Economics of the Firm

1. Economics of the Firm Strategic Pricing Techniques

2. Recall that there is an entire spectrum of market structures Market Structures • Perfect Competition • Many firms, each with zero market share • P = MC • Profits = 0 (Firm’s earn a reasonable rate of return on invested capital) • NO STRATEGIC INTERACTION! • Monopoly • One firm, with 100% market share • P > MC • Profits > 0 (Firm’s earn excessive rates of return on invested capital) • NO STRATEGIC INTERACTION!

3. Most industries, however, don’t fit the assumptions of either perfect competition or monopoly. We call these industries oligopolies • Oligopoly • Relatively few firms, each with positive market share • STRATEGIES MATTER!!! Wireless (2002) Verizon: 30% Cingular: 22% AT&T: 20% Sprint PCS: 14% Nextel: 10% Voicestream: 6% US Beer (2001) Anheuser-Busch: 49% Miller: 20% Coors: 11% Pabst: 4% Heineken: 3% Music Recording (2001) Universal/Polygram: 23% Sony: 15% EMI: 13% Warner: 12% BMG: 8%

4. Market shares are not constant over time in these industries! Airlines (1992) Airlines (2002) American American United United Delta Delta Northwest Northwest Continental Continental US Air SWest While the absolute ordering didn’t change, all the airlines lost market share to Southwest.

5. Another trend is consolidation Retail Gasoline (1992) Retail Gasoline (2001) Shell Exxon/Mobil Chevron Shell Texaco BP/Amoco/Arco Exxon Amoco Chev/Texaco Mobil Total/Fina/Elf BP Conoco/Phillips Citgo Marathon Sun Phillips

6. The key difference in oligopoly markets is that price/sales decisions can’t be made independently of your competitor’s decisions Your Price (-) Monopoly Oligopoly Your N Competitors Prices (+) Oligopoly markets rely crucially on the interactions between firms which is why we need game theory to analyze them!

7. Prisoner’s Dilemma…A Classic! Two prisoners (Jake & Clyde) have been arrested. The DA has enough evidence to convict them both for 1 year, but would like to convict them of a more serious crime. Jake Clyde • The DA puts Jake & Clyde in separate rooms and makes each the following offer: • Keep your mouth shut and you both get one year in jail • If you rat on your partner, you get off free while your partner does 8 years • If you both rat, you each get 4 years.

8. Jake is choosing rows Clyde is choosing columns Clyde Jake

9. Suppose that Jake believes that Clyde will confess. What is Jake’s best response? If Clyde confesses, then Jake’s best strategy is also to confess Clyde Jake

10. Suppose that Jake believes that Clyde will not confess. What is Jake’s best response? If Clyde doesn’t confesses, then Jake’s best strategy is still to confess Clyde Jake

11. Dominant Strategies Jake’s optimal strategy REGARDLESS OF CLYDE’S DECISION is to confess. Therefore, confess is a dominant strategy for Jake Clyde Jake Note that Clyde’s dominant strategy is also to confess

12. Nash Equilibrium The Nash equilibrium is the outcome (or set of outcomes) where each player is following his/her best response to their opponent’s moves Clyde Jake Here, the Nash equilibrium is both Jake and Clyde confessing

13. Repeated Games Jake Clyde The previous example was a “one shot” game. Would it matter if the game were played over and over? Suppose that Jake and Clyde were habitual (and very lousy) thieves. After their stay in prison, they immediately commit the same crime and get arrested. Is it possible for them to learn to cooperate? 0 1 2 3 4 5 Time Play PD Game Play PD Game Play PD Game Play PD Game Play PD Game Play PD Game

14. Repeated Games Jake Clyde We can use backward induction to solve this. 0 1 2 3 4 5 Time Play PD Game Play PD Game Play PD Game Play PD Game Play PD Game Play PD Game Confess Confess Confess Confess Confess Confess Confess Confess Confess Confess Confess Confess Similar arguments take us back to period 0 However, once the equilibrium for period 5 is known, there is no advantage to cooperating in period 4 At time 5 (the last period), this is a one shot game (there is no future). Therefore, we know the equilibrium is for both to confess.

15. Continuous Choice Games – Cournot Competition There are two firms in an industry – both facing an aggregate (inverse) demand curve given by D Aggregate Production Both firms have constant marginal costs equal to $C

16. From firm one’s perspective, the demand curve is given by Treated as a constant by Firm One Solving Firm One’s Profit Maximization…

17. In Game Theory Lingo, this is Firm One’s Best Response Function To Firm 2 Note that this is the optimal output for a monopolist!

18. Further, if Firm two produces It drives price down to MC

19. The game is symmetric with respect to Firm two… Firm 1 Firm 2

20. Firm 1 Competitive Output Monopoly Output There exists a unique Nash equilibrium Firm 2

21. A numerical example… Suppose that the market demand for computer chips (Q is in millions) is given by Intel and Cyrix are both competing in the market and have a marginal cost of $20.

22. Had this market been serviced instead by a monopoly,

23. With competing duopolies

24. One more point… Monopoly Duopoly If both firms agreed to produce 1.25M chips (half the monopoly output), they could split the monopoly profits ($62.5 apiece). Why don’t these firms collude?

25. The previous analysis (Cournot Competition) considered quantity as the strategic variable. Bertrand competition uses price as the strategic variable. Should it matter? P* D Q* Just as before, we have an industry demand curve and two competing duopolies – both with marginal cost equal to c.

26. Cournot Case Bertrand Case D D

27. Price competition creates a discontinuity in each firm’s demand curve – this, in turn creates a discontinuity in profits As in the cournot case, we need to find firm one’s best response (i.e. profit maximizing response) to every possible price set by firm 2.

28. Firm One’s Best Response Function Case #1: Firm 2 sets a price above the pure monopoly price: Case #2: Firm 2 sets a price between the monopoly price and marginal cost Case #3: Firm 2 sets a price below marginal cost Case #4: Firm 2 sets a price equal to marginal cost What’s the Nash equilibrium of this game?

29. Bertrand Equilibrium: It only takes two firm’s in the market to drive prices to marginal cost and profits to zero! • However, the Bertrand equilibrium makes some very restricting assumptions… • Firms are producing identical products (i.e. perfect substitutes) • Firms are not capacity constrained

30. An example…capacity constraints Consider two theatres located side by side. Each theatre’s marginal cost is constant at $10. Both face an aggregate demand for movies equal to Each theatre has the capacity to handle 2,000 customers per day. What will the equilibrium be in this case?

31. If both firms set a price equal to $10 (Marginal cost), then market demand is 5,400 (well above total capacity = 2,000) Note: The Bertrand Equilibrium (P = MC) relies on each firm having the ability to make a crediblethreat: “If you set a price above marginal cost, I will undercut you and steal all your customers!” At a price of $33, market demand is 4,000 and both firms operate at capacity