerships45 15Management, Compensation, and Regulation49 16Price Dispersion and Search Theory51 17Miscellaneous Industrie

6、s53 To the Instructor Before planning the course, I urge the instructor to read carefully the Preface of the book that suggests dierent ways of organizing courses for dierent levels of students and also provides a list of calculus-free topics. The goals of this manual are: To provide the instructor

7、with my solutions for all the problems listed at the end of each chapter; to convey to the instructor my views of what the important concepts in each topic are; to suggest which topics to choose for dierent types of classes and levels of students. Finally, please alert me to any errors or incorrect

8、presentations that you detect in the book and in this manual. (e-mail addresses are given below). Note that the errata les (according to the printing sequence) are posted on the Web in PDF format. Before reporting errors and typos, please view the errata les to see whether the error you found was al

9、ready identied and corrected. Haifa, Israel, (April 14, 2004) E-mail: Backup:OzB Web-page: Catalog-page:/book-home.tcl?isbn=0262691795 This draft:bkman24.tex2004/04/14 17:36 Chapter 2 Basic Concepts in Noncooperative Game Theory An instructor of a short course should limit the

10、discussion of game theory to the four most important concepts in this chapter that are essential for the understanding most of the analyses presented in this book: 1. The denition of a game (Denition 2.1): It is important that the student will understand that a game is not properly dened unless the

11、list of players, the action set of each player, and the payo functions are clearly stated. It is important that the student will understand the meaning of the term outcome as a list of the specic actions chosen by each player (and not a list of payos as commonly assumed by students). 2. Nash equilib

12、rium (Denition 2.4). 3. Welfare comparisons among outcomes (Denition 2.6). 4. Extensive form games, strategies (compare with actions), subgames, and the SPE (De- nition 2.10). I urge the instructor to discuss the issues of existence, uniqueness, and multiple equilibria in class. More precisely, it i

13、s important that the student will know that in order to prove existence, it is sucient to nd only one NE outcome; however, to prove nonexistence, the student must go over all outcomes and show that at least one player benets from unilateral deviation. I believe that the above can be covered in 2 lec

14、tures, or in three hours of instruction. If you wish to devote more time to game theory, you can introduce the equilibrium in dominant actions (Denition 2.3) before teaching the NE equilibrium concept. If you wish to emphasis more game theory, I advise covering repeated games (section 2.3). Answers

15、to Exercises 1.(a) It is straightforward to conclude that R1(a2) = WARif a2=WAR WARif a2=PEACE and R2(a1) = WARif a1=WAR WARif a2=PEACE. That is, WAR is each players best response to each action taken by the other player (hence, WAR is a dominant action for each player). Now, ( a1, a2) = (WAR,WAR) i

16、s a (unique) NE since this outcome is on the best-response function of each player. (b) RJ(aR) = if aR= if aR= and RR(aJ) = if aJ= if aJ= . There does not exist a NE for this game since there does not exist an outcome the is on both best-response functions.That is, RJ() = , but RR() = , but RJ() = ,

17、 but RR() = , so RJ() = , and so on. 2Basic Concepts in Noncooperative Game Theory (c) R(a) = Bif a= L Tif a= R and R(a) = Lif a= T Rif a= B. A NE does not exist for this game since R(L) = B, but R(B) = R, but R(R) = T, so R(T) = L, and so on. 2.(a) If (T,L) is a NE, then (T,L) = a e = (B,L), and (T

18、,L) = b d = (T,R). (b) If (T,L) is an equilibrium in dominant actions, then T has to be a dominant action for player , that is (T,L) = a e = (B,L) and (T,R) = c g = (B,R); and L is a dominant action for player , that is (T,L) = b d = (T,R), and (B,L) = f h = (T,R). Let us observe that the parameter

19、restrictions given in part (a) are also included in part (b) conrming Proposition 2.1 which states that an equilibrium in dominant actions is also a NE. (c)i. (T,L) Pareto dominates (T,R) if (a c and b d) or (a c and b d); ii. (T,L) Pareto dominates (B,R) if (a g and b h) or (a g and b h); iii. (T,L

20、) Pareto dominates (B,L) if (a e and b f) or (a e and b f). (d) Loosely speaking, the outcomes are Pareto noncomparable if one player prefers (T,L) over (B,R), whereas the other player prefers (B,R) over the outcome (T,L). For- mally, either (T,L) = a g = (B,R) but (T,L) = b h = (B,R), or (T,L) = a

21、h = (B,R). 3.(a) There are three Pareto optimal outcomes: i. (n1,n2) = (100,100), where 1(100,100) = 2(100,100) = 100; ii. (n1,n2) = (100,99), where 1(100,99) = 98 and 2(100,99) = 101; iii. (n1,n2) = (99,100), where 1(99,100) = 101 and 2(99,100) = 98; (b) There is no NE for this game.1To prove this,

22、 we have to show that for every outcome (n1,n2), one of the players will benet from changing his or her declared value. Let us look at the following outcomes: 1A typo in the question (rst printing) leads to this undesirable result (see Basu, K. 1994. “The Travelers Dilemma: Paradoxes of Rationality

23、in Game Theory.” American Economic Review 84: 391395; for a mechanism that generates (2,2) as a unique NE outcome). Basic Concepts in Noncooperative Game Theory3 i. If (n1,n2) = (100,100), then player 1 can increase his or her payo to 1= 101 by declaring n1= 99. ii. If (n1,n2) = (99,100), then playe

24、r 2 can increase his or her payo from 2= 98 to 2= 99 by declaring n2= 99. Hence, players always benet from declaring a value of one dollar lower than the other player, and so on. iii. If (n1,n2) = (2,2), then player 1 can increase his or her payo from 1= 2 to 1= 98 by declaring n1= 100. 4.(a) There

25、are several NE outcomes for this game. For example, (LG,SM,SM) is a NE outcome since C(LG,SM,SM) = = C(SM,SM,SM) F(LG,SM,SM) = = = F(LG,LG,SM) G(LG,SM,SM) = = = G(LG,SM,LG). Hence, no rm nds it protable to unilaterally change the type of cars it produces. (b) Again, there are several NE. The outcome

26、 (LG,SM,SM) is also a NE for this game, and the proof is identical to the one given in part (a). 5.(a) There are three subgames: the game itself, and two proper subgames labeled JL (for Jacob left) and JR (for Jacob right). The three subgames are illustrated in Solution-Figure 2.1. Rachel Jacob R= 2

27、 J= 1 R= 0 J= 0 R= 0 J= 0 R= 1 J= 2 R= 0 J= 0 R= 1 J= 2 R= 2 J= 1 R= 0 J= 0 JLJR Solution-Figure 2.1: Three subgames of the dynamic Battle of the Sexes (b) One easy way to nd NE outcomes for an extensive form game is to construct a normal-form representation.2However, the normal-form representation

28、is already given in Table 2.2. Also, equation (2.1) proves that the NE outcomes involve the two players going together either to football or to the opera. Formally, it is easy to verify that the following three outcomes constitute NE: sJ= if sR= if sR= andsR= , 2This subquestion may confuse students

29、 who are already thinking in terms of backward induction. Since our analysis is based on SPE you may want to avoid assigning this subquestion (only). Also, an instructor teaching from the rst printing is urged to change this subquestion to nding the NE for the entire game only; hence, to postpone nd

30、ing the NE for the subgames to the next subquestion, where the NE of the subgames are used to nd the SPE. 4Basic Concepts in Noncooperative Game Theory sJ= if sR= if sR= andsR= , sJ= if sR= if sR= andsR= . (2.1) (c) Using backward induction, we rst construct Jacobs strategy (which constitutes the Na

31、sh equilibria for the two proper subgames). Looking at the proper subgames in Solution-Figure 2.1, we conclude that RJ(aR) = if aR= (subgame JR) if aR= (subgame JL). Now, we look for Rachels strategy (given Jacobs best response). If Rachel plays aR= , then her utility is given by R(,RJ() = 1. In con

32、trast, if Rachel plays aR= , then her utility is given by R(,RJ() = 2 1. Altogether, the strategies sR= aR= andRJ(aR) = if aR= if aR= constitute a unique SPE. (d) No! Jacobs best response is to play whenever Rachel plays . Thus, Jacobs announcement constitutes an incredible threat.3Clearly, Rachel,

33、who knows Jacobs best-response function in the second stage, should ignore Jacobs announcement, since Jacob, himself, would ignore it if Rachel plays in the rst stage. 6.(a) Jacobs expected payo is given by: EJ(,)= 2 + (1 ) 0 + (1 ) 0 + (1 )(1 ) 1 =2 + 3 . Rachels expected payo is given by: ER(,)= 1

34、 + (1 ) 0 + (1 ) 0 + (1 )(1 ) 2 =2 + 3 2 2. (b) The players best-response functions are given by RJ() = 0if 1/3 andRR() = 0if 2/3. The players best-response functions are drawn in Solution-Figure 2.2. (c) Solution-Figure 2.2 demonstrates that (,) = (2/3,1/3) is a NE in mixed actions. Also, note that

35、 the outcomes (0,0) and (1,1) are also NE outcomes in mixed actions and are the same as the pure NE outcomes. 3Instructors: Here is a good opportunity to discuss the concepts of credible and incredible threats. Basic Concepts in Noncooperative Game Theory5 111 111 1 3 RR()RJ() RR() RJ() 2 3 2 3 1 3

36、Solution-Figure 2.2: Best-response functions for the Battle of the Sexes in mixed actions (d) Substituting (,) = (2/3,1/3) into the players payo functions (dened above) yield EJ(2/3,1/3) = ER(2/3,1/3) = 2 3. (e) The best-response functions in Solution-Figure 2.2 intersect three times, meaning that i

37、n the mixed extension game, there are two equilibria: the two pure NE outcomes and one NE in mixed actions. In contrast, Figure 2.3 has only one intersection since in that game NE in pure strategies does not exist, and therefore the best-response functions intersect only once, at the NE in mixed act

38、ions. Chapter 3 Technology, Production Cost, and Demand This chapter summarizes the basic microeconomic tools the students need to know prior to taking this class. My advice for the instructor is not to spend time on this chapter but simply assign this chapter (with or without the exercises) as read

39、ing in the rst class. However, my advice is to return (or refer) to this chapter whenever denitions are needed. For example, when you rst encounter a discussion of returns to scale, I urge you to make a formal denition and refer the students to Denition 3.2. Similarly, when addressing elasticity iss

40、ues, students should be referred to Denition 3.3. Answers to Exercises 1.(a) Let 1. Then, by Denition 3.2, the technology exhibits IRS if (l)(k)= +lk lk, which holds when + 1. Using the same procedure and Denition 3.2, this technology exhibit CRS if + = 1, and DRS if + 0. 2.(a) Let 1. Then, by Denit

41、ion 3.2, the technology exhibits IRS if (l)+ (k)= (l+ k) (l+ k), which holds if 1. Similarly, the technology exhibits DRS if 1. This (quasi-linear) technology exhibits DRS since l + k l + k = (l +k). 4.(a) AC(Q) = TC(Q) Q = F Q + c, and MC(Q) = TC(Q) Q = c. These functions are drawn in Figure 4.2 in

42、 the book. 8Technology, Production Cost, and Demand (b) Clearly, AC(Q) declines with Q. Hence, AC(Q) is minimized when Q = +. (c) Declining average cost function reects an increasing returns to scale technology. 5.(a) Using Denition 3.3, p(Q) Q(p) Q p Q = (1) p Q = 99 Q Q . Hence, p(Q) = 2 when Q =

43、33. (b) From the above, p(Q) = 1 when Q = 99/2 = 49.5. (c) The inverse demand function is given by p(Q) = 99 Q. Therefore, TR(Q) = p(Q)Q = (99Q)Q. Hence, MR(Q) dTR(Q)/dQ = 992Q, which is a special case of Figure 3.3. (d) MR(Q) = 0 when Q = 49.5. That is, the marginal revenue is zero at the output le

44、vel where the demand elasticity is 1 (unit elasticity). (e) Using Figure 3.5, CS(33) = (99 33)66 2 = 2178,andCS(66) = (99 66)33 2 = 544.5 6.(a) p= A Q. Hence,p = A 1 Q 1 . (b) p= Q(p) Q p Q = A()p1 p Q = A()p Ap = . Thus, the elasticity is constant in the sense that it does not vary with the quantit

45、y consumed. (c) The demand is elastic if p 1.The demand is inelastic if 1 p 0, hence if 0 1. (d) By Proposition 3.3, MR = p1 + 1/(). Hence, p MR = 1 1 + 1 = 1 which is independent of Q. Chapter 4 Perfect Competition A perfectly competitive market is characterized by nonstrategic rms, where rms take

46、the market price as given and decide how much to produce (and, whether to enter, if free entry is allowed). Most students probably had some discussion of perfectly competitive markets in their intermediate microeconomics class. However, given the importance of this market structure, I urge the instr

47、uctor to devote some time in order to make sure that the students understand what price-taking behavior means. It is now the right time to emphasize that, in economics, the term competitive refers to price taking behavior of agents.For example, we generally assume that our consumers are competitive,

48、 which means that they do not bargain over prices and take all prices and their income as given. In a competitive market structure, we make a similar assumption about the rms. You may want to emphasize and discuss the following points: 1. The assumption of price taking behavior has nothing to do wit

49、h the number of rms in the industry. For example, one could solve for a competitive equilibrium even in the presence of one rm (see an exercise at the end of this chapter). Note that this confusion often arises since certain market structures yield market allocations similar to the competitive alloc

50、ation when the number of rms increases (see for example subsection 6.1.2 which shows that the Cournot allocation may converge to the competitive allocation when the number of rms increases to innity). 2. A major reason for studying and using alternative (noncompetitive) market structures stems from

51、the fact that the competitive market structure very often “fails” to explain why concentrated industries are observed. 3. Another major reason for studying alternative market structures stems from the nonexis- tence of a competitive equilibrium when rms technologies exhibit IRS. Finally, note that t

52、his chapter does not solve for a competitive equilibrium under decreasing returns to scale technologies for two reasons: (i) other market structures analyzed in this book are also developed mainly for CRS (unit cost) technologies, and (ii) most students are familiar with the DRS from their intermedi

53、ate microeconomics class. However, the exercise at the end of this chapter deals with a DRS technology. Answers to Exercises 1. Firm 1 takes p as given and chooses q1to max q1 1= pq1 wL1= p L 1 wL1. 10Perfect Competition The rst and second order conditions are given by 0 = d1 dL1 = p 2L1 w, d21 d(L1

54、)2 = p 4L3/2 1 0. Hence, q1= L 1= p/(2w). 2. Given that there is only one rm, the supply equals demand equilibrium condition yields that 120 pe= pe/2. Therefore, pe= 80; hence, qe 1 = Qe= pe/2 = 40. 3. From the production function, we can nd the equilibrium employment level to be Le 1 = (qe 1)2 = 16

55、00. Hence, 1= peqe 1 wL e 1= 80 40 1600 = 1600. 4. Given that the rms have the same technologies, they have the same supply functions. Therefore, the supply equals demand condition becomes 120 pe= pe/2 + pe/2, which yields pe= 60, Qe= 120 60 = 60, hence, qe 1 = qe 2 = 30. 5. Clearly, the competitive

56、 price is lower and the aggregate production is higher when the industry consists of two rms. 6. pp = 2q1 q1 pp = 2q2 q2 pp = q1+ q2 Q = q1+ q2 303060 60 120 120 p = 120 Q Solution-Figure 4.1: Competitive equilibrium with two rms Chapter 5 The Monopoly Most students encounter the monopoly problem in

57、 their intermediate microeconomics class. However, the instructor would probably want to make sure that all students fully understand the monopolys choice problem and the eect of price elasticity on the monopolys price, as well as the arguments against monopoly (section 5.2). I also urge the instruc

58、tor not to skip discussing discriminating monopoly (section 5.3). The remaining sections, the cartel (section 5.4), and the durable goods monopolies (sec- tion 5.5) are more optional depending on the instructors tastes and students ability. Answers to Exercises 1.(a) p dQ dp p Q = ap1 p ap = . Hence

59、, the exponential demand function has a constant price elasticity. By Propo- sition 3.3, MR(Q) = p 1 + 1 = p 1 . (b) Equating marginal revenue to marginal cost yields1 MR = pM 1 = c = MC;hence, pM= c 1. (c) As increases, the demand becomes more elastic, hence, the monopoly price must fall. Formally, dpM d = c( 1) c ( 1)2 (nH+ nL)V L/nH V L otherwise. 2Instructors are urged to assign or discuss this