Quantitative Analysis Of Competitive Effects For Antitrust

1. Quantitative Analysis Of Competitive EffectsFor Antitrust Day 2 Luke Froeb Owen Graduate School of Management Vanderbilt University April 2003

2. Topics in Merger Simulation The Cruise Lines Merger Issues in Demand Estimation Mergers in Auction Markets Luke Froeb Owen Graduate School of Management Vanderbilt University

3. The Cruise Lines Merger Luke Froeb Owen Graduate School of Management Vanderbilt University

4. Cruise Line Merger: Outline • Joint work with Steven Tschantz (Math Dept.) • Revenue management and cruise line merger • Revenue management for economists • Nash equilibrium when firms “revenue manage” • Usual ownership effect raises price • Information sharing effect can raise or lower price • Model extensions • Policy conclusions

5. Related Work • “Mergers Among Parking Lots,” J. Econometrics • Capacity constraints on merging lots attenuate price effects by more than constraints on nonmerging lots amplify them

6. Carnival and Princess Revenue Management • Revenue management: problem of matching uncertain demand to available capacity • Hotels, airlines, cruise lines • UK Competition Commission, U.S. FTC, and EC all cleared cruise line merger • Theories considered by the FTC • Filling the ship concern unaffected by merger so no merger effect • No quantity effect, but higher prices to less elastic customers • Were theories correct? What was magnitude?

7. Revenue Mgmt. for Economists • Price is set before demand realized • Fixed capacity (big fixed costs, low marginal cost) • Q = min[demand(p), K] • demand[p] is randomly distributed around mean q[p] • q[p] is a logit function of price • If C(Q) is linear, • E[π(p)] = E[p Q(p) – C(Q(p))] = p E[Q(p)] – C(E[Q(p)]) • Expected profit is a function of expected quantity • Uncertainty can cause price to be higher or lower than the deterministic price depending on the “costs” of over vs. under pricing

8. Typical Profit Curvewith a Rounded Peak

9. Non Binding Capacity Constraint:Underpricing is More Costly

10. Binding Capacity Constraint:Overpricing is More Costly

11. Expected Profit:Uncertainty Implies Higher Prices

12. Expected Profit Curve:Uncertainty Implies Lower Prices

13. It Takes a Lot of Uncertainty to Make a NoticeableDifference

14. Poisson Arrival Process onTop of Logit Choice Model • Poisson arrival process with mean µ • On top of n choice logit demand model • Implies n independent arrival processes with means (siµ)

15. Role of Information • Gamma(α, β) prior on unknown mean arrivals; conjugate to Poisson • Each firmi observes fractionβi (common knowledge), and gets a private signalαi successes • Firm’s posterior information characterized by Gamma(α+ αi, β+ βi) on unknown µ

16. Nash Equilibrium • Optimal price maximizes expected profit as a function of own signal, pi(αi) • Expectation over all possible signals and all possible quantities

17. Optimal Pricing as aFunction of Signal

18. Postmerger Optimal Pricing Functions, i.e. Ownership Effect

19. Deterministic Joint Profit Function

20. Expected Joint Profit Function

21. Merger Numerical Example

22. Numerical Example Continued

23. Dynamic Pricing Strategy

24. Dynamic Pricing Continued

25. Conclusions Based on Examples • Two merger effects • Ownership effect raises price • Information sharing effect can raise or lower price, but always increases quantity • Both effects small and disappear as uncertainty decreases • Firms price to fill the ships, and this profit calculus is unaffected by merger Not technically correct, but very close

26. Open Questions: Conjectures • Can an ownership effect reduce price? • Since dynamic pricing reduces uncertainty, it would also reduce merger effect • Small price discrimination effect

27. Open Questions: Modeling • Modeling price discrimination between two customer types • Modeling dynamic price adjustment • Modeling rejections (currently, overbooked passengers go home disappointed) • Instead allow them to switch to unconstrained carriers, if any • Conjecture: effect is likely to be very small • Estimating or calibrating model to real data

28. Issues in Demand Estimation Luke Froeb Owen Graduate School of Management Vanderbilt University

29. Typical Example • Estimate AIDS demand using scanner data • Instruments • None needed for weekly data LR vs. SR elasticities (Nevo & Hendel) • Prices in other cities Correlated through costs • Results • High variance • Inelastic demand? • Goods are complements?

30. Implementation Critique: Too Many Parameters • AIDS has too many parameters • Confidence intervals very wide • Elasticities for merging products is most important • High variance estimator • Alternatives: logit, nested logit, PD GEV (Bresnahan and Stern), mixed logit (BLP) + census data (Nevo) • In these forms, all goods are substitutes • Lower variance, but possible bias

31. PD GEV, Bresnahan, et al.,i.e., “Non Nested” Logit • Multiple dimensions of differentiation • Dimensions not nested • On technological frontier or not • Branded or not • Example: Goods 1 & 2 have a trait, but not 3 & 4

32. Restricted Demand Forms • Always yields a postmerger price increase • Parties reluctant to admit even small price increase • If we are going to use these tools to evaluate mergers, must adopt different safe harbors e.g., by “granting” small MC reduction

33. 5 demand forms Plotted between competitive and monopoly prices Same competitive price, quantity, and elasticity But different monopoly price Curvature matters Implementation Critique: Higher Derivatives of Demand

34. Implementation Critique: Higher Derivatives of Demand • f(x), f'(x), and f"(x) influence predicted price rise • Need location, velocity, and acceleration, • But observe only location • If we cannot estimate f"(x) • Do sensitivity analysis or linear or logit extrapolation to be conservative • Compensating marginal cost reductions don’t depend on acceleration • MC reductions sufficient to offset price increase • Use as a benchmark against which to evaluate efficiency claims

35. Mergers in Auction Markets Luke Froeb Owen Graduate School of Management Vanderbilt University

36. Second Price, Private Value, Auction Framework • Example: • Private values are {1, 2, 3, 4, 5, 6} • Merger between {5, 6} reduces price to 4 • Mergers between other bidders have no effect • Price effects of mergers depend on • Frequency of 1-2 finish (proportional to shares) • Price change to third highest value (proportional to variance)

37. Simple Functional Form • Model Asymmetry by allowing different bidders to take different numbers of draws Fi(x) = [F(x)]s bidder i takes s draws • Winning probabilities are proportionate to the number of draws, and bigger firms win at better prices • When firms merge, the merged firm gets as many draws as the merging firms took

38. Bidding for Timber

39. Bidding for Timber Continued

40. Localized Merger withLocal Competition

41. Localized Merger with Global Competition

42. Global Merger withLocal Competition

43. Global Merger with Global Competition

44. Auction Summary • The price effects of mergers depend on • Location of merging and nonmerging bidders • Location of tracts • Whether competition is “global” or “local” i.e., whether transport costs are high relative to variance of values. • In general, unilateral are smaller than with price or quantity competition But collusion may be more of a risk

45. Vertical Relationships Luke Froeb Owen Graduate School of Management Vanderbilt University

46. Horizontal Mergers andVertical Restraints • Joint work with Steven Tschantz (Math Dept.) and Gregory Werden (U.S. Department of Justice) • Horizontal mergers • Relative consensus on how to model horizontal restraints—coordinated and unilateral effects • Policy debate is empirical • Vertical restraints • No consensus on how to model vertical restraints • Policy debate is theoretical or on “necessary conditions,” e.g., market share screens

47. Questioning the Consensus on Horizontal Merger Effects • How do vertical restraints affect the standard horizontal merger analysis, which ignores retail sector? • Assuming we have a good vertical theory, can we estimate harm from vertical restraints?

48. Monopoly Retail Sector on Top of Bertrand Manufacturing Sector • Strategic bargaining game (n +1 players) Upstream Bertrand oligopolists (n) make take it or leave it offers to retail monopolist • Retailer chooses the best set of offers • Then, two upstream manufacturers merge Effect of merger is the difference between the pre and postmerger equilibria • What happens to retail prices and quantities?

49. Results: The Retail Sector Matters a Lot • Upstream horizontal mergers can have a variety of effects when “filtered” through retail sector • Transparent retail sector Merger effect same as if retail sector ignored • Opaque retail sector No merger effect • Double marginalization Can amplify OR attenuate merger effects

50. Three Different Games • Game 1: retailer must carry all profitable products Result: Transparent retail sector • Game 2: retailer has option of exclusive dealing Result: Opaque retail sector • Game 3: manufacturers limited to offering wholesale unit prices independent of quantity Result: Double marginalization, which can amplify or attenuate merger effects