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Quantitative Analysis
Of Competitive Effects
For Antitrust
Day 2
Luke Froeb
Owen Graduate School of Management
Vanderbilt University
April 2003
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
The Cruise Lines Merger
Luke Froeb
Owen Graduate School of Management
Vanderbilt University
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
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
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?
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
Typical Profit Curve
with a Rounded Peak
Non Binding Capacity Constraint:
Underpricing is More Costly
Binding Capacity Constraint:
Overpricing is More Costly
Expected Profit:
Uncertainty Implies Higher Prices
Expected Profit Curve:
Uncertainty Implies Lower Prices
It Takes a
Lot of
Uncertainty
to Make a
Noticeable
Difference
Poisson Arrival Process on
Top 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 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
• 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 a
Function of Signal
Postmerger Optimal Pricing
Functions, i.e. Ownership Effect
Deterministic Joint Profit Function
Expected Joint Profit Function
Merger Numerical Example
Numerical Example Continued
Dynamic Pricing Strategy
Dynamic Pricing Continued
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
Open 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: 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 Estimation
Luke Froeb
Owen Graduate School of Management
Vanderbilt University
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?
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
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
prod1 Q
prod2 Q
prod3 Q
prod4 Q
COLUMN
prod1 P
1.56
0.313
0.125
0.125
0.25
prod2 P
0.313
1.56
0.125
0.125
0.25
prod3 P
0.125
0.125
1.56
0.313
0.25
prod4 P
0.125
0.125
0.313
1.56
0.25
ROW
1.
1.
1.
1.
1.
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
Implementation Critique:
Higher Derivatives of Demand
• 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
• 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 Markets
Luke Froeb
Owen Graduate School of Management
Vanderbilt University
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)
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
Bidding for Timber
Variable
Coefficient Standard
$/mbf
Error
Hauling Miles
–2.08
0.48
SBA Status
71.63
16.90
Spread
Parameter
39.66
4.66
Bidding for Timber Continued
Localized Merger with
Local Competition
Localized Merger with
Global Competition
Global Merger with
Local Competition
Global Merger with
Global Competition
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
Vertical Relationships
Luke Froeb
Owen Graduate School of Management
Vanderbilt University
Horizontal Mergers and
Vertical 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
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?
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?
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
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
Retail Effects Illustrated:
White Pan Bread in Chicago
All calibrated to same prices, quantities,
premerger elasticities (logit demand)
Model Calibration
Merger of Brands 1 and 2
Conclusions
• 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 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 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?