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Economics of the Firm

Economics of the Firm. Strategic Pricing Techniques. 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)

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Economics of the Firm

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  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 (Positive Markup) • 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 significant market share • STRATEGIES MATTER!!! Mobile Phones (2011) Nokia: 22.8% Samsung: 16.3% LG: 5.7% Apple: 4.6% ZTE:3.0% Others: 47.6% US Beer (2010) Anheuser-Busch: 49% Miller/Coors: 29% Crown Imports: 5% Heineken USA: 4% Pabst: 3% Music Recording (2005) Universal/Polygram: 31% Sony: 26% Warner: 15% Warner: 10% Independent Labels: 18%

  4. 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! Strategy Matters!!!!!

  5. 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.

  6. Jake is choosing rows Clyde is choosing columns Clyde Jake

  7. 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

  8. 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

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

  10. 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

  11. “Winston tastes good like a cigarette should!” “Us Tareyton smokers would rather fight than switch!”

  12. Price Fixing and Collusion Prior to 1993, the record fine in the United States for price fixing was $2M. Recently, that record has been shattered! In other words…Cartels happen!

  13. Cartels - The Prisoner’s Dilemma The problem facing the cartel members is a perfect example of the prisoner’s dilemma ! Clyde Jake

  14. Cartel Formation • While it is clearly in each firm’s best interest to join the cartel, there are a couple problems: • With the high monopoly markup, each firm has the incentive to cheat and overproduce. If every firm cheats, the price falls and the cartel breaks down • Cartels are generally illegal which makes enforcement difficult! Note that as the number of cartel members increases the benefits increase, but more members makes enforcement even more difficult!

  15. Perhaps cartels can be maintained because the members are interacting over time – this brings is a possible punishment for cheating. Clyde Jake Jake “I plan on cooperating…if you cooperate today, I will cooperate tomorrow, but if you cheat today, I will cheat forever!” 0 1 2 3 4 5 Time Make Strategic Decision Make Strategic Decision Make Strategic Decision Make Strategic Decision Make Strategic Decision Make Strategic Decision

  16. “I plan on cooperating…if you cooperate today, I will cooperate tomorrow, but if you cheat today, I will cheat forever!” Jake Cooperate: $20 $20 $20 $20 $20 $20 Clyde 0 1 2 3 4 5 Time Make Strategic Decision Make Strategic Decision Make Strategic Decision Make Strategic Decision Make Strategic Decision Make Strategic Decision Cheat: $40 $15 $15 $15 $15 $15 Cooperate: $120 Cheat: $115 Clyde should cooperate, right?

  17. We need to use backward induction to solve this. Jake Clyde 0 1 2 3 4 5 Time Make Strategic Decision Make Strategic Decision Make Strategic Decision Make Strategic Decision Make Strategic Decision Make Strategic Decision Regardless of what took place the first four time periods, what will happen in period 5? What should Clyde do here?

  18. We need to use backward induction to solve this. Jake Clyde 0 1 2 3 4 5 Time Make Strategic Decision Make Strategic Decision Make Strategic Decision Make Strategic Decision Make Strategic Decision Make Strategic Decision Cheat Given what happens in period 5, what should happen in period 4? What should Clyde do here?

  19. We need to use backward induction to solve this. Jake Clyde 0 1 2 3 4 5 Time Make Strategic Decision Make Strategic Decision Make Strategic Decision Make Strategic Decision Make Strategic Decision Make Strategic Decision Cheat Cheat Cheat Cheat Cheat Knowing the future prevents credible promises/threats!

  20. Where is collusion most likely to occur? High profit potential • Inelastic Demand (Few close substitutes, Necessities) • Cartel members control most of the market • Entry Restrictions (Natural or Artificial) Low cooperation/monitoring costs • Small Number of Firms with a high degree of market concentration • Similar production costs • Little product differentiation

  21. The Stag Hunt: Two individuals are out on a hunt. Each must make a decision on what to hunt without knowledge of the other individual’s choice • Only one hunter is required to catch a rabbit – a small, sure reward • Two hunters are required to take down a stag – a bigger but riskier reward What’s the equilibrium here?

  22. The Stag Hunt: Two individuals are out on a hunt. Each must make a decision on what to hunt without knowledge of the other individual’s choice If both hunt the stag, neither has an incentive to deviate – an equilibrium! If both hunt the rabbit, neither has an incentive to deviate – an equilibrium!

  23. A quick detour: Expected Value Suppose that I offer you a lottery ticket: This ticket has a 2/3 chance of winning $100 and a 1/3 chance of losing $100. How much is this ticket worth to you? Suppose you played this ticket 6 times: Total Winnings: $200 Attempts: 6 Average Winnings: $200/6 = $33.33

  24. A quick detour: Expected Value Given a set of probabilities, Expected Value measures the average outcome Expected Value = A weighted average of the possible outcomes where the weights are the probabilities assigned to each outcome Suppose that I offer you a lottery ticket: This ticket has a 2/3 chance of winning $100 and a 1/3 chance of losing $100. How much is this ticket worth to you?

  25. Suppose that you believed that your fellow hunter was equally likely to hunt the stag or the rabbit what would you do? 50% 50% If you hunt the rabbit: You are guaranteed a reward of 1 with certainty If you hunt the stag: 50% of the time you get 4, 50% of the time you get 0 In this example, hunting the stag is reward dominant (better average payout), while hunting the rabbit is risk dominant (lower risk)

  26. What if we change the odds…? 10% 90% If you hunt the rabbit: You are guaranteed a reward of 1 with certainty If you hunt the stag: 10% of the time you get 2, 90% of the time you get 0 Now, hunting the rabbit is both reward dominant and risk dominant!! Choosing the stag would never be a good idea here.

  27. Let’s find the odds that make the stag and rabbit equally attractive on average… X% Y% If you hunt the rabbit: You are guaranteed a reward of 1 with certainty If you hunt the stag: For them to be equal on average: X = 25%, Y = 75%

  28. Therefore, in this example, you will only hunt the stag if your fellow hunter hunts the stag at least 25% of the time. Similarly, your fellow hunter will only hunt the stag if you hunt the stag at least 25% of the time. 25% 75% 25% 6.25% 18.75% 75% 18.75% 56.25%

  29. Therefore, in this case, the stag hunt has three possible equilibria: 50% 50% Equilibrium #1: Both players always hunt the stag Equilibrium #2: Both players sometimes hunt the stag (each player must hunt the stag at least 25% of the time) Equilibrium #3: Both players never hunt the stag

  30. Example: The Airline Price Wars Suppose that American and Delta face the given demand for flights to NYC and that the unit cost for the trip is $200. If they charge the same fare, they split the market $500 $220 American 60 180 What will the equilibrium be? Delta

  31. The Airline Price Wars If American follows a strategy of charging $500 all the time, Delta’s best response is to also charge $500 all the time If American follows a strategy of charging $220 all the time, Delta’s best response is to also charge $220 all the time American This game is just like the stag hunt – it has multiple equilibria and the result depends critically on each company’s beliefs about the other company’s strategy Delta

  32. The Airline Price Wars: A Stag Hunt! Suppose American charges $500 with probability Charges $220 with probability Charge $500: American Charge $220: Delta (6%) (19%) (19%) (56%) (75%) (25%)

  33. Lets take the game we started out with…what are the strategies? Player 2 Player 1

  34. Ever Cheat on your taxes? In this game you get to decide whether or not to cheat on your taxes while the IRS decides whether or not to audit you What is the equilibrium to this game?

  35. If the IRS never audited, your best strategy is to cheat (this would only make sense for the IRS if you never cheated) If the IRS always audited, your best strategy is to never cheat (this would only make sense for the IRS if you always cheated) There is no pure strategy equilibrium (i.e. there are no certain strategies)!

  36. Cheating on your taxes! Suppose that the IRS Audits 25% of all returns. What should you do? Cheat: Don’t Cheat: If the IRS audits 25% of all returns, you are better off not cheating. But if you never cheat, they will never audit, …

  37. The only way this game can work is for you to cheat sometime, but not all the time. That can only happen if you are indifferent between the two! Suppose the government audits with probability Doesn’t audit with probability Cheat: Don’t Cheat: If you are indifferent… (83%) (17%)

  38. We also need for the government to audit sometime, but not all the time. For this to be the case, they have to be indifferent! Suppose you cheat with probability Don’t cheat with probability Audit: Don’t Audit: If they are indifferent… (91%) (9%)

  39. Now we have an equilibrium for this game that is sustainable! The government audits with probability Doesn’t audit with probability Suppose you cheat with probability Don’t cheat with probability (7.5%) (1.5%) We can find the odds of any particular event happening…. (75%) (15%) You Cheat and get audited: (1.5%)

  40. In the Movie Air Force One, Terrorists hijack Air Force One and take the president hostage. Can we write this as a game? (Terrorists payouts on left) Terrorists Take Hostages Don’t Take Hostages President (0, 1) Don’t Negotiate Negotiate In the third stage, the best response is to kill the hostages (1, -.5) Terrorists Given the terrorist response, it is optimal for the president to negotiate in stage 2 Kill Don’t Kill Given Stage two, it is optimal for the terrorists to take hostages (-.5, -1) (-1, 1)

  41. Terrorists The equilibrium is always (Take Hostages/Negotiate). How could we change this outcome? Take Hostages Don’t Take Hostages President (0, 1) Suppose that a constitutional amendment is passed ruling out hostage negotiation (a commitment device) Don’t Negotiate Negotiate (1, -.5) Terrorists Without the possibility of negotiation, the new equilibrium becomes (No Hostages) Kill Don’t Kill (-.5, -1) (-1, 1)

  42. Player A A bargaining example…How do you divide $20? Offer Player B Day 1 Accept Reject Player B Two players have $20 to divide up between them. On day one, Player A makes an offer, on day two player B makes a counteroffer, and on day three player A gets to make a final offer. If no agreement has been made after three days, both players get $0. Offer Player A Day 2 Accept Reject Player A Offer Player B Day 3 Accept Reject (0,0)

  43. Player A Offer Player A knows what happens in day 2 and wants to avoid that! Player B Day 1 Player A: $19.99 Player B: $.01 Accept Reject Player B Offer Player B knows what happens in day 3 and wants to avoid that! Player A: $19.99 Player B: $.01 Player A Day 2 Accept Reject Player A Offer If day 3 arrives, player B should accept any offer – a rejection pays out $0! Player B Day 3 Player A: $19.99 Player B: $.01 Accept Reject (0,0)

  44. Player A Lets consider a variation… Offer Player B Day 1 $20 The Shrinking Pie Game: Negotiations are costly. After each round, the pot gets reduced by 50%: Accept Reject Player B Offer Player A Day 2 $10 Accept Reject Player A Offer Player B Day 3 Accept Reject $5 (0,0)

  45. Player A If player B rejects, she gets $5 tomorrow. She will accept anything better than $5 Offer Player A: $5.01 Player B: $14.99 Player B Day 1 $20 Accept Reject Player B Offer If player A rejects, she gets $4.99 in one year. She will accept anything better than $4.99 Player A: $5.00 Player B: $5.00 Player A Day 2 Accept Reject $10 Player A Offer If day 3 arrives, player B should accept any offer – a rejection pays out $0! Player B Day 3 Player A: $4.99 Player B: $.01 Accept Reject $5 (0,0)

  46. Did someone say Batman?

  47. Back to pricing… • Consider the following example. We have two competing firms in the marketplace. • These two firms are selling identical products. • Each firm has constant marginal costs of production. What are these firms using as their strategic choice variable? Price or quantity?

  48. Consider the following scenario…We call this Cournot competition Two manufacturers choose a production target Two manufacturers earn profits based off the market price P S Q1 P* Profit = P*Q1 - TC D Q Q1 + Q2 A centralized market determines the market price based on available supply and current demand Q2 Profit = P*Q2 - TC

  49. For example…suppose both firms have a constant marginal cost of $20 Two manufacturers choose a production target Two manufacturers earn profits based off the market price P S Q1 = 1 $60 Profit = 60*1 – 20 = $40 D Q 3 A centralized market determines the market price based on available supply and current demand Q2 = 2 Profit = 60*2 – 40 = $80

  50. Let’s figure out the strategies… Suppose that you are firm 1. You know that firm #2 has set a production level of 1

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