1、27,Oligopoly,Oligopoly,A monopoly is an industry consisting a single firm. A duopoly is an industry consisting of two firms. An oligopoly is an industry consisting of a few firms. Particularly, each firms own price or output decisions affect its competitors profits.,Oligopoly,How do we analyze marke

2、ts in which the supplying industry is oligopolistic? Consider the duopolistic case of two firms supplying the same product.,Quantity Competition,Assume that firms compete by choosing output levels. If firm 1 produces y1 units and firm 2 produces y2 units then total quantity supplied is y1 + y2. The

3、market price will be p(y1+ y2). The firms total cost functions are c1(y1) and c2(y2).,Quantity Competition,Suppose firm 1 takes firm 2s output level choice y2 as given. Then firm 1 sees its profit function as Given y2, what output level y1 maximizes firm 1s profit?,Quantity Competition; An Example,S

4、uppose that the market inverse demand function isand that the firms total cost functions are,and,Quantity Competition; An Example,Then, for given y2, firm 1s profit function is,Quantity Competition; An Example,Then, for given y2, firm 1s profit function is,So, given y2, firm 1s profit-maximizingoutp

5、ut level solves,Quantity Competition; An Example,Then, for given y2, firm 1s profit function is,So, given y2, firm 1s profit-maximizingoutput level solves,I.e., firm 1s best response to y2 is,Quantity Competition; An Example,y2,y1,60,15,Firm 1s “reaction curve”,Quantity Competition; An Example,Simil

6、arly, given y1, firm 2s profit function is,Quantity Competition; An Example,Similarly, given y1, firm 2s profit function is,So, given y1, firm 2s profit-maximizingoutput level solves,Quantity Competition; An Example,Similarly, given y1, firm 2s profit function is,So, given y1, firm 2s profit-maximiz

7、ingoutput level solves,I.e., firm 1s best response to y2 is,Quantity Competition; An Example,y2,y1,Firm 2s “reaction curve”,45/4,45,Quantity Competition; An Example,An equilibrium is when each firms output level is a best response to the other firms output level, for then neither wants to deviate fr

8、om its output level. A pair of output levels (y1*,y2*) is a Cournot-Nash equilibrium if,and,Quantity Competition; An Example,and,Quantity Competition; An Example,and,Substitute for y2* to get,Quantity Competition; An Example,and,Substitute for y2* to get,Quantity Competition; An Example,and,Substitu

9、te for y2* to get,Hence,Quantity Competition; An Example,and,Substitute for y2* to get,Hence,So the Cournot-Nash equilibrium is,Quantity Competition; An Example,y2,y1,Firm 2s “reaction curve”,60,15,Firm 1s “reaction curve”,45/4,45,Quantity Competition; An Example,y2,y1,Firm 2s “reaction curve”,48,60

10、,Firm 1s “reaction curve”,8,13,Cournot-Nash equilibrium,Quantity Competition,Generally, given firm 2s chosen outputlevel 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.,Quantity Competition,Similarly, give

11、n firm 1s chosen outputlevel 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.,Quantity Competition,y2,y1,Firm 2s “reaction curve”,Firm 1s “reaction curve”,Cournot-Nash equilibrium y1* = R1(y2*) and y2* = R2

12、(y1*),Iso-Profit Curves,For firm 1, an iso-profit curve contains all the output pairs (y1,y2) giving firm 1 the same profit level P1. What do iso-profit curves look like?,y2,y1,Iso-Profit Curves for Firm 1,With y1 fixed, firm 1s profitincreases as y2 decreases.,y2,y1,Increasing profitfor firm 1.,Iso

13、-Profit Curves for Firm 1,y2,y1,Iso-Profit Curves for Firm 1,Q: Firm 2 chooses y2 = y2.Where along the line y2 = y2 is the output level thatmaximizes firm 1s profit?,y2,y2,y1,Iso-Profit Curves for Firm 1,Q: Firm 2 chooses y2 = y2.Where along the line y2 = y2 is the output level thatmaximizes firm 1s

14、 profit? A: The point attaining thehighest iso-profit curve for firm 1.,y2,y1,y2,y1,Iso-Profit Curves for Firm 1,Q: Firm 2 chooses y2 = y2.Where along the line y2 = y2 is the output level thatmaximizes firm 1s profit? A: The point attaining thehighest iso-profit curve for firm 1. y1 is firm 1s best

15、response to y2 = y2.,y2,y1,y2,y1,Iso-Profit Curves for Firm 1,Q: Firm 2 chooses y2 = y2.Where along the line y2 = y2 is the output level thatmaximizes firm 1s profit? A: The point attaining thehighest iso-profit curve for firm 1. y1 is firm 1s best response to y2 = y2.,y2,R1(y2),y2,y1,y2,R1(y2),y2”,

16、R1(y2”),Iso-Profit Curves for Firm 1,y2,y1,y2,y2”,R1(y2”),R1(y2),Firm 1s reaction curvepasses through the “tops” of firm 1s iso-profitcurves.,Iso-Profit Curves for Firm 1,y2,y1,Iso-Profit Curves for Firm 2,Increasing profitfor firm 2.,y2,y1,Iso-Profit Curves for Firm 2,Firm 2s reaction curvepasses t

17、hrough the “tops” of firm 2s iso-profitcurves.,y2 = R2(y1),Collusion,Q: Are the Cournot-Nash equilibrium profits the largest that the firms can earn in total?,Collusion,y2,y1,y1*,y2*,Are there other output levelpairs (y1,y2) that givehigher profits to both firms?,(y1*,y2*) is the Cournot-Nashequilib

18、rium.,Collusion,y2,y1,y1*,y2*,Are there other output levelpairs (y1,y2) that givehigher profits to both firms?,(y1*,y2*) is the Cournot-Nashequilibrium.,Collusion,y2,y1,y1*,y2*,Are there other output levelpairs (y1,y2) that givehigher profits to both firms?,(y1*,y2*) is the Cournot-Nashequilibrium.,

19、Collusion,y2,y1,y1*,y2*,(y1*,y2*) is the Cournot-Nashequilibrium.,Higher P2,Higher P1,Collusion,y2,y1,y1*,y2*,Higher P2,Higher P1,y2,y1,Collusion,y2,y1,y1*,y2*,y2,y1,Higher P2,Higher P1,Collusion,y2,y1,y1*,y2*,y2,y1,Higher P2,Higher P1,(y1,y2) earnshigher profits forboth firms than does (y1*,y2*).,C

20、ollusion,So there are profit incentives for both firms to “cooperate” by lowering their output levels. This is collusion. Firms that collude are said to have formed a cartel. If firms form a cartel, how should they do it?,Collusion,Suppose the two firms want to maximize their total profit and divide

21、 it between them. Their goal is to choose cooperatively output levels y1 and y2 that maximize,Collusion,The firms cannot do worse by colluding since they can cooperatively choose their Cournot-Nash equilibrium output levels and so earn their Cournot-Nash equilibrium profits. So collusion must provid

22、e profits at least as large as their Cournot-Nash equilibrium profits.,Collusion,y2,y1,y1*,y2*,y2,y1,Higher P2,Higher P1,(y1,y2) earnshigher profits forboth firms than does (y1*,y2*).,Collusion,y2,y1,y1*,y2*,y2,y1,Higher P2,Higher P1,(y1,y2) earnshigher profits forboth firms than does (y1*,y2*).,(y1

23、”,y2”) earns stillhigher profits forboth firms.,y2”,y1”,Collusion,y2,y1,y1*,y2*,(y1,y2) maximizes firm 1s profitwhile leaving firm 2s profit at the Cournot-Nash equilibrium level.,Collusion,y2,y1,y1*,y2*,(y1,y2) maximizes firm 1s profitwhile leaving firm 2s profit at the Cournot-Nash equilibrium lev

24、el.,(y1,y2) maximizes firm2s profit while leaving firm 1s profit at the Cournot-Nash equilibrium level.,_,_,Collusion,y2,y1,y1*,y2*,The path of output pairs thatmaximize one firms profit while giving the other firm at least its C-N equilibrium profit.,Collusion,y2,y1,y1*,y2*,The path of output pairs

25、 thatmaximize one firms profit while giving the other firm at least its C-N equilibrium profit. One of these output pairs must maximize the cartels joint profit.,Collusion,y2,y1,y1*,y2*,(y1m,y2m) denotesthe output levelsthat maximize thecartels total profit.,Collusion,Is such a cartel stable? Does o

26、ne firm have an incentive to cheat on the other? I.e., if firm 1 continues to produce y1m units, is it profit-maximizing for firm 2 to continue to produce y2m units?,Collusion,Firm 2s profit-maximizing response to y1 = y1m is y2 = R2(y1m).,Collusion,y2,y1,y2 = R2(y1m) is firm 2sbest response to firm

27、 1 choosing y1 = y1m.,R2(y1m),y1 = R1(y2), firm 1s reaction curve,y2 = R2(y1), firm 2s reaction curve,Collusion,Firm 2s profit-maximizing response to y1 = y1m is y2 = R2(y1m) y2m. Firm 2s profit increases if it cheats on firm 1 by increasing its output level from y2m to R2(y1m).,Collusion,Similarly,

28、 firm 1s profit increases if it cheats on firm 2 by increasing its output level from y1m to R1(y2m).,Collusion,y2,y1,y2 = R2(y1m) is firm 2sbest response to firm 1 choosing y1 = y1m.,R1(y2m),y1 = R1(y2), firm 1s reaction curve,y2 = R2(y1), firm 2s reaction curve,Collusion,So a profit-seeking cartel

29、in which firms cooperatively set their output levels is fundamentally unstable. E.g., OPECs broken agreements.,Collusion,So a profit-seeking cartel in which firms cooperatively set their output levels is fundamentally unstable. E.g., OPECs broken agreements. But is the cartel unstable if the game is

30、 repeated many times, instead of being played only once? Then there is an opportunity to punish a cheater.,Collusion y2) = (24 y1 y2)y1 y21.,Collusion y2) = (24 y1 y2)y1 y21. The value of y1 that is firm 1s best response to y2 solves,Collusion y2) = (24 y1 y2)y1 y21. Similarly,Collusion y2) = (24 y1

31、 y2)y1 y21. Similarly, The C-N equilibrium (y*1,y*2) solves y1 = R1(y2) and y2 = R2(y1) y*1 = y*2 = 48.,Collusion y2) = (24 y1 y2)y1 y21. y*1 = y*2 = 48. So each firms profit in the C-N equilibrium is *1 = *2 = (144)(48) 482 $46 each period.,Collusion An Example,The market inverse demand function is

32、 p = 60 - yT. The firms cost functions are c1(y1) = y12 and c2(y2) = 15y2 + y22. Firm 2 is the follower. Its reaction function is,Stackelberg Games; An Example,The leaders profit function is therefore,Stackelberg Games; An Example,The leaders profit function is therefore,For a profit-maximum for fir

33、m 1,Stackelberg Games; An Example,Q: What is firm 2s response to the leaders choice,Stackelberg Games; An Example,Q: What is firm 2s response to the leaders choice A:,Stackelberg Games; An Example,Q: What is firm 2s response to the leaders choice A:,The C-N output levels are (y1*,y2*) = (13,8) so th

34、e leader produces more than its C-N output and the follower produces less than its C-N output. This is true generally.,Stackelberg Games,y2,y1,y1*,y2*,(y1*,y2*) is the Cournot-Nashequilibrium.,Higher P2,Higher P1,Stackelberg Games,y2,y1,y1*,y2*,(y1*,y2*) is the Cournot-Nashequilibrium.,Higher P1,Fol

35、lowers reaction curve,Stackelberg Games,y2,y1,y1*,y2*,(y1*,y2*) is the Cournot-Nashequilibrium. (y1S,y2S) is the Stackelberg equilibrium.,Higher P1,y1S,Followers reaction curve,y2S,Stackelberg Games,y2,y1,y1*,y2*,(y1*,y2*) is the Cournot-Nashequilibrium. (y1S,y2S) is the Stackelberg equilibrium.,y1S

36、,Followers reaction curve,y2S,Price Competition,What if firms compete using only price-setting strategies, instead of using only quantity-setting strategies? Games in which firms use only price strategies and play simultaneously are Bertrand games.,Bertrand Games,Each firms marginal production cost

37、is constant at c. All firms set their prices simultaneously. Q: Is there a Nash equilibrium?,Bertrand Games,Each firms marginal production cost is constant at c. All firms set their prices simultaneously. Q: Is there a Nash equilibrium? A: Yes. Exactly one.,Bertrand Games,Each firms marginal product

38、ion cost is constant at c. All firms set their prices simultaneously. Q: Is there a Nash equilibrium? A: Yes. Exactly one. All firms set their prices equal to the marginal cost c. Why?,Bertrand Games,Suppose one firm sets its price higher than another firms price.,Bertrand Games,Suppose one firm set

39、s its price higher than another firms price. Then the higher-priced firm would have no customers.,Bertrand Games,Suppose one firm sets its price higher than another firms price. Then the higher-priced firm would have no customers. Hence, at an equilibrium, all firms must set the same price.,Bertrand Games,Suppose the common price set by all firm is higher than marginal cost c.,Bertrand Games,Suppose the common price set by all firm is higher than marginal cost c. Then one firm can just slightly lower its p