Quantitative Analysis Quantitative Analysis Of Competitive EffectsOf Competitive Effects

For AntitrustFor Antitrust

Luke FroebOwen Graduate School of Management

Vanderbilt University April 2003

Day 2Day 2

Topics in Merger SimulationTopics in Merger Simulation

The Cruise Lines MergerIssues in Demand EstimationMergers in Auction Markets

Luke FroebOwen Graduate School of Management

Vanderbilt University

The Cruise Lines MergerThe Cruise Lines Merger

Luke FroebOwen Graduate School of Management

Vanderbilt University

Cruise Line Merger: OutlineCruise 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

Related Related WorkWork

“Mergers Among Parking Lots,” J. Econometrics

Capacity constraints on merging lots attenuate price effects by more than constraints on nonmerging lots amplify them

Carnival and Princess Carnival and Princess Revenue ManagementRevenue 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?

Revenue Mgmt. for EconomistsRevenue 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

Typical Profit CurveTypical Profit Curvewith a Rounded Peakwith a Rounded Peak

Non Binding Capacity Constraint:Non Binding Capacity Constraint:Underpricing is More CostlyUnderpricing is More Costly

Binding Capacity Constraint:Binding Capacity Constraint:Overpricing is More CostlyOverpricing is More Costly

Expected Profit:Expected Profit:Uncertainty Implies Higher PricesUncertainty Implies Higher Prices

Expected Profit Curve: Expected Profit Curve: Uncertainty Implies Lower PricesUncertainty Implies Lower Prices

It Takes a It Takes a Lot of Lot of

Uncertainty Uncertainty to Make a to Make a NoticeableNoticeable

DifferenceDifference

Poisson Arrival Process onPoisson Arrival Process onTop of Logit Choice ModelTop 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)

Role of InformationRole of Information Gamma(α, β) prior on

unknown mean arrivals; conjugate to Poisson

Each firmi observes fraction βi (common knowledge), and gets a private signal αi successes

Firm’s posterior information characterized by Gamma(α + αi, β + βi) on unknown µ

Nash Equilibrium Nash Equilibrium • Optimal price maximizes expected profit as a

function of own signal, pi(αi)

• Expectation over all possible signals and all possible quantities

Optimal Pricing as aOptimal Pricing as aFunction of SignalFunction of Signal

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

Deterministic Joint Profit FunctionDeterministic Joint Profit Function

Expected Joint Profit FunctionExpected Joint Profit Function

Merger Numerical ExampleMerger Numerical Example

Numerical Example ContinuedNumerical Example Continued

Dynamic Pricing StrategyDynamic Pricing Strategy

Dynamic Pricing ContinuedDynamic Pricing Continued

Conclusions Based on ExamplesConclusions 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

Open Questions: ConjecturesOpen Questions: Conjectures

• Can an ownership effect reduce price?• Since dynamic pricing reduces

uncertainty, it would also reduce merger effect

• Small price discrimination effect

Open Questions: ModelingOpen 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

Issues in Demand EstimationIssues in Demand Estimation

Luke FroebOwen Graduate School of Management

Vanderbilt University

Typical ExampleTypical Example• Estimate AIDS demand using scanner data• Instruments

• None needed for weekly dataLR vs. SR elasticities (Nevo & Hendel)

• Prices in other citiesCorrelated through costs

• Results• High variance• Inelastic demand?• Goods are complements?

Implementation Critique: Implementation Critique: Too Many ParametersToo 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

PD GEV, Bresnahan, et al.,PD GEV, Bresnahan, et al.,i.e., “Non Nested” Logiti.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

prod1P prod2P prod3P prod4P ROWprod1Q 1.56 0.313 0.125 0.125 1.prod2Q 0.313 1.56 0.125 0.125 1.prod3Q 0.125 0.125 1.56 0.313 1.prod4Q 0.125 0.125 0.313 1.56 1.COLUMN 0.25 0.25 0.25 0.25 1.

Restricted Demand FormsRestricted 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

Implementation Critique: Implementation Critique: Higher Derivatives of DemandHigher Derivatives of Demand

• 5 demand formsPlotted betweencompetitive andmonopoly prices

• Same competitive price, quantity, and elasticity

• But different monopoly price

• Curvature matters

Implementation Critique: Implementation Critique: Higher Derivatives of DemandHigher 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

Mergers in Auction MarketsMergers in Auction Markets

Luke FroebOwen Graduate School of Management

Vanderbilt University

Second Price, Private Value, Second Price, Private Value, Auction FrameworkAuction 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)

Simple Functional FormSimple 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

Bidding for TimberBidding for Timber

Variable Coefficient

$/mbf

Standard

Error

Hauling Miles –2.08 0.48

SBA Status 71.63 16.90

Spread

Parameter

39.66 4.66

Bidding for Timber ContinuedBidding for Timber Continued

Localized Merger withLocalized Merger withLocal CompetitionLocal Competition

Localized Merger with Localized Merger with Global CompetitionGlobal Competition

Global Merger withGlobal Merger withLocal CompetitionLocal Competition

Global Merger with Global Merger with Global CompetitionGlobal Competition

Auction SummaryAuction 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

Vertical RelationshipsVertical Relationships

Luke FroebOwen Graduate School of Management

Vanderbilt University

Horizontal Mergers andHorizontal Mergers andVertical RestraintsVertical 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

Questioning the Consensus on Questioning the Consensus on Horizontal Merger EffectsHorizontal 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?

Monopoly Retail Sector on Top of Monopoly Retail Sector on Top of Bertrand Manufacturing SectorBertrand 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?

Results: The Retail Sector Results: The Retail Sector Matters a LotMatters 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

Three Different GamesThree Different Games

• Game 1: retailer must carry all profitable productsResult: Transparent retail sector

• Game 2: retailer has option of exclusive dealingResult: 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

Retail Effects Illustrated: Retail Effects Illustrated: White Pan Bread in ChicagoWhite Pan Bread in Chicago

All calibrated to same prices, quantities, premerger elasticities (logit demand)

Model CalibrationModel Calibration

Merger of Brands 1 and 2Merger of Brands 1 and 2

ConclusionsConclusions

• Retail sector can matter a lot in horizontal merger analysis• Constant percentage markup usually assumed,

which is transparent case• Not correct if actual case is “opaque” or

“double marginalization”

• Empirical identification of retail game• Games have negative, zero, and positive

wholesale margins, respectively

Unanswered QuestionsUnanswered Questions

• How do retailer’s behave?• Vendor managed inventory• Complex nonlinear contracts with promotional

allowances, quantity discounts:Is two part pricing a good metaphor?

• The n by k case (n mfgs, k retailers)• Retailers compete on selection, price,

convenience• Does opaque equilibrium hold for n by k case?

Damages from Vertical RestraintsDamages from Vertical Restraints

• Two actual cases:• US v. Dentsply, controlled distribution channel• Private case, firm favored its own retail arm

with lower prices• Questions raised:

• How much does distribution channel or MC affect the price setting equilibrium?

• How much more profit would the injured firms have made absent the vertical restraints?