Transcript The Role of Econometric Analysis in Antitrust

Competitive Revenue
Management: Evaluating
Mergers Among Cruise Lines
Luke Froeb & Steven Tschantz
Vanderbilt University
April 5, 2003
IIOC, Boston
"Structural Empirical Models for Merger Analysis"
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Talk outline
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Revenue mgt. and cruise line merger
Revenue mgt. for economists
Nash equilibrium when firms “revenue
manage”
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Preliminary conclusions based on few numerical
examples
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Usual ownership effect raises price
Information-sharing effect can raise or lower price
Model extensions
Policy conclusions
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Related
Work
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"Mergers
Among Parking
Lots," J.
Econometrics.
Constraints on
merging lots
attenuate price
effects by more
than constraints
on non-merging
lots amplify
them
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Carnival-Princess & Revenue
Mgt.
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Revenue management: problem of matching
uncertain demand to available capacity.
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British Competition Commission, U.S. FTC, EC
all cleared cruise line merger
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Hotels, airlines, cruise lines
filling-the-ship concern unaffected by mergerno
price change
No quantity effect, but higher prices to less-elastic
customers
Analysis of usual market power concerns
Were theories correct? What was Magnitude?
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Revenue Mgt. for Economists
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Set price before demand realized.
Fixed capacity (big fixed costs, low marginal cost)
Q=min[demand(p), K]
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demand[p] is log normally distributed with mean of q[p];
σ/µ=40%
q[p] is a logit function of price.
If C(Q) is linear,
With uncertainty, firms price higher or lower than
deterministic price depending on which side of
deterministic profit peak is steeper.
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Typical Profit Curve
with a Rounded Peak
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Non-binding capacity constraint:
Steeper on left side
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Binding capacity constraint:
Steeper on right side
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Expected profit curve:
price increases w/uncertainty
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Expected profit curve:
price decreases w/uncertainty
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It takes a lot of uncertainty to
make a noticeable difference
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Poisson arrival process
on top of logit choice model
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Poisson arrival
process with mean µ
On top of n-choice
logit demand model
Implies n
independent arrival
processes with
means (siµ)
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Role of information
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Gamma(α, β) prior on
unknown mean arrivals
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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
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Nash Equilibrium
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Optimal price maximizes expected profit
as a function of own signal, pi(αi)
Expectation over all possible signals and
all possible quantities
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Individual profit, deterministic
and expected
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Individual profit, deterministic
and expected
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Optimal pricing as a function of
signal
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Post merger optimal pricing
functions, i.e. ownership effect
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Joint profit function, determinate
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Joint profit function, expected
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Merger numerical example
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Merger numerical example
(cont.)
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Extension:
Dynamic pricing strategy
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Dynamic pricing (cont.)
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Conclusions based on numerical
examples
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Two merger effects
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Ownership effect raises price
Information-sharing effect raises or lowers price
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But always increases quantity
Both effects small and disappear as
uncertainty decreases
Confirm basic intuition from parking lot paper,
i.e. firms price to fill the ships, and this profit
calculus is unaffected by merger.
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Open Questions
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Conjectures
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Can we find an ownership effect that reduces price?
Since dynamic pricing reduces uncertainty, it would also
reduce merger effect.
Small price discrimination effect.
Models to be built
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Price discrimination between two customer types
Dynamic price adjustment
Modeling rejections (currently, overbooked passengers go
home disappointed)
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Instead allow them to switch to unconstrained carriers, if any
Conjecture that this is likely to be very small.
How to estimate or calibrate model to real data
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