ECON 115. Industrial Organization

Transcription

1 ECON 115 Industrial Organization

2 1. Cournot and Bertrand Reprised 2. First and Second Movers 3. The Stackelberg Model 4. Quantity vs. Price Competition 5. Credibility 6. Preparing for the 2 nd Midterm

3 First Hour Cournot and Bertrand reprised Sequential games First and second movers Stackelberg Duopoloy Model Stackelberg vs. Cournot Price competition and first and second movers Second Hour Credibility and competition in market entry games. Selten s Chain Store Paradox Practice problem Preparing for the second midterm

4 The past two weeks we have studied two models of oligopolistic behavior: Cournot and Bertrand Cournot competition is quantity-based. The main takeaways are: Given P = A BQ, each competitors produces q = (A- C)/3B. Total output is 2*[(A-C)/3B]. This is more than monopoly but less then under perfect competition. For multiple firms, P = A - B(q q N ) - Bq 1. The demand for Firm 1 is P = (A - BQ -1 ) - Bq 1 Profitmaximizing q* 1 = (A - c)/2b - Q -1 /2 Price = (A Nc)/(N+1) = A/(N+1) + Nc/(N=1) Therefore as N P C 4

5 Bertrand is price competition. Here there are two main takeaways. Under standard Bertrand competition, price ends up equaling cost (competitive outcome). With product differentiation present, the firms profit maximizing prices are p 1 = p 2 = c + t, where c is marginal cost and t is transport costs or (metaphorically) the value that consumers place on having a product close to their tastes. Prices and profits rise. 5

6 We now move to the final oligopoly model. There are three dominant oligopoly models: Cournot Bertrand Stackelberg These models are distinguished by: The decision variable that firms choose The timing of the underlying game Today we concentrate on the Stackelberg model. 6

7 We now move to the final oligopoly model. There are three dominant oligopoly models: Cournot Bertrand Stackelberg These models are distinguished by: The decision variable that firms choose The timing of the underlying game Today we concentrate on the Stackelberg model. 7

8 Both the Cournot and Bertrand models are examples of simultaneous games. We assume both firms move simultaneously and the market interaction is once-and-for-all. In a wide variety of markets firms compete sequentially. One firm makes a move. For example it may introduce a new product or ad campaign and The second firms sees this move and responds. 8

9 Sequential games are also called dynamic games. These games may create a first-mover advantage; or create a second-mover advantage; or may allow an early mover to preempt the market. Therefore, sequential move games can generate very different equilibria from simultaneous move games. 9

10 We are going to examine the Stackelberg duopoly model. This is similar to the Cournot model in that it is output (quantity) based. However, as we will see, it has one major difference: firms choose quantities sequentially rather than simultaneously. 10

11 Choosing output sequentially means the leader sets its output first, and visibly, and the follower then sets its output. The firm moving first has a leadership advantage. It can anticipate the follower s actions and can therefore manipulate the follower. However, for this to work the leader must be able to commit to its choice of output. 11

12 Assume there are two firms with identical products. Marginal cost for each firm is c Firm 1 is the market leader and chooses q 1 Firms 1 also knows how Firm 2 will react because, if demand is linear (P = A BQ = A B(q 1 + q 2 ), the residual demand for Firm 2 is: P = (A Bq 1 ) Bq 2 Therefore, Firm 1 knows that Firm 2 will maximize profits by equating its marginal revenue [MR = (A Bq 1 ) 2Bq 2 ] to c. 12

13 MR 2 = (A - Bq 1 ) 2Bq 2 MC = c q* 2 = (A - c)/2b - q 1 /2 Demand for firm 1 is: P = (A - Bq 2 ) Bq 1 Industrial Equate marginal Organization revenue with marginal cost This is firm 2 s best response function q 2 But firm 1 knows what q 2 is going to be (A c)/2b Firm 1 knows that this is how firm 2 will react to firm 1 s output choice So firm 1 can anticipate firm 2 s reaction P = (A - Bq* 2 ) Bq 1 P = (A - (A-c)/2) Bq 1 /2 P = (A + c)/2 Bq 1 /2 (A c)/4b S Equate marginal revenue with marginal cost R 2 Marginal revenue for firm 1 is: MR 1 = (A + c)/2 - Bq 1 (A + c)/2 Bq 1 = c q* 1 = (A c)/2b q* 2 = (A c)4b (A c)/2 Solve this equation for output q 1 q 1 (A c)/b 13

14 Aggregate output is 3(A-c)/4B So the equilibrium price is (A+3c)/4 Firm 1 s profit is (A-c) 2 /8B Firm 2 s profit is (A-c) 2 /16B q 2 (Ac)/B R 1 (A-c)/2B Firm 1 s best response function is like firm 2 s Compare this with the Cournot equilibrium We know that the Cournot equilibrium is: (A-c)/3B (A-c)/4B C S q C 1 = q C 2 = (A-c)/3B R 2 The Cournot price is (A+c)/3 (A-c)/3B (A-c)/2B q 1 (A-c)/ B Profit to each firm is (A-c) 2 /9B 14

15 Aggregate output is 3(A-c)/4B So the equilibrium price is (A+3c)/4 Firm 1 s profit is (A-c) 2 /8B Firm 2 s profit is (A-c) 2 /16B We know that the Cournot equilibrium is: q C 1 = q C 2 = (A-c)/3B q 2 (Ac)/B R 1 (A-c)/2B (A-c)/3B (A-c)/4B Leadership benefits the leader firm 1 but harms the follower firm 2 C Leadership benefits consumers but reduces aggregate profits S R 2 The Cournot price is (A+c)/3 (A-c)/3B (A-c)/2B q 1 (A-c)/ B Profit to each firm is (A-c) 2 /9B 15

16 It is crucial that the leader can commit to its output choice. Without such commitment Firm 2 would ignore any stated intent by Firm 1 to produce (A c)/2b units and the only equilibrium would be the Cournot equilibrium. So how does Firm 1 commit? (1) Prior reputation (2) Investment in additional capacity (3) Place the stated output on the market 16

17 Clearly, in this example, being the first mover is advantageous. But is moving first always better than following? This example was based on output. What happens if we are looking at price competition? 17

18 With price competition matters are different: the first move does NOT have an advantage. Suppose, again, products are identical but the first-mover commits to a price greater than marginal cost. The second-mover will undercut this price and take the market. Therefore the first-mover will set price at P = MC. This is identical to simultaneous game played under Bertrand competition. 18

19 Now suppose that products are differentiated. To analyze this, we will use the spatial model developed in Chapter 7. Suppose that there are two firms but now Firm 1 can set and commit to its price first. Further, we know each firm s demand function, and Firm 2 s best response function. 19

20 Demand to firm 1 is D 1 (p 1, p 2 ) = N(p 2 p 1 + t)/2t Demand to firm 2 is D 2 (p 1, p 2 ) = N(p 1 p 2 + t)/2t Best response function for firm 2 is p* 2 = (p 1 + c + t)/2 Firm 1 knows this, so demand to firm 1 is D 1 (p 1, p* 2 ) = N(p* 2 p 1 + t)/2t = N(c +3t p 1 )/4t Profit to firm 1 is then π 1 = N(p 1 c)(c + 3t p 1 )/4t Differentiate with respect to p 1 : π 1 / p 1 = N(c + 3t p 1 p 1 + c)/4t = N(2c + 3t 2p 1 )/4t Equating this to 0 and solving gives: p* 1 = c + 3t/2 20

21 p* 1 = c + 3t/2 Substitute into the best response function for firm 2 p* 2 = (p* 1 + c + t)/2 p* 2 = c + 5t/4 Prices are higher than in the simultaneous case: p* = c + t Firm 1 sets a higher price than firm 2 and so has lower market share: c + 3t/2 + tx m = c + 5t/4 + t(1 x m ) x m = 3/8 Profit to firm 1 is then π 1 = 18Nt/32 Profit to firm 2 is π 2 = 25Nt/32 Price competition gives a second mover advantage. 21

22 Dynamic games require firms move in sequence and that they can commit to the moves they make. This is a reasonable assumption with quantity but less obvious with prices. And with no credible commitment, a solution to a dynamic game becomes very different: Cournot first-mover cannot maintain output; Bertrand firm cannot maintain price. Consider the following market-entry game. Can a market be pre-empted by a first-mover? 22

23 To illustrate these issues, we will use this example. Assume there are (1) Two companies Microhard (incumbent) and Newvel (entrant). (2) Newvel makes its decision first: to enter or to stay out of Microhard s market. (3) Microhard then chooses: to accommodate or fight. The pay-off matrix follows. 23

24 The Pay-Off Matrix Microhard Fight Accommodate Newvel Enter Stay Out (0, 0) (2, 2) (1, 5) (1, 5) 24

25 Microhard s option to Fight is a strategy. Microhard will fight if Newvel enters but otherwise remains placid. Similarly, Accommodate is also a strategy. Microhard allows Newvel to compete in its market. Are the actions called for by a particular strategy credible? Is the promise to Fight if Newvel enters believable? If not, then the associated equilibrium is suspect. The matrix-form ignores timing. Therefore, we should represent the game in its extensive form to highlight sequence of moves. 25

26 Newvel N1 The example again eliminated What if Newvel decides to Enter? Enter (2,2) M2 Stay Out (1,5) Fight Fight is Accommodate (0,0) (2,2) Microhard is better to Accommodate Newvel will choose to Enter since Microhard will Accommodate Enter, Accommodate is the unique equilibrium for this game 26

27 What if Microhard competes in other markets? Does threatening in one market affect competitors in other markets? The answer may appear to be yes, that threatening in one market may deter entry in another. However, Selten s Chain-Store Paradox arises. 27

28 Selten s Chain-Store Paradox. Assume 20 markets established sequentially. Will the Firm fight in the first few as a means to prevent entry in later ones? NO!! This is the paradox. Suppose the Firm fights in the first 19 markets, will it fight in the 20 th? With just one market left, we are in the same situation as described above. Enter, Accommodate becomes the only equilibrium. Fighting in the 20 th market won t help in subsequent markets. There are no subsequent markets! So, fight strategy will not be adapted in the 20 th market. 28

29 Now consider the 19 th market. The only reason to fight in the 19 th market is to convince a potential entrant in the 20 th market that the Firm is a fighter. But Firm will not Fight in the 20 th market. So Enter, Accommodate becomes the unique equilibrium for this market, too. What about the 18 th market? Fight only influences entrants in the 19 th and 20 th markets. But the threat to Fight in these markets is not credible. Enter, Accommodate is again the equilibrium. By repetition, we see that the Firm will not Fight in any market. 29

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31 CAVEAT: Stackleberg: Quantity Competition ONLY Bertrand: No capacity constraints and no product differentiation

32 The Second Midterm Matching and Multiple Choice PLUS Two problem short answers. You will do a problem and provide a short answer related to the problem s outcome. 32

33 Read Chapters 9, 10 and 11. Look at the examples I will post. Look CLOSELY at the Slides Know the difference between Cournot, Bertrand and Stackelberg outcomes. Understand basics of game theory and Nash equilibria. 33