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Slides 6(Chapter 11)2Review Cournot competiti.docx
- 1. Slides 6 (Chapter 11) 2 Review: Cournot competition and Shell is firm 2). given the decision of the other firm � �1,�2 = � − �(�1 + �2) � �� = ��� for � = 1,2 Equilibrium and Profits �1 ∗ = �2 ∗ = �−�
- 2. 3� �� = 2(a − c)/3b and �� = �/3 + 2c/3 �1 = �2 = (� − �) 2/9� 4 Stackelberg competition �1 first �2 � �1,�2 = � − �(�1 + �2) � �� = ��� for � = 1,2 5 How do we solve this problem?
- 3. makes more profits? 6 Problem of the follower �2 �1, �2 = � − � �1 + �2 �2 − ��2 ��2 �1,�2 ��2 = � − 2��2 − b�1 − c = 0 �2 �1 = (� − � − ��1)/2� 7 Problem of the leader �1 �1, �2 = � − � �1 + �2 �1 �1 − ��1 �2 �1 = (� − � − ��1)/2�
- 4. �1 �1,�2 = � + � − ��1 /2 �1 − ��1 ��1 �1, �2 ��1 = � − � 2 − ��1 = 0 Equilibrium and profits �1 ∗ = �−� 2� �2 ∗ = �−�−��1 ∗ 2� = �−� 4�
- 5. �� = 3(a − c)/4b and �� = �/4 + 3c/4 �1 = (� − �) (� + �)/4� �2 = (� − �) (� + �)/8� Equilibrium and profits with Cournot competition Slides 7 (Chapter 12) 2 Entry
- 6. pricing: Set low price to force exit 3 Two-stage game: Bresnahan and Reiss 1991 whether to enter or not � � � where � is market size � � firms enter, variable profit per custom is � � with �� � /�� ≤ 0
- 7. 4 How many firms? � = 1,2,…,� is �� �,� = �� � − � � firms we need � ≥ �/� � � is large we get lot of firms with small � � � Example: Entry with BP/Shell Cournot Demand is � � = � − �� � �� = ��� for � = 1,2 Example: Entry with BP/Shell Cournot
- 8. �1 = �2 = (� − �) 2/9� �1 = (� − �) 2/4� Example: Entry with BP/Shell Cournot � = 10, � = 1, and � = 2 �1 = �2 = 7 � 1 9 �1 = 16 � = 10 only BP enters Example: Entry with BP/Shell Cournot � = 6. What can BP do?
- 9. �1 �������� = �1 � = 4 �2 = 2, � = 4, and �2 = 4 Example: Entry with BP/Shell Cournot � < 4, BP needs �1 �������� > 4 to deter entry! � is too low Example: Entry with BP/Shell Cournot � = 1
- 10. What �1 �������� is needed to deter entry? �2 given �1 = �1 �������� �2 = 4 − 1 2 �1 �������� 2 ≤ 1 if �1 �������� ≥ 6 Example: Entry with BP/Shell Cournot �1 �������� = 6 and �1 = 12
- 11. �1 = 8 �1 �������� = 6 and deters entry! Slides 8 (Chapter 14) 2 What did we learn from static oligopoly models? th two firms competing “non-cooperatively” both firms to “over produce” (or “under price”) relative to monopoly behavior
- 12. 3 Can the firms do better? “better” equilibrium, compared to the Cournot or Bertrand Nash equilibria l show that supporting collusive behavior requires that the firms compete more than once 4 Collusion and cartels discipline and reduce competition between a group of suppliers
- 13. territories 5 Collusion and cartels t to prevent 6 Collusion and cartels – the law illegal to form any agreement in restraint of trade
- 14. reason analysis: Is there a legitimate, welfare- enhancing reason to permit the activity? 7 Collusion and cartels – the law Justice (DOJ) ison sentences for executives found guilty competitor!!! 8 Some cartels are never formed Putnam, CEO Braniff Air: Do you have a suggestion for me? Crandall, CEO American Airlines: Yes, I have a suggestion
- 15. for you. Raise your damn fares 20%. I’ll raise mine the next morning. Putnam: Robert, we... Crandall: You’ll make more money and I will too... Putnam: We can’t talk about pricing! Crandall: Oh (expletive deleted), Howard. We can talk about any damn thing we want to talk about. Conversation taped by DOJ, 2/21/82 9 Collusion and cartels -legally binding threats or self- interest
- 16. 10 Collusion and cartels which are legal e are known as tacit collusion 11 Thinking about the economics
- 17. eaters? (enforcement of the collusive agreement) 12 An example before we dive into theory: the lysine cartel -1990s, several international firms conspired to fix worldwide lysine prices Largest conspirator was Archer Daniels Midland (ADM). Huge grain and seed company. executive (Mark Whitacre) who was involved in a different case cartel meetings
- 18. 13 Now a major motion picture! 14 An example before we dive into theory: the lysine cartel convicted on separate embezzlement charges 15 FBI Recordings of the lysine cartel in to their meeting, and about their biggest
- 19. customer (Tyson Foods) sitting in. —one of the Japanese firms doesn’t want to meet in Hawaii because it’s in the U.S. “trade association” 16 FBI Recordings of the lysine cartel —to the penny per pound—for the US and Canada cheaters. It will use its excess capacity -of-year compensation scheme buy from another firm
- 20. Slides 9 (Chapter 14) 2 Bertrand competition � � = 10 − � � �� = 2�� for � = 1,2 -shot game �∗ = 2 and �∗ = 0 for both of them! �� = 6 and �∗ = 8 ---incentives to deviate 3 Do repeated interactions help?
- 21. �� in period 1 �� in period 2 if both played �� in 1 �� in period 2 is not credible. It is just a one-shot Bertrand, so �2 = � ∗ = 2 So period 1 NE is also Bertrand 4 Continues… iods? -shot Bertrand! Then, last but one is also Bertrand! ….
- 22. 5 Infinitely repeated game is probability α the game will continue to the next period! – α the game will end ount rare is δ = α / (1 + r) Continues… ��� per-period
- 23. �� = � �=0 δ���� �� �1� = �2� = � ∗ Continues… � = �� � = �� if �1� = �2� = � � for all s < t � = 2 otherwise (punish if deviates!) rm can be better off by deviating Continues…
- 24. �1 = �2 = 2 �1 = �2 = � � better off by deviating Collusive subgame �� − � �� now �� = � �=0 δ� 1 2 �� =
- 25. 1 1 − δ 1 2 �� �� Collusive subgame 1 1 − δ 1 2 �� ≥ �� 1 2 be very patient ---large δ
- 26. 1. Differentiated Bertrand competition versus price leadership. The demand for two brands of laundry detergent, Wave (W) and Rah (R), are given by the following demands: Qw = 80 – 2pW + pR QR = 80 – 2pR + pW The firms have identical cost functions, with a constant marginal cost of 10. The firms compete in prices. (a) What is the best response function for each firm? (that is, what is firm W's optimal price as a function of firm R’s price, and vice-versa?) What is the equilibrium to the one-shot pricing game? What are the profits of each firm? (b) Suppose the manufacturer of Wave could commit to setting pw before the manufacturer of Rah could set pR. How would this change the equilibrium? What are the profits of each firm in this case? Should Wave take advantage of this commitment possibility? Why or why not? (c) Is there a first or second-mover advantage in this game? First-mover advantage is like the
- 27. conventional Stackelberg quantity-leadership story, while second-mover advantage is reversed. Explain the intuition for your answer, and compare / contrast with the Stackelberg quantity-setting story. 2. Entry deterrence via quantity pre-commitment. The U.S. market for hand sanitizer is controlled by a monopoly (firm I, for incumbent) that has a total cost given by TC(qI) = 0.025 2 I q and MC(qI) = 0.05qI. The market demand for hand sanitizer is given by P = 50 – 0.1Q. Under monopoly, Q = QI. (a) What is the monopolist’s optimal price and output? (b) Now let there be a foreign firm (firm E, for entrant) that is considering entry into the market. Because the entrant must ship hand sanitizer all the way across the ocean, its costs are higher. Specifically, the entrant’s costs are given by TC(qE) = 10qE + 0.025 2
- 28. E q and MC(qE) = 10 + 0.05qE. Suppose that the incumbent monopolist has committed to the monopoly output level. What is the residual demand faced by the entrant? How much output will the entrant export to the U.S.? What will be the U.S. price of hand sanitizer? (c) Show that the monopolist would need to commit to produce 400 units in order to deter entry of the foreign firm. (Hint: figure out the monopolist’s output level q* such that the entrant loses money if it exports anything other than zero.) What are the incumbent’s profits if it commits to this output level and deters entry? (d) If the incumbent decides to accommodate entry, what quantity will it commit to? (e) Will the incumbent deter or accommodate entry in this market? 3. Collusion and punishment. Suppose the market demand for lumber is given by:
- 29. There are two symmetric producers in the market, each with a constant marginal cost of 10. (a) What are the monopoly price, quantity, and profits in this market? (b) What are the Cournot price, quantities, and profits in this market? (c) Suppose the two firms compete in the following infinitely repeated game: (i) Each firm produces qi = q * (ii) If any firm produces q>q*, then each firm believes that both will revert to the one- shot Cournot quantity qc, forever. What is the critical value of the firms’ discount factor δ such that q* = 0.5Qm (where Qm is the monopoly output) is the equilibrium outcome to this game? (d) Suppose the firms instead set price, given the cost functions above and no capacity constraints. What is the equilibrium price and quantity to this one-shot stage game? (e) Let the firms in part (d) compete repeatedly in the following infinitely repeated Bertrand game:
- 30. (i) Each firm sets pi = p * (ii) If any firm produces p<p*, then each firm believes that both will revert to the one- shot Bertrand price pB, forever. What is the critical value of the firms’ discount factor δ such that p* = pm is the equilibrium outcome to this game? Which type of competition, price or quantities, is more likely to sustain the monopoly outcome? Why? 4. Factors affecting the sustainability of collusion. Consider an infinitely repeated Bertrand trigger pricing game (for example, question 3(e) above). Describe how each of the following conditions would affect the sustainability of a collusive outcome, if at all. (a) The government’s Competition Commission announces plans to publish a monthly list of all transactions prices and volumes in this market, in an effort to improve “market transparency” for consumers.
- 31. (b) Recent regulations require users of the product to convert to less environmentally- hazardous substitutes over the next five years. At that point, production and sales of this product will be banned.