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Contingent Pricing to Reduce Price Risks

Author(s): Eyal Biyalogorsky and Eitan GerstnerSource: Marketing Science, Vol. 23, No. 1 (Winter, 2004), pp. 146-155Published by: INFORMSStable URL: http://www.jstor.org/stable/30036663

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MARKETING SCIENCE iNVol.23, No. 1, Winter2004, pp. 146-155IssN0732-2399 EISSN526-548X 04 2301 0146 DOI 0.1287/mksc.1030.0030c 2004 INFORMSResearch Note

Contingent P r i c i n g to R e d u c e P r i c e R i s k sEyal Biyalogorsky, Eitan GerstnerUniversity of California,Davis, GraduateSchool of Management,Davis, California95616{[email protected],[email protected]}

the price for a product may be set too low, causing the seller to leave money on the table, or too high,driving away potential buyers. Contingent pricing can be useful in mitigatingthese problems. In contingentpricing arrangements,price is contingent on whether the seller succeeds in obtaining a higher price withina specified period. We show that if the probability of obtaining the high price is not too high, sellers profitfrom using contingent pricing while economic efficiency increases. The optimal contingent pricing structuredepends on the buyer's risk attitude-a deep discount is most profitable f buyers are risk prone. A consolationreward is most profitable if buyers are risk averse. To motivate buyers to participate in a contingent pricingarrangement,the seller must provide sufficient incentives. Consequently,buyers also benefit from contingentpricing. In addition, because the buyers with the highest willingness-to-pay get the product, contingent pricingincreasesthe efficiency of resourceallocation.Keywords:pricing; price risks;contingent selling formats;standbys; price discrimination;pricing underuncertaintyHistory: This paper was received March11, 2002, and was with the authors 2 months for 3 revisions;processed by Vithala Rao.

Introduction* Owners who put their house on the marketdeclined an immediate offer that was $10,000 belowthe asking price. The house remained on the marketfor another year before finally being sold for $15,000less than the original offer.* Participants in a conference offered to pay topdollar for additional meeting rooms at a hotel. Thehotel manager offered compensation to other cus-tomers if they would agree to stay at a nearby hotel,but many declined the offer.* Three weeks prior to the date of a booked wed-ding, another party insisted on booking the same dateand was willing to pay $15,000 more. The owneroffered the first party $10,000 to reschedule, but theydeclined.The above anecdotes (all from the authors' per-sonal experiences) illustrate the risks that sellers facein setting prices: (1) losing the opportunity to sell ata low price when they wait for a high-price customerwho does not arrive and ultimately having to salvagethe product at an even lower price (as illustrated inthe first anecdote); (2) rejecting a high-price buyerbecause a low-price offer has already been accepted(as illustrated in the last two anecdotes). The poten-tial losses from such risks can be large, especially forproducts that must be sold within a specified time

(for example, services such as airline flights, vaca-tion packages, advertising, and transportation). In theabove anecdotes the sellers could have improved theirprofits using contingent pricing.It is no surprise that contingent pricing was notused in those cases. There are only a few examplesof the use of contingent pricing methods in indus-try, and those examples resulted from trial and errorrather than the application of a coherent body ofknowledge. One of the goals of theory models inmarketing is to go beyond and challenge commonmanagerial practices (Shugan 2002). In this paperwe continue this tradition, attempting to rectifythe dearth of understanding of contingent pricing,demonstrate its benefits, and describe the conditionsunder which it should be used.To illustrate, suppose that the home owners fromthe first anecdote had offered the first potential buyer$2,000 in exchange for 30 days to consider the offer.At the end of that period, the sellers, having receivedno better offer, could have accepted the original one,gaining an additional $13,000 in profit from the sale.By paying the $2,000, the sellers could have locked inthe original offer and still looked for a higher price.Although there is a cost for the sellers to lock in thelow-price offer, the expected gain from the increasedflexibility could exceed this cost, thus making thearrangement attractive.146


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Biyalogorsky and Gerstner: Contingent Pricing to ReducePrice RisksMarketingScience23(1),pp. 146-155, c2004 INFORMS 147This hypothetical alternative is an example of con-tingent pricing. We define contingent pricing as anarrangement to sell a product at a low price if theseller does not succeed in obtaining a higher priceduring a specified period. If a higher price is obtainedduring the arranged time period, the original sale

does not take place, and the first potential buyerreceives the agreed-upon compensation. Otherwise,the original buyer receives the product for the agreed-upon price.This research addresses the following questions:(1) When should a seller use contingent pricing?(2) How much can contingent pricing improveprofits? (3) What factors impact the profitability ofcontingent pricing and optimal contingent pricingarrangements? (4) How does a consumer's risk atti-tude affect the optimal contingent pricing arrange-ment? (5) Is contingent pricing economically efficient?We first describe the literature related to contingentpricing and then present a simple theoretical modelfor recommending when and how to use contingentpricing arrangements. We will demonstrate that con-tingent pricing can improve profits substantially andis economically efficient. We conclude by discussingthe results and their implications.Literature ReviewThis paper is related to several research streams. First,there is a tradition in marketing of looking at con-tingent arrangements to reduce a buyer's risks in atransaction. Such arrangements include satisfactionguarantees-arrangements under which buyers canreturn unsatisfactory products and receive refunds(Davis et al. 1995, Moorthy and Srinivasan 1995,Fruchter and Gerstner 1999). Such an arrangementreduces the buyer's risk of purchasing a poor product.Similarly, price guarantees are designed to reduce thebuyer's risk of paying too much. The buyer receivesa refund from the seller if she finds an advertisedlower price by another seller (Salop 1986, Belton 1987,Zhang 1995, Jain and Srivastava 2000), making theprice contingent on whether the customer finds alower price. The research on satisfaction and priceguarantees concentrates on mechanisms that reducethe risks customers face when purchasing products.However, sellers also face risks in these transactions.This study thus looks at the problem of reducingsellers' price risks and focuses on contingent pricingas a way to do that.One stream of research that considers sellers' risksis literature on overbooking (Desiraju and Shugan1999). Airlines overbook flights to mitigate the riskposed by passengers who have reservations but donot show up. Biyalogorsky et al. (1999) showed thatsuch overbooking can be profitable even if all the pas-sengers show up, as long as there are large differences

in passengers' valuation. Deliberate overselling com-bined with consolation rewards is example of contin-gent pricing in the airline industry.By contrast, this paper considers all possible typesof contingent pricing in a general setting, thus pro-viding a more complete characterization of the condi-tions under which contingent pricing is profitable. Inaddition, we derive the optimal structure of contin-gent pricing arrangements and consider the impact ofbuyers' risk attitudes.Literature on contingent contracts is also related.Parties can fail to trade because of disagreementsabout the likelihood of future events (Bazerman andGillespie 1999). Contracts that specify outcomes con-tingent on a realized future state can help solve thisproblem. In this paper, we examine situations where abuyer and seller have the same information about theseller's likelihood of obtaining a high price. Therefore,the benefits of contingent pricing lie not in align-ing the beliefs of the parties but in the flexibility thecontract offers to the seller in responding to futuredemand.This study is also related to research on price dis-counting and clearance sales (Conlisk et al. 1984,Stockey 1981, Lazear 1986, Pashigian 1988, Pashigianand Bowen 1991, Smith and Achabal 1998, Sallstrom2001). The purpose of such discounts is either toprice-discriminate between consumers with differentwillingness-to-pay (WTP) or to reduce inventory risk.We show that there are times when contingent pric-ing relies on a similar form of discounts. However,depending on the conditions, contingent pricing maytake different forms that do not involve price dis-counts.

Contingent pricing contracts rely on the fact thatbuyers often purchase products or services wellbefore anticipated consumption. Shugan and Xie(2000) showed that one implication of the separa-tion of purchase and consumption is the usefulnessof advance selling. In their model, buyers are uncer-tain about their valuations in the consumption period.Sellers cannot price-discriminate because willingness-to-pay is private information. Xie and Shugan (2001)showed that advance selling can help a monopolyexploit buyers' uncertainty about future valuationsand extract more surplus than through spot-selling,which takes place only in the consumption period.Png (1989) showed that reservations are the best pric-ing strategy when risk-averse customers are uncertainabout their valuations.

Both advance selling and reservation methods focuson the effects of buyers' uncertainty about valuations.Our work instead focuses on the implications of sepa-ration of purchase and consumption when the buyersare certain about their valuations but the seller is not


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Biyalogorsky and Gerstner: Contingent Pricing to ReducePrice Risks148 MarketingScience23(1),pp. 146-155,@2004 INFORMScertain about future demand. This provides opportu-nity to use contingent pricing in which the seller waitsuntil the uncertainty is resolved. In advance selling,the seller prefers to complete the transaction beforethe uncertainty is resolved.Harris and Raviv (1981) showed that, when poten-tial demand exceeds capacity, some type of prioritiz-ing whereby customers with higher valuations havethe first opportunity to obtain the product is optimal.In a model geared toward utility services, Harris andRaviv (1981) and Wilson (1989) suggested accomplish-ing this by using a nonlinear priority pricing menuwhere customers wishing to have higher service pri-ority pay a higher price. Revenue/yield managementapproaches prioritize over a fixed capacity by allo-cating it into predefined classes that are opened andclosed dynamically, depending on demand conditions(Weatherford and Bodily 1992, Desiraju and Shugan1999, McGill and Van Ryzin 1999). Our paper adds tothis literature by showing that one can use contingentpricing to implement such prioritizing. Contingentpricing can be used when other methods do not applyor to complement methods like revenue management.

The ModelOur model captures several crucial elements that leadto the consideration of contingent pricing.(1) Demand Is Spread Over TimeDemand is spread over time, i.e., consumers do notshow up at the same time. As a result, the sellerfaces a risk in waiting for a high-price consumer,because the opportunity to sell at the lower pricemay not be available later. To capture this in asimple way, consider a seller offering a unique prod-uct. Demand is spread over two periods, with differ-ent consumers appearing during each period. Suchspreading of demand over time is nearly universal.For example, some consumers reserve movie ticketsdays in advance, while others show up at the boxoffice minutes before the movie starts.(2) Purchase and Consumption Can Occur atDifferent Times (Shugan and Xie 2000, Xie andShugan 2001)Thus, we assume that consumption only takes placeat the end of Period 2. This corresponds to situationsinvolving time-sensitive categories such as flights,sporting events, and restaurant meals. Moreover, itdescribes situations where consumers are willing todefer consumption or purchases for various reasons.For example, many consumers will wait for salesbefore buying durable products.

(3) Demand for the Product Can ExceedIts AvailabilitySuch short-term imbalances are common in made-to-stock systems. We model this by assuming thatthe seller has a single unit for sale and that thesize of potential demand in each period is for oneunit. Therefore, the seller faces demand for two units,which raises the issues of how and to whom to sell thesingle available unit. Formally, we make the followingassumptions.

ASSUMPTION 1 (PERIOD 1 DEMAND). With probabil-ity 1,a consumer ppearsn Period1. Theconsumer aluestheproduct t VL ndhas a utility unctionover ncomeUL.Theminimum cceptable tilityfroma transactions U,.ASSUMPTION 2 (PERIOD 2 DEMAND). With probabil-ity q,a consumer ppearsn Period2. Theconsumer aluesthe product at vH (vH > vL) and has a utility function

over incomeUH.The minimumacceptable tility from atransaction is UH.The consumer's utility from buying the product ata price p is UL,HvL, H- p). Let

pL{IP IUL(VL p) - ULI (1)andPH=tP IUH(VH p) = UH}. (2)

Equations (1) and (2) define the willingness-to-pay ofPeriod 1 and Period 2 consumers.ASSUMPTION 3 (WILLINGNESS-TO-PAY). Period con-sumers exhibithigher willingness-to-pay han Period 1consumers (i.e., PH> PL).ASSUMPTION 4 (SEPARATION OF PERIODS). (a) Con-sumers eavethemarket t the endof eachperiod.(b) The imingofconsumer ppearances exogenous ndconsumers annotchangetheperiod n whichtheyappearin responseo sellerprices.The second-period consumer is willing to pay morefor the product. The seller, however, is uncertainif a consumer will show up in the second period.Moreover, the first-period consumer leaves the mar-

ket before this uncertainty is resolved (see Assump-tion 4a). Therefore, waiting for a high-valuationconsumer is risky.The assumption that second-period consumersexhibit higher willingness-to-pay reflects behavior inindustries like travel. Assuming a strict sequence ofarrivals, however, is not necessary. As long as theprobability that a consumer willing to pay a higherprice will follow a consumer with low willingness-to-pay is high enough, the results hold.Assumption 4a states that consumers who, forwhatever reason, are not able to buy the product leavethe market. This can occur, for example, if consumers


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Biyalogorsky and Gerstner: Contingent Pricing to ReducePriceRisksMarketingScience23(1),pp. 146-155,@2004INFORMS 149continue to search until they find the product else-where. Such behavior leads to some probability thatthe seller will lose a potential customer if the pricequoted is too high. In Assumption 4, we assume thatthis probability is one.

AsSUMPTION 5 (SUPPLY). The seller has one unit tosell.Production akesplacebeforehebeginning fPeriod1at a cost c. No sellingor transaction ostsare incurred.The fact that no selling costs are incurred meansthat dealing with more consumers or engaging ina more complex contract such as contingent pricingis not more expensive than a fixed price strategy.Furthermore, because production takes place beforePeriod 1, the production cost is sunk and there are norelevant costs that impact the pricing decision.In many markets, sellers have access to secondarychannels that enable them to dispose of unsold

merchandise. For example, unsold goods can beshipped to overseas markets. In our model, theseller may still have an unsold unit at the end ofPeriod 2. Access to salvage markets may impact pric-ing decisions. We model this access as follows:ASSUMPTION (SALVAGE). The sellercan sell the unitfor salvageat a prices (s < PL).Consumers o not haveaccessto thesalvagemarket.The condition that s < PL guarantees that the sellerprefers to sell to the low willingness-to-pay consumerover salvaging the unit.We now consider which pricing strategy the sellershould pursue and under what conditions. Weassume that there is full information in the market.The only uncertainty is whether a high WTP con-sumer will appear in the second period, with theprobability of this event known. Further, we assumethat the time frame covered by the model is suffi-ciently short so that the effect of the discount rate canbe ignored.

Low-Price StrategyUnder the low-price strategy, the seller targets lowWTP consumers and forgoes the opportunity to sellto high WTP consumers. The reservation price of thelow WTP consumer is PL (Equation (1)); therefore, theprofit-maximizing price is pL.The seller is guaranteeda sale at this price, and the expected profit is

L=PL. (3)High-Price StrategyUnder the high-price strategy, the seller targets highWTP consumers and forgoes the opportunity to sellto low WTP consumers. The reservation price of thehigh WTP consuemr is PH (Equation (2)); therefore,the profit-maximizing price is PH. The seller will sell

with probability q and will otherwise salvage the unitfor s, leading to an expected profit ofH = qPH (1 - q)s. (4)

Comparing the expected profit from high- and low-price strategies (Equations (3) and (4)), we find that ahigh-price strategy is preferred if

PL SqH> (5)PH - SContingent Pricing StrategyThe seller offers the first-period consumer the oppor-tunity to participate in a contingent pricing contract.This contract gives the seller the right to sell the unitto the first-period consumer at the end of the secondperiod for an agreed-upon price of PL- T1, with T,being a discount off the consumer's WTP. The con-tract specifies a payment (a consolation reward), T2,to the consumer if the consumer does not get theproduct.From the consumer's perspective, the contingentprice contract is a gamble with the probability 1 - qthat she will receive the product at a price of PL- T,and with the probability q that she will get a paymentof T2.The consumer will agree to the contract only ifthe compound utility of this gamble is at least as highas her reservation utility UL.A contingent contract effectively keeps the first-period consumer in the market until the end of thesecond period, enabling the seller to follow a high-price strategy of setting the price at PH in the secondperiod. If a high WTP consumer appears, the sellersells that consumer the product and gives the first-period consumer the agreed payment of T2.The Optimal Contingent Pricing ContractThe optimal contingent pricing contract maximizesthe seller's expected profit subject to the first-periodconsumer receiving his reservation utility. The seller'sexpected profit is

c = (P - T2)+(1 - q)(PL T), (6)where the first term is the difference between thesecond-period price and the payment given to thefirst-period consumer if a high WTP consumerappears, and the second term is the price agreed uponwith the first-period consumer. Equation (6) can berewritten as

cp(T1,T2)= qPH (1- q)pL [qT2 (1 - q)T1], (7)where the first two terms are the expected revenuefrom a contingent contract and the last term is theexpected cost of the contract. Because the expectedrevenue does not depend on the structure of the


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Biyalogorsky and Gerstner: Contingent Pricing to Reduce Price Risks150 MarketingScience23(1),pp. 146-155,@2004INFORMS

contract, the seller's problem is to minimize theexpected cost, subject to satisfying the participationconstraint of the first-period consumer. Clearly, theseller will choose contract terms such that the partic-ipation constraint will be binding while minimizingthe expected cost.Consider the case where the first-period consumeris risk neutral. The consumer's expected utility fromthe contract is qT2+ (1 - q)(vL - PL+ T1) and the par-ticipation constraint is

qT2+ (1 - q)(VL PL+ T1)= UL. (8)Rearranging terms, we can rewrite Equation (8) as

qT2+ (1 - q)Tl = UL - (1 - q)(vL- PL). (9)The left-hand side of Equation (9) is the expected costof the contract for the seller. If the consumer is riskneutral, the expected cost is a constant and is givenby the right-hand side of Equation (9), which is inde-pendent of the contract structure. Thus, an infiniteset of possible contracts will satisfy the participationconstraint at a minimum cost for the seller.To satisfy the participation constraint of a consumerwho is not risk neutral, the seller has to pay a riskpremium in addition to the compensation required bya risk-neutral consumer. The risk premium is approxi-mately -(U"/U')(0a2/2) (see Pratt 1964), with 0-2 beingthe variance of the risky prospect {vL PL+ T1 withprobability 1 - q; T2with probabilityq}.

2 = q(1 - q)2[(T2 - T1) (vL - PL)]2+ (1 - q)q2[(vL - PL) - (T2 - T1)]2. (10)

Let (VL - p - Tir, T2r) be a contract that satisfies aparticularconsumer. We can write that asU" 0-2-2

Zr=ZIn U' 2 'U" 0.2 (11)T2r T2n U' 22nlj 2

By construction, (T1n,T2,,)satisfy the participationconstraint of a risk-neutral consumer with the samereservation utility. The expected cost of the contractfor the seller isU" o-2qT2r (1- q)Tr = qT2n (1 - q)T1n U

U' 2UL-1-q)vL-p) U'2 '(12)where the last equality in Equation (12) is obtained bysubstituting the equality from Equation (9). The onlyterm that depends on the choice of contracts is thevariance term.

The seller wants to minimize the expected costof the contract. For a risk-averse consumer, the lastterm in Equation (12) is positive because U"/U' isnegative. The expected cost is minimized in this caseif 0-2 is zero. From Equation (10) we see that setting(Tl = 0, T2 = vL - PL) minimizes o-2 (U2 = 0). Further,any other contract that minimizes 0-2 must have bothT1,T2strictly greater than the corresponding optimalvalues for this contract. Therefore, none of the otherpossible contracts satisfy the participation constraintwith equality (i.e., they are not profit maximizing). If aconsumer is risk averse, the best contract is offeringno discount on the price if the first-period consumerreceives the unit and a consolation payment of vL PLif he does not receive the unit.For a risk-prone consumer, the last term in Equa-tion (12) is negative because U"/U' is positive. Theexpected cost is minimized in this case if -2 ismaximized. From Equation (10) we see that settingT2*o zero maximizes U2. Thus, if a consumer is riskprone, the best contract is offering a deep discounton the price if the first-period consumer receives theunit and nothing otherwise. We can summarize thesefindings in the following result.RESULT 1. The optimal contingent pricing contractstructures are:

(a) When consumers are risk averse: A price PLif the consumer receives the product and a consola-tion reward of T2* VL PLif the consumer does notreceive the product.(b) When consumers are risk prone: A special dis-count of T1* ff the price PLif the consumer receivesthe product and nothing otherwise.(c) When consumers are risk neutral: All contractstructures that satisfy the participation constraint withequality are optimal.Result 1 states that the seller should match the con-tract structure to the risk attitude of the consumer:Risk-averse consumers are given a consolation reward(the least risky); risk-prone consumers are given adeep discount (the most risky). Intuitively, this isbecause all contingent pricing contracts that satisfythe consumer's participation constraint produce thesame revenue; therefore, the seller's objective is reallyto minimize the expected cost of the contract. Thisis achieved when the contract is tailored to the con-sumer's risk attitude.Comparing Contingent Pricing to the Low- andHigh-Price StrategiesWe now determine when contingent pricing is pre-ferred over low- and high-price strategies.To facilitate this, we first show that the expectedcost of a contingent pricing contract for the seller isequal to or less than q(vL-PL). Specifically, it is equalto this amount if the first-period consumer is risk


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Biyalogorsky and Gerstner: Contingent Pricing to Reduce Price RisksMarketingScience23(1),pp. 146-155,c 2004 INFORMS 151averse or risk neutral and lower if the first-periodconsumer is risk prone.The expected cost of a contingent pricing con-tract is given in Equation (12). For a risk-averseconsumer, o-2 = 0, and for a risk-neutral consumer,U"/U'= O. Further, from the definition of p, we seethat UL= VLPL. Thus, for a risk-averse or risk-neutral consumer, the expected cost equals q(vL- PL).For a risk-prone consumer, the last term in Equa-tion (12) is negative; therefore, the expected cost islower than it is for a risk-averse consumer.

Substituting this maximum possible expected costinto the profit function (7), we find that the minimumpossible expected profit under an optimal contingent-pricing contract isICP (T1, T2)= PL+ q(PH VL). (13)

Comparing this expected profit to the expectedprofit from a low-price strategy, which is p (see Equa-tion (3)), we find Result 2.RESULT 2. Contingent pricing is more profitablethan a low-price strategy if the second-period con-sumer's willingness-to-pay is greater than the valua-tion of the first-period consumer (i.e., if PH> VL).Because a low-price strategy is more profitable thana high-price strategy for low q (see Equation (5)), itfollows that contingent pricing is the most profitablestrategy for low q if PH> VL.Moreover, if the first-period consumer is risk prone, contingent pricing ismost profitable, even for some limited range wherePHis not greater than vL.Comparing Icp to HH leads to the following condi-tion for contingent pricing being more profitable thana high-price strategy:

PL S ,q qA (14)VL - SThus, contingent pricing is preferred to a high-pricestrategy if the probability that a high WTP consumerwill appear is sufficiently low. Recall that the expectedcost when consumers are risk prone is lower, andtherefore the expected profit from contingent pricingin this case is higher than HIcp. f qs is the probability

for which the expected profit from contingent pricingis equal to the expected profit from a high-price strat-egy when consumers are risk prone, it follows thatqs > qA"RESULT 3. Contingent pricing is more profitablethan a high-price strategy when the probability of ahigh WTP consumer appearing is less than qAif con-sumers are risk averse or risk neutral and less than qs(qs > qA) if consumers are risk prone.Combining Results 2 and 3, we can state Result 4.RESULT 4. Contingent pricing is the most profitablestrategy if the second-period consumer's willingness-to-pay is greater than the valuation of the first-period

consumer (PH> VL) and the probability that a con-sumer will appear in the second period is low (q


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Biyalogorsky and Gerstner: Contingent Pricing to Reduce Price Risks152 MarketingScience23(1),pp. 146-155,@2004INFORMSat a higher value of q if consumers are risk pronebecause it is easier to convince risk-prone consumersto participate in contingent contracts, and thereforethe cost curve for risk-prone consumers lies below theone for risk-averse and risk-neutral consumers.The threshold at which contingent pricing is nolonger better than a high-price strategy is determinedby the interplay of the opportunity loss and theexpected cost of the contract. The opportunity lossdepends on the difference between the low-valuationconsumer's WTP and the salvage value, PL S. Thecost of the contract depends on the consumer's mini-mum required utility UL = U(vL - PL).Therefore, thethreshold will be higher if (a) the WTP PLis higher(because the opportunity loss is larger), (b) the sal-vage value is lower (the opportunity loss is larger), or(c) the consumer's valuation of the product is lower(because the cost of the contingent contract is smaller).An Illustrative ExampleThe profit improvement from the use of contingentpricing can be substantial as we demonstrate usingthe following example. Assume that low WTP is $200,high WTP $800, and VL$350, with the probabilityof a high WTP consumer being 0.25 and the salvagevalue being 0. These values are chosen to resemblea reasonable situation for a coach seat on a domesticU.S. flight as of the time of writing.For this example, the expected profit of a low pricestrategy is $200, and the expected profit of a high-pricestrategy is $200 as well (0.25 * 800 + [1 - 0.25] * 0 =200). The results outlined in this paper can be used todetermine the profit improvement from using contin-gent pricing, and the optimal contract to offer.

Risk-Averse Consumers. From Result 1 we knowthat the optimal contract for risk-averse consumersconsists of a consolation reward. In this case thereward amount is $150 (350 - 200 = 200). Therefore,the seller's expected profit (using Equation (6)) is$312.5 (0.25 * [800 - 150] + [1 - 0.25] * 200 = 312.5).This is a substantial $112.5 or about 56% improvementin the expected profit as a result of using contingentpricing. Further, as the minimum acceptable utilityof the consumer decreases the seller's expected profitincreases, and the profit improvement can be as highas 100%.Risk-Prone Consumers. In this case the results

depend on the specific characteristics of the utilityfunction. We will assume that the utility function isU(x) = x2/150, which gives UL = 150 (the same asthe value assumed for the risk-averse case above).The participation constraint requires that the expectedutility from the contingent contract is at least as highas her reservation utility, i.e., 0.25 * U(0) + [1 - 0.25] *U(350-200+ T1)= 150. Solving for the discount T1we

get T1= $23. This is a significantly lower figure thanthe $150 compensation required by the risk-averseconsumer. Indeed the seller's expected profit in thiscase is $332.75, which is higher than the expectedprofit of $312.5 in the risk-averse case, and of coursehigher than the expected profit of $200 of the high-and low-price strategies.It is also easily verified that given the optimal con-tingent pricing offers above, a risk-averse consumerprefers the consolation reward offer to the deep dis-count, and a risk-prone consumer (with the assumedutility function) prefers the deep discount offer tothe consolation reward. Thus, it is possible to offera menu consisting of these two offers, and allow theconsumers to self-select the offer of their choice.Economic EfficiencyBesides improving the expected profit of the seller,contingent pricing also improves efficiency comparedto low- and high-price strategies.First, although the seller's profit improves withcontingent pricing, no consumer is worse off. Thefirst-period consumer pays PL (or less in the case ofa deep discount contract) for the product, the sameamount as in a low-price strategy. Further, the com-pensation offered in the contingent contract satis-fies the participation constraint of the consumer, thusguaranteeing the same expected utility as in a low-price strategy. Similarly, the second-period consumergets the product for a price of PH, which is equalto that of a high-price strategy. Thus, the expectedconsumer surplus does not decrease, and the seller'sprofit increases.From an economic efficiency perspective, it is desir-able to allocate a unit to the highest valuationconsumer. Thus, the product should be sold to thesecond-period consumer if that consumer appears,and to the first-period consumer otherwise (insteadof salvage). The low- and high-price strategies donot allocate the product efficiently. Using a low-pricestrategy, the first-period consumer gets the producteven if a second-period consumer shows up. Usinga high-price strategy, the product must be salvagedif a second-period consumer does not show up eventhough a first-period consumer existed. Contingentpricing, on the other hand, leads to efficient allocation.A second-period consumer who appears gets the unit;if a second-period consumer does not appear, thefirst-period consumer gets the unit, and salvage is notneeded. Therefore, we have Result 5.

RESULT 5. Contingent pricing helps allocate prod-ucts efficiently.In conclusion, contingent pricing improves sellerprofit, overall consumer surplus, and allocative effi-ciency, thus creating a win-win-win outcome.


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Biyalogorsky and Gerstner: Contingent Pricing to ReducePrice RisksMarketingScience23(1),pp. 146-155,02004 INFORMS 153DiscussionThe opening anecdotes of the paper describe realevents, in which sellers facing price risks, could haveused contingent pricing to reduce those risks. In noneof these cases was contingent pricing actually used.An important message of this paper is that contingentpricing is a useful tool to reduce sellers' price risks,and that sellers in different industries can benefitfrom using it. We show that, compared to a constanthigh- or low-price strategy, contingent pricing (a) mit-igates the expected losses from price risks, (b) canbe profitable regardless of buyers' risk attitudes evenif buyers are more risk averse than sellers are, (c)benefits buyers as well as sellers, and (d) improveseconomic efficiency. We also show that the optimalcontingent pricing structure depends on buyers' riskattitudes (price discount is most profitable when cus-tomers are risk prone, and consolationrewards are mostprofitable otherwise).The results are particularly important for indus-tries in which unsold products are highly perish-able and when variation in willingness-to-pay ishigh. Examples of such industries include air-lines, travel, advertising, transportation, and factoryproduction. Contingent pricing can allow these sell-ers to seek high prices but keep back-up customersfor any excess capacity in case high prices cannotbe obtained. Contingent pricing is useful in mitigat-ing price risks resulting from imbalances betweeninventory/capacity and demand. Clearly, sellers fac-ing "hard" capacity constraints, such as airlines, canbenefit from contingent pricing. However, almost anyseller may face (at least in the short term) imbalancesbetween capacity and demand. If supply chains can-not address these imbalances quickly, contingent pric-ing may prove beneficial. Thus, a store that has towait six months for replenishment of trendy fashionitems and a car dealer that is running out of a favoredcolor of a popular model are both candidates for theapplication of contingent pricing.More generally, the opportunities to use contin-gent pricing will increase as it becomes easier andcheaper to implement sophisticated pricing mecha-nisms through the Internet. For example, Internetshopping agents could make fees contingent on thenumber of hits or the size of the audience (Iyer andPazgal 2003).The results are important to policy makers becausethey show that contingent pricing improves resourceallocation. Products end up with the customers whovalue them most, and the customers who do not getproducts receive adequate compensation. Therefore,everybody wins. Policy makers should be mindfulof the welfare benefits of contingent pricing in mak-ing decisions that impact the opportunity to use suchmethods.

The beneficial effects of contingent pricing arisebecause these methods offer incentives to low-priceconsumers to remain active in the market. They alsoallow sellers to continue looking for higher payingcustomers, thus providing added flexibility becausethere is no need to commit to a fixed price. Price canbe high if such a customer shows up, and low if high-price customers do not appear. In addition, the factthat low-price consumers remain active allows sell-ers to increase profits using price discrimination. Theseller price discriminates by offering a menu of prob-abilistic goods--one good is low priced but uncertain,while the other is high priced and certain. Thus, con-tingent pricing allows both added flexibility and theability to practice price discrimination.Implementation IssuesContingent pricing benefits consumers as well assellers. However, sellers have to recognize that con-sumers are not used to such programs and in somecases may perceive them as inequitable. To avoidconsumer backlash, firms that implement contin-gent pricing programs need to educate consumersabout them, and perhaps provide additional appeal-ing features. Consider a pay-for-play program, wherethe consumer receives an up-front payment regard-less of the outcome (i.e., a contingent contract withT, = T2= const). This contract is not optimal as weshow in Result 1, but may serve to alleviate consumerconcerns and encourage buy-in, and therefore mightbe used in some cases.An important issue for the seller is how to ensurethat the first-period consumer remains active in themarket and committed to the contingent pricingarrangement. In the formal model we assumed thatthe seller and consumer enter into an explicit con-tractual arrangement. This is a viable option in mar-kets where consumers and sellers already employdetailed contracts. This is true for many business-to-business markets. A good example are arrangementsin standby equity rights offers (see Bohern et al. 1997,Eckbo and Masulis 1992, Singh 1996). Housing, pro-vides a consumer market example of contracts thatalready include cancellation and other contingencyclauses, which could be easily modified to imple-ment contingent pricing. Indeed, the few anecdoteswe encountered suggest that it is not hard to convincehouse buyers to enter into contingent pricing arrange-ments, although the practice is not widespread.Some markets possess institutional characteristicsthat guarantee that a consumer, who made a com-mitment to pay for a service, will participate in con-tingent pricing arrangements even without explicitcontracts. For example, a guest must physically showup to claim a hotel room. Thus, the seller is assuredthat the buyer will show up and has the opportunityto implement contingent pricing.


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Biyalogorsky and Gerstner: Contingent Pricing to Reduce Price Risks154 MarketingScience23(1), pp. 146-155,@2004INFORMSIn other markets, however, the institutional charac-teristics are not as conducive and contracting is toocostly; an example is most fashion items. In such situ-ations our formal model is not directly applicable. It isimportant to understand, however, that the real issueis the ability of the seller to increase the probability

that the first-period consumer will remain active inthe market, contracting being one way to achieve thisbut not the only one. Consider an ad that promises areduced price at a certain time in the future. One pos-sible effect of such an ad is to increase the probabilitythat price-sensitive consumers will wait until the pricegoes down (instead of buying a lesser quality product,etc.). This example is consistent with a deep discountcontingent price, and is similar to some clearancesale practices such as the Filene's Basement Auto-matic Price Reduction plan. We conjecture that suchnoncontractually binding approaches can be used toimplement contingent pricing.Sellers need to figure out ways to tailor contingentpricing arrangements to customers who are heteroge-neous in their risk attitude and product valuations.There may be situations in which sellers cannot distin-guish between risk-averse and risk-prone buyers, oreven know their proportions in the population. Onepossible approach is to offer a menu of contingentpricing arrangements, allowing each customer to self-select the most appealing contract. At first cut, firmscan offer two types of arrangements: a consolationreward that will appeal to risk-averse customers, anda deep discount arrangement that will appeal to suf-ficiently risk-tolerant customers. A case in point is thelast minute e-mail notices used by the travel industryto notify potential customers of low price offers. Suchlast minute arrangements appeal to risk-tolerant cus-tomers but not to risk-averse ones, and can be usedas an effective way to implement deep discount con-tingent pricing. By adding another arrangement thatoffer consolation rewards firms can offer a menu ofcontingent pricing arrangements fairly easily.Sellers must also be aware that the timeframe setfor the contract is important. We assumed that con-sumers' minimum acceptable utility remains fixedover time. The longer the length of the contingentpricing contract, however, the less likely it is thatthis assumption holds, either because buyers' pref-erences are time dependent or because of externalshocks. In the housing market, for example, economicfactors that affect supply and demand may changewhat is acceptable to buyers. How to design effectivecontingent programs in such a case is an interestingquestion for future research.Future ResearchThe assumptions underlying our model include amonopoly setting with only a single unit available for

sale and strict separation between the periods. Oneavenue for future research is to consider the effects ofrelaxing the assumptions. The results hold up if theseparation-between-periods assumption is relaxed,and they should not change in a general N unit modeland in a competitive setting. An interesting ques-tion in a competitive setting is whether equilibriumis symmetric (i.e., whether all firms use contingentpricing or not, and if not, which ones do). Other inter-esting extensions to the model include the addition ofbuyer uncertainty and information asymmetry. Onepossibility under these conditions is to use advanceselling strategies (Xie and Shugan 2001) and to con-sider how they substitute/complement contingentpricing strategies.This paper presents a theory on how to design prof-itable contingent pricing arrangements. The resultsraise a number of issues that need to be empiricallyaddressed. Consumers' reaction to and acceptance ofcontingent pricing arrangements are important empir-ical issues that can be tested through, for exam-ple, laboratory experiments. Behavioral reactions maylead to implications that are different from the onesour normative economic model suggests. Anotherempirical issue is how to measure the profit impact ofcontingent pricing. Data from the few industries thatuse contingent pricing (such as airlines and financialservices) can be used to estimate the profit impact bycomparing actual results to the likely outcomes if con-tingent pricing had not been used. As contingent pric-ing methods become more common, it will becomepossible to compare realized average prices whencontingent pricing is and is not used. Our theory pre-dicts that sellers who use contingent pricing will real-ize higher prices compared to those who do not usethis pricing technique.AcknowledgmentsThis researchhas benefited from the excellent commentsofthe editor, the area editor, two anonymous reviewers, andthe participantsof the marketing seminars at the Univer-sity of CaliforniaGraduate School of Management,Davis;atBerkeley'sHaas School of Business; at INSEAD, France;atthe University of Florida Marketing ResearchRetreat2001;and, in particular, rom the help and comments of JinhongXie and Prasad Naik and the work of Michal Gerstnerinediting.ReferencesBazerman, Max H., James J. Gillespie. 1999. Betting on thefuture:The virtues of contingent contracts.HarvardBus. Rev.(September-October)-8.Belton,TerrenceM. 1987.A model of duopoly and meetingor beat-ing competition.Internat. . Indust.Organ.5(4)399-417.Biyalogorsky,Eyal, Ziv Carmon, Gila E. Fruchter,EitanGerstner.1999. Oversellingwith opportunistic cancellations.MarketingSci. 18(4)605-610.


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