Competitive Strategy

1. Competitive Strategy

2. Key Concept: • Demand elasticity controls profitability and • Demand elasticity depends on reactions of competitors. • If competitors match price moves, demand is relatively inelastic but • If they don’t match, demand may be very elastic.

3. Competitors’ Responses • To assess demand conditions and efficacy of a pricing strategy, • Need to predict how rivals will respond. • No simple general answer - we will review several different frameworks for analyzing this.

4. Pharmaceutical Example • New drug goes through various life stages: • On patent - no competition. • Still on patent but another patented competitor. • Off patent - generic competitors. • Clearly pricing policy differs by stage.

5. Pharmaceutical Example • We know how to price in the first stage here - set MR = MC, and possibly price discriminate. • Follow through the other stages. First assume one other competitor with a patented drug with similar therapeutic value.

6. Suppose two competitors 1 & 2 face the following market demand curve: P = 30 - Q where Q is the total production of both firms (i.e., Q = Q1 + Q2). Also, suppose both firms have marginal cost: MC1 = MC2 = 0 Monopolistic Competition and Oligopoly

7. Price 30 Demand curve Quantity 30

8. Two Competitors • Each tries to choose production level in response to output of the other. • In choosing output level, firm indirectly chooses (or determines) price, as price is determined by total output (it and the competitor) and market demand conditions.

9. Reaction Curve • A reaction curve for firm 1 specifies for each output level of firm 2 what is firm 1’s best response, i.e. firm 1’s most profitable output level given that of firm 2. • A reaction curve for firm 2 is the same with the 1s and 2s interchanged.

10. Determine the reaction curve for Firm 1. To maximize profit, the firm sets marginal revenue equal to marginal cost. Firm 1’s total revenue R1 is given by: R1 = PQ1 = (30 - Q)Q1 = 30 Q1 - (Q1 + Q2)Q1 = 30 Q1 - (Q1)2 - Q2Q1

11. The firm’s marginal revenue MR1 is just the incremental revenue R1 resulting from an incremental change in output Q1: MR1 = R1/Q1 = 30 - 2 Q1 - Q2

12. Now, setting MR1 equal to zero (the firm’s marginal cost), and solving for Q1, we find: Firm 1’s Reaction Curve: Q1 = 15 - 1/2 Q2 (*) The same calculation applies to Firm 2: Firm 2’s Reaction Curve: Q2 = 15 - 1/2 Q1 (**)

13. Firm 2’s Reaction Curve Cournot Equilibrium 10 Firm 1’s Reaction Curve 10 Duopoly Example Q1 30 Q2 30

14. Figure shows reaction curves and the Cournot-Nash equilibrium. Note that Firm 1’s reaction curve shows its output Q1 in terms of Firm 2’s output Q2 Similarly, Firm 2’s reaction curve shows Q2 in terms of Q1. (Since the firm’s are identical, the two reaction curves have the same form. They look different because one gives Q1 in terms of Q2, and the other gives Q2 in terms of Q1)

15. The equilibrium output levels are the values for Q1 and Q2 that are at the intersection of the two reaction curves, i.e., that are the solution to equations (*) and (**). By replacing Q2 in firm 1’s reaction curve with the expression on the right-hand side of firm 2’s, you can verify that the equilibrium output levels are: Cournot Equilibrium: Q1 = Q2 = 10

16. The total quantity produced is therefore Q = Q1 + Q2 = 20 so the equilibrium market price is P = 30 - Q = 10

17. The equilibrium is at the intersection of the two curves. At this point each firm is maximizing its own profit, given its competitor’s output We have assumed that the two firms compete with each other. Suppose, instead, that the antitrust laws were relaxed and the two firms could collude.

18. Suppose the firms set their outputs to maximize total profit of the two taken together, and agree to split that profit evenly Total profit is maximized by choosing total output Q so that marginal revenue equals marginal cost, which in this example is zero

19. R = PR = (30 - Q)Q = 30Q - Q2 so the marginal revenue is MR = R/Q = 30 - 2Q Setting MR equal to zero, total profit is maximized when Q = 15 Total revenue for the two firms is:

20. Firm 2’s Reaction Curve For the firm, collusion is the best outcome followed by the Cournot Equilibrium and then the competitive equilibrium Competitive Equilibrium (P = MC; Profit = 0) 15 Cournot Equilibrium Collusive Equilibrium 10 7.5 Firm 1’s Reaction Curve Collusion Curve 7.5 10 15 Duopoly Example Q1 30 Q2 30

21. Any combination of outputs Q1 and Q2 that add up to 15 maximizes total profit The curve Q1 + Q2 = 15, called the contract curve, is therefore all pairs of outputs Q1 and Q2 that maximize total profit. If the firms agree to share the profits equally, they will each produce half of the total output: Q1 = Q2 = 7.5

22. More Competition • As number of firms increases, equilibrium output points moves towards “competitive equilibrium.” • With more competition total output rises & price falls, as do profits for each firm. • Competition makes each firm’s demand more elastic & reduces its margin & its best output level.

23. Duopoly Example Q1 30 More competition: profits & prices fall Competitive Equilibrium (many firms) 15 10 Cournot Equilibrium (2 firms) Monopolist Q2 15 30 10

24. A Different Model of Competitive Interaction • Prisoners’ Dilemma model • Represents tension between cooperative and competitive behavior. • Central feature in any cooperation between potentially competitive entities - firms in a cartel, OPEC members, opposed political parties.

25. Prisoners’ Dilemma • Two competitors • Each has constant cost at $4 per unit • Two pricing options: $8 or $6 • Both high: sell 2.5 million annually each • Both low: sell 3.5 million annually each • One high, one low, then former sells 1.25 million, latter 6 million

27. Note: profits = (price - cost) * sales = $(8-4) * 2.5 = 10, etc.

28. For each firm, a low price is the best strategy, whatever the other firm does. It is therefore a dominant strategy, a strategy which is best whatever the choice of the other player, so the outcome is (7, 7). This is in spite of the fact that both could be better off if both charged high prices. This is an example of a prisoners’ dilemma game.

29. Note that (7, 7) is a Nash Equilibrium in the sense that if firm 1 plays low then low is 2’s best response and vice versa: at (7, 7) each is making its best move given the move of the other. This is the definition of a Nash Equilibrium.

30. Collusion and PD • Collusive solution in previous diagrams has a PD structure. • Stability of cartels - OPEC. • Christies, Sothebys and the Justice Department.

31. Now change the payoff matrix slightly:

32. Now low is no longer the dominant strategy for firm 1: low is best for 1 if 2 plays high but high is best if 2 plays low. Now 1 should always do the opposite of 2. But for 2 nothing has changed: low is dominant. What will be the outcome?

33. 1 cannot decide what to do unless it knows what 2 will do. So it has to forecast 2’s move. But 1 can tell that 2’s best move is low, so 1 should forecast that 2 will choose low. In this case, 1 should choose high: hence the outcome will be (high, low) = (6, 12). This is a Nash Equilibrium. Here 2 has no incentive to move to high.

34. Now consider this case:

35. Neither firm has a dominant strategy: the best move for each depends on what the other does - presumable the most common case. What are the Nash equilibria here? One is (low, high) = (12, 6). Another is (high, low) = (6, 12). Which is realized depends on who moves first, or who stakes out a claim to a market of product first. (Think of preemptive announcements, “vaporware”, etc.)

36. Finally, go back to the prisoners’ dilemma case:

37. Here low is a dominant strategy for each firm, so the outcome should be (7, 7). Now suppose the game is played repeatedly, say every month the same two firms face each other in the same market. Consider the following strategy:

38. Firm 1 picks high in period 1 and in period 2. Then firm 1 keeps on picking high as long as firm 2 picked high in the previous period. But if 2 picked low in the previous period, firm 1 picks low forever - or for a very long time. This is called a “tit-for-tat” strategy or a “punishment” strategy.

39. What is 2’s best response to this strategy? If it plays low the payoff is (12, 12, 7, 7, 7, 7,…). If it picks high the payoff is (10, 10, 10, 10,…). Clearly the payoff to picking high is greater. So the best response to the “punishment” or “tit-for-tat” strategy is to cooperate and the (10, 10) outcome will result. This outcome is sometimes referred to as “tacit collusion”.

40. Polystyrene Base Case

41. MAXCO-Gambit CaseCalculation of Expected Value 1 3 0.051 2 6 0.162 3 10 0.37 4 17 0.79 5 28 1.596 6 18 1.206 7 8 0.616 8 4 0.348 9 3 0.194 10 1 0.107 11 1 0.117 12 1 0.127 13 1 0.137 EV: 5.83

42. The MAXCO - Gambit Case • Suppose G believes M will bid EV (EV = 5.83) • What should G bid? • Not bid if true value < 5.83: bid 5.9 if true value > 5.9 • In particular, G will not bid true value if it expects M to bid EV

43. Should M bid EV? • When does M win if it bids EV? • If G bids true value, then M loses if true value > EV and • M wins in true value < EV • So for M bidding EV can lead to “winners curse” if G bids true value