北京大学中级微观经济学Ch27-OligopolyPPT优秀课件

1、1 Chapter Twenty-Seven Oligopoly 2 Oligopoly uA monopoly is an industry consisting a single firm. uA duopoly is an industry consisting of two firms. uAn oligopoly is an industry consisting of a few firms. Particularly, each firms own price or output decisions affect its competitors profits. 3 Oligop

2、oly uHow do we analyze markets in which the supplying industry is oligopolistic? uConsider the duopolistic case of two firms supplying the same product. 4 Quantity Competition uAssume that firms compete by choosing output levels. uIf firm 1 produces y1 units and firm 2 produces y2 units then total q

3、uantity supplied is y1 + y2. The market price will be p(y1+ y2). uThe firms total cost functions are c1(y1) and c2(y2). 5 Quantity Competition uSuppose firm 1 takes firm 2s output level choice y2 as given. Then firm 1 sees its profit function as uGiven y2, what output level y1 maximizes firm 1s prof

4、it? 1 1212111 (;)()().yyp yyycy 6 Quantity Competition; An Example uSuppose that the market inverse demand function is and that the firms total cost functions are p yy TT () 60 cyy 111 2 () cyyy 2222 2 15(). and 7 Quantity Competition; An Example (;)().yyyyyy 121211 2 60 Then, for given y2, firm 1s

5、profit function is 8 Quantity Competition; An Example (;)().yyyyyy 121211 2 60 Then, for given y2, firm 1s profit function is So, given y2, firm 1s profit-maximizing output level solves y yyy 1 121 60220 . 9 Quantity Competition; An Example (;)().yyyyyy 121211 2 60 Then, for given y2, firm 1s profit

6、 function is So, given y2, firm 1s profit-maximizing output level solves y yyy 1 121 60220 . I.e. firm 1s best response to y2 is yRyy 1122 15 1 4 (). 10 Quantity Competition; An Example y2 y1 60 15 Firm 1s “reaction curve” yRyy 1122 15 1 4 (). 11 Quantity Competition; An Example (;)().yyyyyyy 211222

7、2 2 6015 Similarly, given y1, firm 2s profit function is 12 Quantity Competition; An Example (;)().yyyyyyy 2112222 2 6015 Similarly, given y1, firm 2s profit function is So, given y1, firm 2s profit-maximizing output level solves y yyy 2 122 6021520 . 13 Quantity Competition; An Example (;)().yyyyyy

8、y 2112222 2 6015 Similarly, given y1, firm 2s profit function is So, given y1, firm 2s profit-maximizing output level solves y yyy 2 122 6021520 . I.e. firm 1s best response to y2 is yRy y 221 1 45 4 (). 14 Quantity Competition; An Example y2 y1 Firm 2s “reaction curve” yRy y 221 1 45 4 (). 45/4 45

9、15 Quantity Competition; An Example uAn equilibrium is when each firms output level is a best response to the other firms output level, for then neither wants to deviate from its output level. uA pair of output levels (y1*,y2*) is a Cournot-Nash equilibrium if yRy 221 * (). yRy 112 * () and 16 Quant

10、ity Competition; An Example yRyy 1122 15 1 4 * () yRy y 221 1 45 4 * * (). and 17 Quantity Competition; An Example yRyy 1122 15 1 4 * () yRy y 221 1 45 4 * * (). and Substitute for y2* to get y y 1 1 15 1 4 45 4 * * 18 Quantity Competition; An Example yRyy 1122 15 1 4 * () yRy y 221 1 45 4 * * (). a

11、nd Substitute for y2* to get y y y 1 1 1 15 1 4 45 4 13 * * * 19 Quantity Competition; An Example yRyy 1122 15 1 4 * () yRy y 221 1 45 4 * * (). and Substitute for y2* to get y y y 1 1 1 15 1 4 45 4 13 * * * Hencey2 4513 4 8 * . 20 Quantity Competition; An Example yRyy 1122 15 1 4 * () yRy y 221 1 4

12、5 4 * * (). and Substitute for y2* to get y y y 1 1 1 15 1 4 45 4 13 * * * Hencey2 4513 4 8 * . So the Cournot-Nash equilibrium is (,)(, ). * yy 12 13 8 21 Quantity Competition; An Example y2 y1 Firm 2s “reaction curve” 60 15 Firm 1s “reaction curve” yRyy 1122 15 1 4 (). yRy y 221 1 45 4 (). 45/4 45

13、 22 Quantity Competition; An Example y2 y1 Firm 2s “reaction curve” 48 60 Firm 1s “reaction curve” yRyy 1122 15 1 4 (). 8 13 Cournot-Nash equilibrium yy 12 13 8 * ,. yRy y 221 1 45 4 (). 23 Quantity Competition 1 1212111 (;)()()yyp yyycy 1 1 121 12 1 11 0 y p yyy p yy y cy () () (). Generally, given

14、 firm 2s chosen output level y2, firm 1s profit function is and the profit-maximizing value of y1 solves The solution, y1 = R1(y2), is firm 1s Cournot- Nash reaction to y2. 24 Quantity Competition 22112222 (;)()()yyp yyycy 2 2 122 12 2 22 0 y p yyy p yy y cy () () (). Similarly, given firm 1s chosen

15、 output level y1, firm 2s profit function is and the profit-maximizing value of y2 solves The solution, y2 = R2(y1), is firm 2s Cournot- Nash reaction to y1. 25 Quantity Competition y2 y1 Firm 1s “reaction curve” Firm 1s “reaction curve”yRy 112 (). Cournot-Nash equilibrium y1* = R1(y2*) and y2* = R2

16、(y1*) y2 * yRy 221 (). y1 * 26 Iso-Profit Curves uFor firm 1, an iso-profit curve contains all the output pairs (y1,y2) giving firm 1 the same profit level 1. uWhat do iso-profit curves look like? 27 y2 y1 Iso-Profit Curves for Firm 1 With y1 fixed, firm 1s profit increases as y2 decreases. 28 y2 y1

17、 Increasing profit for firm 1. Iso-Profit Curves for Firm 1 29 y2 y1 Iso-Profit Curves for Firm 1 Q: Firm 2 chooses y2 = y2. Where along the line y2 = y2 is the output level that maximizes firm 1s profit? y2 30 y2 y1 Iso-Profit Curves for Firm 1 Q: Firm 2 chooses y2 = y2. Where along the line y2 = y

18、2 is the output level that maximizes firm 1s profit? A: The point attaining the highest iso-profit curve for firm 1. y2 y1 31 y2 y1 Iso-Profit Curves for Firm 1 Q: Firm 2 chooses y2 = y2. Where along the line y2 = y2 is the output level that maximizes firm 1s profit? A: The point attaining the highe

19、st iso-profit curve for firm 1. y1 is firm 1s best response to y2 = y2. y2 y1 32 y2 y1 Iso-Profit Curves for Firm 1 Q: Firm 2 chooses y2 = y2. Where along the line y2 = y2 is the output level that maximizes firm 1s profit? A: The point attaining the highest iso-profit curve for firm 1. y1 is firm 1s

20、 best response to y2 = y2. y2 R1(y2) 33 y2 y1 y2 R1(y2) y2” R1(y2”) Iso-Profit Curves for Firm 1 34 y2 y1 y2 y2” R1(y2”) R1(y2) Firm 1s reaction curve passes through the “tops” of firm 1s iso-profit curves. Iso-Profit Curves for Firm 1 35 y2 y1 Iso-Profit Curves for Firm 2 Increasing profit for firm

21、 2. 36 y2 y1 Iso-Profit Curves for Firm 2 Firm 2s reaction curve passes through the “tops” of firm 2s iso-profit curves. y2 = R2(y1) 37 Collusion uQ: Are the Cournot-Nash equilibrium profits the largest that the firms can earn in total? 38 Collusion y2 y1y1* y2* Are there other output level pairs (y

22、1,y2) that give higher profits to both firms? (y1*,y2*) is the Cournot-Nash equilibrium. 39 Collusion y2 y1y1* y2* Are there other output level pairs (y1,y2) that give higher profits to both firms? (y1*,y2*) is the Cournot-Nash equilibrium. 40 Collusion y2 y1y1* y2* Are there other output level pair

23、s (y1,y2) that give higher profits to both firms? (y1*,y2*) is the Cournot-Nash equilibrium. 41 Collusion y2 y1y1* y2* (y1*,y2*) is the Cournot-Nash equilibrium. Higher 2 Higher 1 42 Collusion y2 y1y1* y2* Higher 2 Higher 1 y2 y1 43 Collusion y2 y1y1* y2* y2 y1 Higher 2 Higher 1 44 Collusion y2 y1y1

24、* y2* y2 y1 Higher 2 Higher 1 (y1,y2) earns higher profits for both firms than does (y1*,y2*). 45 Collusion uSo there are profit incentives for both firms to “cooperate” by lowering their output levels. uThis is collusion. uFirms that collude are said to have formed a cartel. uIf firms form a cartel

25、, how should they do it? 46 Collusion uSuppose the two firms want to maximize their total profit and divide it between them. Their goal is to choose cooperatively output levels y1 and y2 that maximize my yp yyyycycy(,)()()()(). 1212121122 47 Collusion uThe firms cannot do worse by colluding since th

26、ey can cooperatively choose their Cournot-Nash equilibrium output levels and so earn their Cournot-Nash equilibrium profits. So collusion must provide profits at least as large as their Cournot-Nash equilibrium profits. 48 Collusion y2 y1y1* y2* y2 y1 Higher 2 Higher 1 (y1,y2) earns higher profits f

27、or both firms than does (y1*,y2*). 49 Collusion y2 y1y1* y2* y2 y1 Higher 2 Higher 1 (y1,y2) earns higher profits for both firms than does (y1*,y2*). (y1”,y2”) earns still higher profits for both firms. y2” y1” 50 Collusion y2 y1y1* y2* y2 y1 (y1,y2) maximizes firm 1s profit while leaving firm 2s pr

28、ofit at the Cournot-Nash equilibrium level. 51 Collusion y2 y1y1* y2* y2 y1 (y1,y2) maximizes firm 1s profit while leaving firm 2s profit at the Cournot-Nash equilibrium level. y2 _ y2 _ (y1,y2) maximizes firm 2s profit while leaving firm 1s profit at the Cournot-Nash equilibrium level. _ _ 52 Collu

29、sion y2 y1y1* y2* y2 y1 y2 _ y2 _ The path of output pairs that maximize one firms profit while giving the other firm at least its CN equilibrium profit. 53 Collusion y2 y1y1* y2* y2 y1 y2 _ y2 _ The path of output pairs that maximize one firms profit while giving the other firm at least its CN equi

30、librium profit. One of these output pairs must maximize the cartels joint profit. 54 Collusion y2 y1y1* y2* y2m y1m (y1m,y2m) denotes the output levels that maximize the cartels total profit. 55 Collusion uIs such a cartel stable? uDoes one firm have an incentive to cheat on the other? uI.e. if firm

31、 1 continues to produce y1m units, is it profit-maximizing for firm 2 to continue to produce y2m units? 56 Collusion uFirm 2s profit-maximizing response to y1 = y1m is y2 = R2(y1m). 57 Collusion y2 y1 y2m y1m y2 = R2(y1m) is firm 2s best response to firm 1 choosing y1 = y1m. R2(y1m) y1 = R1(y2), fir

32、m 1s reaction curve y2 = R2(y1), firm 2s reaction curve 58 Collusion uFirm 2s profit-maximizing response to y1 = y1m is y2 = R2(y1m) y2m. uFirm 2s profit increases if it cheats on firm 1 by increasing its output level from y2m to R2(y1m). 59 Collusion uSimilarly, firm 1s profit increases if it cheat

33、s on firm 2 by increasing its output level from y1m to R1(y2m). 60 Collusion y2 y1 y2m y1m y2 = R2(y1m) is firm 2s best response to firm 1 choosing y1 = y1m. R1(y2m) y1 = R1(y2), firm 1s reaction curve y2 = R2(y1), firm 2s reaction curve 61 Collusion uSo a profit-seeking cartel in which firms cooper

34、atively set their output levels is fundamentally unstable. uE.g. OPECs broken agreements. 62 The Order of Play uSo far it has been assumed that firms choose their output levels simultaneously. uThe competition between the firms is then a simultaneous play game in which the output levels are the stra

35、tegic variables. 63 The Order of Play uWhat if firm 1 chooses its output level first and then firm 2 responds to this choice? uFirm 1 is then a leader. Firm 2 is a follower. uThe competition is a sequential game in which the output levels are the strategic variables. 64 The Order of Play uSuch games

36、 are von Stackelberg games. uIs it better to be the leader? uOr is it better to be the follower? 65 Stackelberg Games uQ: What is the best response that follower firm 2 can make to the choice y1 already made by the leader, firm 1? 66 Stackelberg Games uQ: What is the best response that follower firm

37、 2 can make to the choice y1 already made by the leader, firm 1? uA: Choose y2 = R2(y1). 67 Stackelberg Games uQ: What is the best response that follower firm 2 can make to the choice y1 already made by the leader, firm 1? uA: Choose y2 = R2(y1). uFirm 1 knows this and so perfectly anticipates firm

38、2s reaction to any y1 chosen by firm 1. 68 Stackelberg Games uThis makes the leaders profit function 1 1121111 s yp yRyycy()()(). 69 Stackelberg Games uThis makes the leaders profit function uThe leader then chooses y1 to maximize its profit level. 1 1121111 s yp yRyycy()()(). 70 Stackelberg Games u

39、This makes the leaders profit function uThe leader chooses y1 to maximize its profit. uQ: Will the leader make a profit at least as large as its Cournot-Nash equilibrium profit? 1 1121111 s yp yRyycy()()(). 71 Stackelberg Games uA: Yes. The leader could choose its Cournot-Nash output level, knowing

40、that the follower would then also choose its C-N output level. The leaders profit would then be its C-N profit. But the leader does not have to do this, so its profit must be at least as large as its C-N profit. 72 Stackelberg Games; An Example uThe market inverse demand function is p = 60 - yT. The

41、 firms cost functions are c1(y1) = y12 and c2(y2) = 15y2 + y22. uFirm 2 is the follower. Its reaction function is yRy y 221 1 45 4 (). 73 Stackelberg Games; An Example 1 112111 2 1 1 11 2 11 2 60 60 45 4 195 4 7 4 s yyRyyy y y yy yy ()() () . The leaders profit function is therefore 74 Stackelberg G

42、ames; An Example 1 112111 2 1 1 11 2 11 2 60 60 45 4 195 4 7 4 s yyRyyy y y yy yy ()() () . The leaders profit function is therefore For a profit-maximum, 195 4 7 2 13 9 11 yys. 75 Stackelberg Games; An Example Q: What is firm 2s response to the leaders choicey s 1 13 9 ? 76 Stackelberg Games; An Ex

43、ample Q: What is firm 2s response to the leaders choice A: y s 1 13 9 ? yRy ss 221 4513 9 4 7 8 (). 77 Stackelberg Games; An Example Q: What is firm 2s response to the leaders choice A: y s 1 13 9 ? yRy ss 221 4513 9 4 7 8 (). The C-N output levels are (y1*,y2*) = (13,8) so the leader produces more

44、than its C-N output and the follower produces less than its C-N output. This is true generally. 78 Stackelberg Games y2 y1y1* y2* (y1*,y2*) is the Cournot-Nash equilibrium. Higher 2 Higher 1 79 Stackelberg Games y2 y1y1* y2* (y1*,y2*) is the Cournot-Nash equilibrium. Higher 1 Followers reaction curv

45、e 80 Stackelberg Games y2 y1y1* y2* (y1*,y2*) is the Cournot-Nash equilibrium. (y1S,y2S) is the Stackelberg equilibrium. Higher 1 y1S Followers reaction curve y2S 81 Stackelberg Games y2 y1y1* y2* (y1*,y2*) is the Cournot-Nash equilibrium. (y1S,y2S) is the Stackelberg equilibrium. y1S Followers reac

46、tion curve y2S 82 Price Competition uWhat if firms compete using only price-setting strategies, instead of using only quantity-setting strategies? uGames in which firms use only price strategies and play simultaneously are Bertrand games. 83 Bertrand Games uEach firms marginal production cost is con

47、stant at c. uAll firms set their prices simultaneously. uQ: Is there a Nash equilibrium? 84 Bertrand Games uEach firms marginal production cost is constant at c. uAll firms simultaneously set their prices. uQ: Is there a Nash equilibrium? uA: Yes. Exactly one. 85 Bertrand Games uEach firms marginal

48、production cost is constant at c. uAll firms simultaneously set their prices. uQ: Is there a Nash equilibrium? uA: Yes. Exactly one. All firms set their prices equal to the marginal cost c. Why? 86 Bertrand Games uSuppose one firm sets its price higher than another firms price. 87 Bertrand Games uSu

49、ppose one firm sets its price higher than another firms price. uThen the higher-priced firm would have no customers. 88 Bertrand Games uSuppose one firm sets its price higher than another firms price. uThen the higher-priced firm would have no customers. uHence, at an equilibrium, all firms must set the same price. 89 Bertrand Games uSuppose th