AEM 4160: Strategic Pricing
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AEM 4160: Strategic Pricing Prof.: Jura Liaukonyte Lecture 9 Advanced Booking and Pricing with capacity constraints. Lecture Plan. HW 3 Reading for next class: HBS Case “ Gardasil ” INSTEAD of Tuesday, March 5 th class: Experiment in a Lab Tacit Collusion and Price Matching

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AEM 4160: Strategic PricingProf.: Jura LiaukonyteLecture 9 Advanced Booking and Pricing with capacity constraints

Lecture plan
Lecture Plan

  • HW 3

  • Reading for next class: HBS Case “Gardasil”

  • INSTEAD of Tuesday, March 5th class: Experiment in a Lab

  • Tacit Collusion and Price Matching

  • Advanced booking

  • Pricing with capacity constraints

  • Overbooking

  • “Advanced Selling for Services”

    • HBS case for your reading

  • .

  • Friday 3/1: 12:30 pm start time 2:30 pm start timeMonday 3/4:  12:15 pm start time  2:20 pm start time  4:30 pm start timeTuesday 3/5:  12:20 pm start  2:30 pm start  4:30 pm start

Practices that facilitate tacit pricing
Practices that Facilitate Tacit Pricing

  • Firms can facilitate cooperative pricing by

    • Price leadership

    • Advance announcement of price changes

    • Most favored customer clauses

    • Price Matching

Price leadership
Price Leadership

  • The price leader in the industry announces price changes ahead of others and they match the leader’s price

  • The system of price leadership can break down if the leader does not retaliate if one of the follower firms defects

Example cell phone industry
Example: Cell Phone Industry

Tacit collusion
Tacit Collusion

  • How does it work?

    • Industry is an oligopoly

      • Top four firms dominate almost the entire market

    • Homogenous products

      • Same phone (e.g. iPhone from AT&T or Verizon?), data services (text, e-mail, etc)

      • Agreement on price is easier to come by and cheating is easier to catch

    • Nondurable goods

      • Less incentive to cheat because it is a one-time sale product rather than a product from which sellers could gain a series of sales

Tacit collusion pre announced rate changes
Tacit Collusion: Rate Changes

  • Service providers typically pre-announce rate changes they plan on implementing

    • Advanced notice gives competing firms time to respond

    • Can test the market and competitors

Tacit collusion infrequent high changes in rates
Tacit Collusion: High Changes in Rates

  • Rate changes in the industry have been high and infrequent, yet coordinated across all four firms

    • FOCUS: Text Messages

      • Supply is almost unlimited so in a competitive market prices should decrease not increase over time

        • Since 2005 price per text has doubled. (IBISworld)

        • Service providers do not claim that these increases were driven by higher costs so other methods must be at work.

Price matching guarantees
Price Matching Guarantees

  • Price matching guarantees

    • Helps a firm to protect its consumers and charge a high price.

    • It makes your competitor “soft.”

    • Takes away the benefit for your competitor to undercut your price.

Counter intuitive

Price matching guarantee is simply a mechanism for tacit collusion or competition reduction between firms.

Any offer of the price matching guarantee means effectively taking away any gains that its competitor might get from cutting price.

If a firm offers a price matching guarantee, then a search consumer will buy from it because the consumer knows that in the event that there is a lower price offered in the market the consumer is insured that it will match that price.

Since price matching takes away the gain from price cutting, no firm cuts price and price competition is reduced.


  • Two firms: Firm 1 and Firm 2

  • Two prices: low ($4) or high ($5 )

  • 3000 captive consumers per firm

  • 4000 floating go to firm with lowest price


  • Two firms: Firm 1 and Firm 2

  • Two prices: low ($4) or high ($5 )

  • 3000 captive consumers per firm

  • 4000 floating go to firm with lowest price

Contracting with customers
Contracting with Customers

  • The game is a prisoner’s dilemma

    • Both firms prefer: {High, High}

    • Only equilibrium: {Low , Low}

    • Cannot credibly promise to play High

    • Even if committed to High, other firm would still respond with Low

  • How to resolve this?

    • Third party contracts with customers

Price matching
Price Matching

  • If one firm charges low, it does not gain any additional customers, since the competitor “automatically” matches it.

  • What is the effect on the game?

Price matching1
Price Matching

Advanced booking and yield management preconditions
Advanced Booking and Yield Management Preconditions

  • Most effective if:

    • the product is perishable and can be sold in advance

    • the capacity is limited and can’t be increased easily

    • the market/customers can be segmented

    • the variable costs are low

    • the demand varies and is unknown at time of decisions

    • the products and prices can be adjusted to the market

Some u s airline industry observations
Some U.S. airline industry observations

  • From 95-99 (the industry’s best 5 years ever) airlines earned 3.5 cents on each dollar of sales:

    • The US average for all industries is around 6 cents.

    • From 90-99 the industry earned 1 cent per $ of sales.

  • Carriers typically

    fill 72.4% of seats while the

    break-even load is 70.4%.


American: DFW-LAX All Tickets Sold in 2004Q4

Advanced selling
Advanced Selling

Requires an inverse relationship between consumer price sensitivity and customer arrival time.

Less price sensitive customers are unwilling to purchase in the advance period so that advance purchases are made to only low-valuation customers

Similar to traditional models of second-degree price discrimination.

Advanced booking
Advanced Booking

  • Consumers making reservations differ in their probability of showing up to collect the good or the service at the pre-agreed time of delivery.

  • Firms can save on unused capacity costs, generated by consumers’ cancellations and no-shows, by varying the degree of partial refunds

  • Airline companies in selling discounted tickets where cheaper tickets allow for a very small refund (if any) on cancellations,

    • Whereas full-fare tickets are either fully-refundable or subject to low penalty rates.

Advanced booking and partial refunds
Advanced Booking and Partial Refunds

Partial refunds are used to control for the selection of potential customers who make reservations but differ with respect to their cancellation probabilities.

Capacity constraints
Capacity Constraints

  • Examples of fixed supply – capacity constraints:

    • Travel industries (fixed number of seats, rooms, cars, etc).

    • Advertising time (limited number of time slots).

    • Telecommunications bandwidth.

    • Size of the AEM business program.

    • Doctor’s availability for appointments.

The park hyatt philadelphia
The Park Hyatt Philadelphia

  • 118 King/Queen rooms.

  • Hyatt offers a rL= $159 (low fare) discount fare targeting leisure travelers.

  • Regular fare is rH= $225 (high fare) targeting business travelers.

  • Demand for low fare rooms is abundant.

  • Let D be uncertain demand for high fare rooms.

  • Assume most of the high fare (business) demand occurs only within a few days of the actual stay.

  • Objective: Maximize expected revenues by controlling the number of low fare rooms sold.

Yield management decisions
Yield management decisions

  • The booking limit is the number of rooms to sell in a fare class or lower.

  • The protection level is the number of rooms you reserve for a fare class or higher.

  • Let Q be the protection level for the high fare class. Q is in effect while selling low fare tickets.

  • Since there are only two fare classes, the booking limit on the low fare class is 118 – Q:

    • You will sell no more than 118-Q low fare tickets because you are protecting (or reserving) Q seats for high fare passengers.



Q seats protected for

high fare passengers

Sell no more than the low

fare booking limit, 118 - Q

The connection to the newsvendor
The connection to the newsvendor

  • A single decision is made before uncertain demand is realized.

  • There is an overage cost:

    • D: Demand for high fare class; Q: Protection level for high fare class

    • If D < Q then you protected too many rooms (you over protected) ...

    • … so some rooms are empty which could have been sold to a low fare traveler.

  • There is an underage cost:

    • If D > Q then you protected too few rooms (you under protected) …

    • … so some rooms could have been sold at the high fare instead of the low fare.

  • Choose Q to balance the overage and underage costs.

Too much and too little costs much” and “too little” costs

  • Overage cost:

    • If D < Q we protected too many rooms and earn nothing on Q - D rooms.

    • We could have sold those empty rooms at the low fare, so Co = rL.

  • Underage cost:

    • If D > Q we protected too few rooms.

    • D – Q rooms could have been sold at the high fare but were sold instead at the low fare, so Cu = rH – rL

Balancing the risk and benefit of ordering a unit
Balancing the risk and benefit of ordering a unit

  • Ordering one more unit increases the chance of overage

    • Expected loss on the Qth unit = Co x F(Q), where F(Q) = Prob{Demand <= Q)

  • The benefit of ordering one more unit is the reduction in the chance of underage:

    • Expected benefit on the Qth unit = Cu x (1-F(Q))

As more units are ordered,

  • the expected benefit from ordering one unit decreases

  • while the expected loss of ordering one more unit increases.

Graphical analysis


Expected marginal benefit

of understocking

Expected gain or loss .

Expected marginal loss

of overstocking

Graphical Analysis

Expected profit maximizing order quantity
Expected profit maximizing order quantity

  • To minimize the expected total cost of underage and overage, order Q units so that the expected marginal cost with the Qth unit equals the expected marginal benefit with the Qth unit:

  • Rearrange terms in the above equation ->

  • The ratio Cu / (Co + Cu) is called the critical ratio.

  • Hence, to minimize the expected total cost of underage and overage, choose Q such that we don’t have lost sales (i.e., demand is Q or lower) with a probability that equals the critical ratio

Optimal protection level
Optimal protection level

  • Optimal high fare protection level:

    • Optimal low fare booking limit = 118 – Q*

  • Choosing the optimal high fare protection level is a Newsvendor problem with properly chosen underage and overage costs.

    • Recall: Co = rL; Cu = rH – rL

Hyatt example
Hyatt example

  • Critical ratio:

    • Demand for high fare is uncertain, but has a normal distribution with a mean of 30 and Standard deviation of 10.

    • See the Excel File Posted on the course website for calculations.

    • You can use normdist(Q,mean,, 1)=0.29 Excel function to solve for Q (see column E).

  • Answer: 25 rooms should be protected for high fare travelers. Similarly, a booking limit of 118-25 = 93 rooms should be applied to low fare reservations.

Revenue management overbooking

Revenue Management:

Hold the reservation
Hold the reservation!

Ugly reality cancellations and noshows
Ugly reality: cancellations and noshows

  • Approximately 50% of reservations get cancelled at some point in time.

  • In many cases (car rentals, hotels, full fare airline passengers) there is no penalty for cancellations.

  • Problem:

    • the company may fail to fill the seat (room, car) if the passenger cancels at the very last minute or does not show up.

  • Solution:

    • sell more seats (rooms, cars) than capacity.

  • Danger:

    • some customers may have to be denied a seat even though they have a confirmed reservation.

    • Passengers who get bumped off overbooked domestic flights to receive

      • Up-to $400 if arrive <= 2 hours after their original arrival time

      • Up-to $800 if arrive >= 2 hours after their original arrival time

        • According to April 16, 2008 decision of the Transportation Department

Hyatt s problem
Hyatt’s Problem

  • The forecast for the number of customers that do not show up

    ( X ) is Normal distribution with mean 9 and Standard Deviation 3.

  • The cost of denying a room to the customer with a confirmed reservation is $350 in ill-will (loss of goodwill) and penalties.

  • How many rooms (y) should be overbooked (sold in excess of capacity)?

  • setup:

    • Single decision when the number of no-shows in uncertain.

    • Insufficient overbooking:

    • Overbooking demand=X>y=Overbooked capacity.

    • Excessive overbooking: Overbooking demand=X <y=Overbooked capacity.

Overbooking solution
Overbooking solution

  • Underage cost when insufficient overbooking

    • if X >y then we could have sold X-y more rooms…

    • … to be conservative, we could have sold those rooms at the low fare, Cu = rL.

  • Overage cost when excessive overbooking

    • if X <y then we bumped y-X customers …

    • … and incur an overage cost Co = $350 on each bumped customer.

  • Optimal overbooking level:

  • Critical ratio:

Optimal overbooking level
Optimal overbooking level

  • Normal Distribution

    • Mean=9

    • Standard Dev. 3

  • Optimal number of overbooked rooms is y=7.

  • Hyatt should allow up to 118+7 reservations.

  • There is about F(7)=25.24% chance that Hyatt will find itself turning down travelers with reservations.

Advance selling
Advance Selling

  • Buyers make purchase commitments before the tie of service delivery.

  • Most common benefit:

    • Price discount and guarantee of future capacity

    • Recent development in technology make it appropriate for nearly al services

    • Electronic tickets

    • Smart cards

    • Biometrics

Technology and advanced sales
Technology and Advanced Sales

  • A service provider can improve profits by selling the service in advance when the customer has uncertainty.

    • prevent the resale of advance tickets (arbitrage).

    • lower the actual transaction costs associated with advance sales for both service providers and buyers.

    • allow far more complex price schedules involving either bundles of services or purchases with complex restrictions on customer usage.

    • provide more information about buyers and demand over time.

Arbitrage old problem
Arbitrage: old problem

  • less profitable or perhaps makes it completely unprofitable.

    • very profitable buyers, who would have been willing to pay a high spot price, now purchase from the arbitrageur at a lower price. Profits go to the arbitrageur of the ticket rather than the service provider.

Advanced selling and the new technology
Advanced Selling and The New Technology

  • There are two ways that new technology (such as electronic tickets) benefits advance selling by discouraging or preventing the resale of

    • To hide the true value of a ticket.

    • by recording buyer identities on the tickets.

New technology
New Technology

  • New technologies allow far more complex transactions.

  • These transactions can involve service packages with non-linear pricing, bundling, and variable consumption periods.

  • For example, a hotel package can sell:

    • A three-night stay at a lower price than a two-night stay,

    • or it can bundle a 3-night stay with a dinner, a breakfast, and, perhaps, tickets to local events.

    • Highly complex packages are possible for many services from car washes to landscaping services.

Demand learning
Demand Learning

Moreover, prices as well as all package components can continuously change over time as the service provider learns demand and available capacity changes (e.g., due to cancellations).

The service provider can now instantaneously adjust to changing conditions.

Overbooking becomes more calculated and more common

Estimate your demand
Estimate your demand

With these new technologies, sellers can run advance-selling experiments

By limiting quantities sold, learn more about buyer reactions and current demand conditions.