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1、Chapter Twenty-SevenOligopolyOligopolyuA 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.OligopolyuHow do w
2、e analyze markets in which the supplying industry is oligopolistic?uConsider the duopolistic case of two firms supplying the same product.Quantity CompetitionuAssume that firms compete by choosing output levels.uIf firm 1 produces y1 units and firm 2 produces y2 units then total quantity supplied is
3、 y1 + y2. The market price will be p(y1+ y2).uThe firms total cost functions are c1(y1) and c2(y2).Quantity CompetitionuSuppose firm 1 takes firm 2s output level choice y2 as given. Then firm 1 sees its profit function asuGiven y2, what output level y1 maximizes firm 1s profit? 11212111(;)()().yyp y
4、yycy Quantity Competition; An ExampleuSuppose that the market inverse demand function isand that the firms total cost functions arep yyTT() 60cyy1112() cyyy2222215(). andQuantity Competition; An Example (;)().yyyyyy121211260 Then, for given y2, firm 1s profit function isQuantity Competition; An Exam
5、ple (;)().yyyyyy121211260 Then, for given y2, firm 1s profit function isSo, given y2, firm 1s profit-maximizingoutput level solves yyyy112160220 .Quantity Competition; An Example (;)().yyyyyy121211260 Then, for given y2, firm 1s profit function isSo, given y2, firm 1s profit-maximizingoutput level s
6、olves yyyy112160220 .I.e. firm 1s best response to y2 isyRyy11221514 ().Quantity Competition; An Exampley2y16015Firm 1s “reaction curve”yRyy11221514 ().Quantity Competition; An Example (;)().yyyyyyy211222226015 Similarly, given y1, firm 2s profit function isQuantity Competition; An Example (;)().yyy
7、yyyy211222226015 Similarly, given y1, firm 2s profit function isSo, given y1, firm 2s profit-maximizingoutput level solves yyyy21226021520 .Quantity Competition; An Example (;)().yyyyyyy211222226015 Similarly, given y1, firm 2s profit function isSo, given y1, firm 2s profit-maximizingoutput level so
8、lves yyyy21226021520 .I.e. firm 1s best response to y2 isyRyy2211454 ().Quantity Competition; An Exampley2y1Firm 2s “reaction curve”yRyy2211454 ().45/445Quantity Competition; An ExampleuAn equilibrium is when each firms output level is a best response to the other firms output level, for then neithe
9、r wants to deviate from its output level.uA pair of output levels (y1*,y2*) is a Cournot-Nash equilibrium if yRy221*(). yRy112*() andQuantity Competition; An ExampleyRyy11221514*() yRyy2211454*(). andQuantity Competition; An ExampleyRyy11221514*() yRyy2211454*(). andSubstitute for y2* to getyy111514
10、454* Quantity Competition; An ExampleyRyy11221514*() yRyy2211454*(). andSubstitute for y2* to getyyy111151445413* Quantity Competition; An ExampleyRyy11221514*() yRyy2211454*(). andSubstitute for y2* to getyyy111151445413* Hencey2451348*. Quantity Competition; An ExampleyRyy11221514*() yRyy2211454*(
11、). andSubstitute for y2* to getyyy111151445413* Hencey2451348*. So the Cournot-Nash equilibrium is(,)(, ).*yy1213 8 Quantity Competition; An Exampley2y1Firm 2s “reaction curve”6015Firm 1s “reaction curve”yRyy11221514 ().yRyy2211454 ().45/445Quantity Competition; An Exampley2y1Firm 2s “reaction curve
12、”4860Firm 1s “reaction curve”yRyy11221514 ().813Cournot-Nash equilibrium yy1213 8*,. yRyy2211454 ().Quantity Competition 11212111(;)()()yyp yyycy 11121121110yp yyyp yyycy ()()().Generally, given firm 2s chosen outputlevel y2, firm 1s profit function isand the profit-maximizing value of y1 solvesThe
13、solution, y1 = R1(y2), is firm 1s Cournot-Nash reaction to y2.Quantity Competition 22112222(;)()()yyp yyycy 22122122220yp yyyp yyycy ()()().Similarly, given firm 1s chosen outputlevel y1, firm 2s profit function isand the profit-maximizing value of y2 solvesThe solution, y2 = R2(y1), is firm 2s Cour
14、not-Nash reaction to y1.Quantity Competitiony2y1Firm 1s “reaction curve”Firm 1s “reaction curve”yRy112 ().Cournot-Nash equilibriumy1* = R1(y2*) and y2* = R2(y1*)y2*yRy221 ().y1*Iso-Profit CurvesuFor firm 1, an iso-profit curve contains all the output pairs (y1,y2) giving firm 1 the same profit level
15、 1.uWhat do iso-profit curves look like?y2y1Iso-Profit Curves for Firm 1With y1 fixed, firm 1s profitincreases as y2 decreases.y2y1Increasing profitfor firm 1.Iso-Profit Curves for Firm 1y2y1Iso-Profit Curves for Firm 1Q: Firm 2 chooses y2 = y2.Where along the line y2 = y2 is the output level thatma
16、ximizes firm 1s profit?y2y2y1Iso-Profit Curves for Firm 1Q: 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.y2y1y2y1Iso-Profit Curves for Firm 1Q: Firm 2 chooses y2 = y2.Where along th
17、e 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.y2y1y2y1Iso-Profit Curves for Firm 1Q: Firm 2 chooses y2 = y2.Where along the line y2 = y2 is the output level thatmaximizes firm 1s
18、profit? A: The point attaining thehighest iso-profit curve for firm 1. y1 is firm 1s best response to y2 = y2.y2R1(y2)y2y1y2R1(y2)y2”R1(y2”)Iso-Profit Curves for Firm 1y2y1y2y2”R1(y2”)R1(y2)Firm 1s reaction curvepasses through the “tops”of firm 1s iso-profitcurves.Iso-Profit Curves for Firm 1y2y1Iso
19、-Profit Curves for Firm 2Increasing profitfor firm 2.y2y1Iso-Profit Curves for Firm 2Firm 2s reaction curvepasses through the “tops”of firm 2s iso-profitcurves.y2 = R2(y1)CollusionuQ: Are the Cournot-Nash equilibrium profits the largest that the firms can earn in total? Collusiony2y1y1*y2*Are there
20、other output levelpairs (y1,y2) that givehigher profits to both firms?(y1*,y2*) is the Cournot-Nashequilibrium.Collusiony2y1y1*y2*Are there other output levelpairs (y1,y2) that givehigher profits to both firms?(y1*,y2*) is the Cournot-Nashequilibrium.Collusiony2y1y1*y2*Are there other output levelpa
21、irs (y1,y2) that givehigher profits to both firms?(y1*,y2*) is the Cournot-Nashequilibrium.Collusiony2y1y1*y2*(y1*,y2*) is the Cournot-Nashequilibrium.Higher 2Higher 1Collusiony2y1y1*y2*Higher 2Higher 1y2y1Collusiony2y1y1*y2*y2y1Higher 2Higher 1Collusiony2y1y1*y2*y2y1Higher 2Higher 1(y1,y2) earnshig
22、her profits forboth firms thandoes (y1*,y2*).CollusionuSo 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, how should they do it?CollusionuSuppose the two firms w
23、ant to maximize their total profit and divide it between them. Their goal is to choose cooperatively output levels y1 and y2 that maximize myyp yyyycycy(,)()()()().1212121122 CollusionuThe firms cannot do worse by colluding since they can cooperatively choose their Cournot-Nash equilibrium output le
24、vels and so earn their Cournot-Nash equilibrium profits. So collusion must provide profits at least as large as their Cournot-Nash equilibrium profits.Collusiony2y1y1*y2*y2y1Higher 2Higher 1(y1,y2) earnshigher profits forboth firms thandoes (y1*,y2*).Collusiony2y1y1*y2*y2y1Higher 2Higher 1(y1,y2) ea
25、rnshigher profits forboth firms thandoes (y1*,y2*).(y1”,y2”) earns stillhigher profits forboth firms.y2”y1”Collusiony2y1y1*y2*y2y1(y1,y2) maximizes firm 1s profitwhile leaving firm 2s profit at the Cournot-Nash equilibrium level. Collusiony2y1y1*y2*y2y1(y1,y2) maximizes firm 1s profitwhile leaving f
26、irm 2s profit at the Cournot-Nash equilibrium level. y2_y2_(y1,y2) maximizes firm2s profit while leaving firm 1s profit at the Cournot-Nash equilibrium level._ _Collusiony2y1y1*y2*y2y1y2_y2_The path of output pairs thatmaximize one firms profit while giving the other firm at least its CN equilibrium
27、 profit.Collusiony2y1y1*y2*y2y1y2_y2_The path of output pairs thatmaximize one firms profit while giving the other firm at least its CN equilibrium profit. One of these output pairs must maximize the cartels joint profit.Collusiony2y1y1*y2*y2my1m(y1m,y2m) denotesthe output levelsthat maximize thecar
28、tels total profit.CollusionuIs such a cartel stable?uDoes one firm have an incentive to cheat on the other?uI.e. if firm 1 continues to produce y1m units, is it profit-maximizing for firm 2 to continue to produce y2m units?CollusionuFirm 2s profit-maximizing response to y1 = y1m is y2 = R2(y1m).Coll
29、usiony2y1y2my1my2 = R2(y1m) is firm 2sbest response to firm1 choosing y1 = y1m.R2(y1m)y1 = R1(y2), firm 1s reaction curvey2 = R2(y1), firm 2s reaction curveCollusionuFirm 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
30、output level from y2m to R2(y1m).CollusionuSimilarly, firm 1s profit increases if it cheats on firm 2 by increasing its output level from y1m to R1(y2m).Collusiony2y1y2my1my2 = R2(y1m) is firm 2sbest response to firm1 choosing y1 = y1m.R1(y2m)y1 = R1(y2), firm 1s reaction curvey2 = R2(y1), firm 2s r
31、eaction curveCollusionuSo a profit-seeking cartel in which firms cooperatively set their output levels is fundamentally unstable.uE.g. OPECs broken agreements.The Order of PlayuSo far it has been assumed that firms choose their output levels simultaneously.uThe competition between the firms is then
32、a simultaneous play game in which the output levels are the strategic variables.The Order of PlayuWhat 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
33、the strategic variables.The Order of PlayuSuch games are von Stackelberg games.uIs it better to be the leader?uOr is it better to be the follower?Stackelberg GamesuQ: What is the best response that follower firm 2 can make to the choice y1 already made by the leader, firm 1?Stackelberg GamesuQ: What
34、 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).Stackelberg GamesuQ: 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 an
35、d so perfectly anticipates firm 2s reaction to any y1 chosen by firm 1.Stackelberg GamesuThis makes the leaders profit function 11121111syp yRyycy()()(). Stackelberg GamesuThis makes the leaders profit functionuThe leader then chooses y1 to maximize its profit level. 11121111syp yRyycy()()(). Stacke
36、lberg GamesuThis makes the leaders profit functionuThe leader chooses y1 to maximize its profit.uQ: Will the leader make a profit at least as large as its Cournot-Nash equilibrium profit? 11121111syp yRyycy()()(). Stackelberg GamesuA: Yes. The leader could choose its Cournot-Nash output level, knowi
37、ng 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.Stackelberg Games; An ExampleuThe market inverse demand function is p = 60 - yT. The f
38、irms cost functions are c1(y1) = y12 and c2(y2) = 15y2 + y22.uFirm 2 is the follower. Its reaction function isyRyy2211454 ().Stackelberg Games; An Example 11121112111121126060454195474syyRyyyyyyyyy()()(). The leaders profit function is thereforeStackelberg Games; An Example 1112111211112112606045419
39、5474syyRyyyyyyyyy()()(). The leaders profit function is thereforeFor a profit-maximum,19547213 911 yys.Stackelberg Games; An ExampleQ: What is firm 2s response to theleaders choiceys113 9 ?Stackelberg Games; An ExampleQ: What is firm 2s response to theleaders choiceA:ys113 9 ?yRyss2214513 947 8 ().S
40、tackelberg Games; An ExampleQ: What is firm 2s response to theleaders choiceA:ys113 9 ?yRyss2214513 947 8 ().The C-N output levels are (y1*,y2*) = (13,8)so the leader produces more than itsC-N output and the follower produces lessthan its C-N output. This is true generally.Stackelberg Gamesy2y1y1*y2
41、*(y1*,y2*) is the Cournot-Nashequilibrium.Higher 2Higher 1Stackelberg Gamesy2y1y1*y2*(y1*,y2*) is the Cournot-Nashequilibrium.Higher 1Followersreaction curveStackelberg Gamesy2y1y1*y2*(y1*,y2*) is the Cournot-Nashequilibrium. (y1S,y2S) is theStackelberg equilibrium.Higher 1y1SFollowersreaction curve
42、y2SStackelberg Gamesy2y1y1*y2*(y1*,y2*) is the Cournot-Nashequilibrium. (y1S,y2S) is theStackelberg equilibrium.y1SFollowersreaction curvey2SPrice CompetitionuWhat if firms compete using only price-setting strategies, instead of using only quantity-setting strategies?uGames in which firms use only p
43、rice strategies and play simultaneously are Bertrand games.Bertrand GamesuEach firms marginal production cost is constant at c.uAll firms set their prices simultaneously.uQ: Is there a Nash equilibrium?Bertrand GamesuEach firms marginal production cost is constant at c.uAll firms simultaneously set
44、their prices.uQ: Is there a Nash equilibrium?uA: Yes. Exactly one.Bertrand GamesuEach firms marginal 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?Bertrand
45、 GamesuSuppose one firm sets its price higher than another firms price.Bertrand GamesuSuppose one firm sets its price higher than another firms price.uThen the higher-priced firm would have no customers.Bertrand GamesuSuppose one firm sets its price higher than another firms price.uThen the higher-p
46、riced firm would have no customers.uHence, at an equilibrium, all firms must set the same price.Bertrand GamesuSuppose the common price set by all firm is higher than marginal cost c.Bertrand GamesuSuppose the common price set by all firm is higher than marginal cost c.uThen one firm can just slight
47、ly lower its price and sell to all the buyers, thereby increasing its profit.Bertrand GamesuSuppose the common price set by all firm is higher than marginal cost c.uThen one firm can just slightly lower its price and sell to all the buyers, thereby increasing its profit.uThe only common price which
48、prevents undercutting is c. Hence this is the only Nash equilibrium.Sequential Price GamesuWhat if, instead of simultaneous play in pricing strategies, one firm decides its price ahead of the others.uThis is a sequential game in pricing strategies called a price-leadership game.uThe firm which sets
49、its price ahead of the other firms is the price-leader.Sequential Price GamesuThink of one large firm (the leader) and many competitive small firms (the followers).uThe small firms are price-takers and so their collective supply reaction to a market price p is their aggregate supply function Yf(p).S
50、equential Price GamesuThe market demand function is D(p).uSo the leader knows that if it sets a price p the quantity demanded from it will be the residual demanduHence the leaders profit function isL pD pYpf( )( )( ). (p).Y(D(p)c(p)Yp(D(p)(p)fLfL Sequential Price GamesuThe leaders profit function is