Vanderbilt University

1

Competitive Revenue Management: Evaluating

Mergers Among Cruise Lines

Luke Froeb & Steven TschantzVanderbilt University

April 5, 2003IIOC, Boston

"Structural Empirical Models for Merger Analysis"

Vanderbilt University

2

Talk outline Revenue mgt. and cruise line merger Revenue mgt. for economists Nash equilibrium when firms “revenue

manage” Preliminary conclusions based on few

numerical examples Usual ownership effect raises price Information-sharing effect can raise or lower price

Model extensions Policy conclusions

Vanderbilt University

3

RelatedWork

"Mergers Among Parking Lots," J. Econometrics.

Constraints on merging lots attenuate price effects by more than constraints on non-merging lots amplify them

Vanderbilt University

4

Carnival-Princess & Revenue Mgt. Revenue management: problem of matching

uncertain demand to available capacity. Hotels, airlines, cruise lines

British Competition Commission, U.S. FTC, EC all cleared cruise line merger filling-the-ship concern unaffected by mergerno

price change No quantity effect, but higher prices to less-

elastic customers Analysis of usual market power concerns Were theories correct? What was

Magnitude?

Vanderbilt University

5

Revenue Mgt. for Economists Set price before demand realized. Fixed capacity (big fixed costs, low marginal

cost) Q=min[demand(p), K]

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.

Vanderbilt University

6

Typical Profit Curvewith a Rounded Peak

Vanderbilt University

7

Non-binding capacity constraint:Steeper on left side

Vanderbilt University

8

Binding capacity constraint:Steeper on right side

Vanderbilt University

9

Expected profit curve:price increases w/uncertainty

Vanderbilt University

10

Expected profit curve: price decreases w/uncertainty

Vanderbilt University

11

It takes a lot of uncertainty to make a noticeable difference

Vanderbilt University

12

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)

Vanderbilt University

13

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

Vanderbilt University

14

Nash Equilibrium Optimal price maximizes expected

profit as a function of own signal, pi(αi)

Expectation over all possible signals and all possible quantities

Vanderbilt University

15

Individual profit, deterministic and expected

Vanderbilt University

16

Individual profit, deterministic and expected

Vanderbilt University

17

Optimal pricing as a function of signal

Vanderbilt University

18

Post merger optimal pricing functions, i.e. ownership effect

Vanderbilt University

19

Joint profit function, determinate

Vanderbilt University

20

Joint profit function, expected

Vanderbilt University

21

Merger numerical example

Vanderbilt University

22

Merger numerical example(cont.)

Vanderbilt University

23

Extension:Dynamic pricing strategy

Vanderbilt University

24

Dynamic pricing (cont.)

Vanderbilt University

25

Conclusions based on numerical examples Two merger effects

Ownership effect raises price Information-sharing effect raises or lowers price

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.

Vanderbilt University

26

Open Questions Conjectures

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 Price discrimination between two customer types Dynamic price adjustment Modeling rejections (currently, overbooked passengers

go home disappointed) 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