Refunds and collusion in service industries

Journal of Economics and Business 60 (2008) 502–516

Refunds and collusion in service industries Staffan Ringbom a , Oz Shy b,∗ a

Department of Economics, Swedish School of Economics, P.O. Box 479, 00101 Helsinki, Finland b Department of Economics, University of Michigan, Ann Arbor, MI 48109-1220, USA

Received 28 February 2007; received in revised form 5 November 2007; accepted 6 November 2007

Abstract This paper investigates industry-wide agreements on joint refund policies, and how they influence price competition. We compute the profit of fully-colluding, competing, and semicolluding service providers who offer refunds to those consumers who do not show up at the time of service. Our main findings are that both a monopoly serving all consumer types, and semicollusive service providers offer full refunds. In contrast, competing service providers offer only partial refunds. Finally, refund policies are investigated under moral hazard behavior. © 2007 Elsevier Inc. All rights reserved. JEL Classification: D4; L1; L41; M2 Keywords: Refunds; Partial refunds; Collusion on refunds; Moral hazard

1. Introduction Semicollusion refers to the practice of explicit or implicit non-price agreements among brand producing firms, generally intended to weaken price competition. For example, for many years, researchers of Industrial Organizations have been debating whether research joint ventures (RJVs) should be allowed, and to what degree they generate price increases above the competitive levels. In this paper we examine the effects of colluding on refund levels. In principle, colluding on refunds should be more alarming than ordinary semicollusive practices because refunds can be viewed as a component of the price. The purpose of this paper is to explore precisely the issue

∗

Corresponding author. E-mail addresses: [email protected] (S. Ringbom), [email protected] (O. Shy).

0148-6195/$ – see front matter © 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.jeconbus.2007.11.002

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how collusion on refunds affects the intensity of price competition, profits, and consumer welfare, and to compare it to the fully collusive monopoly market structure. It is hard to come by examples in which service providers or producers explicitly coordinate and declare a joint industry-wide refund policy. Although very little is known about how refunds affect price competition, firms may avoid contracting on a joint industry refund policy fearing that some antitrust measures may be taken against their actions. However, from time to time we do see some indications that firms facilitate the enactment of industry-wide refund policies. For example, the International Air Transport Association (IATA) has been assisting in adopting the an accounting system in which one feature of this system includes a “refund application processing module” which would handle the entire refund process. Refunds are also practiced by merchants linked to the same payment system such as major credit/charge card organizations. These payment systems enable consumers to present a case to card issuers whenever a service is not delivered to their satisfaction and to request a “chargeback” on their cards. In the present paper, we formally introduce competition into service industries that utilize advance booking systems in which some consumers do not show up when the service is delivered. Our purpose is to investigate how industry-wide collusion on a joint refund policy affects price competition and therefore consumer welfare. Our analysis applies to industries providing services like travel arrangements (airline, train, bus, hotel, car rental), or repair, maintenance, education, and so on. These industries are characterized by services that are time dependent and non-storable. This means that both buyers and sellers must commit to a certain predetermined time at which the service is set to be delivered. Therefore, service providers tend to utilize advance reservation systems as part of their business and marketing strategies. We show that both a monopoly serving all consumer types and semicollusive service providers offer full refunds. In contrast, competing service providers offer only partial refunds. The main findings of the present research are as follows: (a) Competition in prices and refund levels generates lower refund levels compared with a cartel acting as a monopoly. This result implies that higher refunds can be used to extract more surplus from consumers because consumers view refunds as an insurance against their own no-shows. (b) Semicollusion, in which firms compete in prices but set a common industry-wide refund policy, results in having firms agreeing to provide full refunds. Thus, semicollusion may hurt consumers just as a fully colluding cartel does. This happens because committing on refunds serves as a commitment on higher expected costs, which are then rolled over onto consumers in the form of higher prices. Lastly, and less surprisingly, (c) moral hazard reduces firms’ incentives to provide refunds, where colluding on providing no refund may also be obtained as an equilibrium outcome. In the Economics literature there are a few papers analyzing the refundability option as a means for segmenting the market or the demand. Most studies have focused on a single seller. Contributions by Gale and Holmes (1992, 1993) compare a monopolist’s advance bookings with socially-optimal ones. Gale (1993) analyzes consumers who learn their preferences only after they are offered an advance purchase option. On this line, (Davis, Gerstner, & Hagerty, 1995), Miravete (1996), Che (1996), and Courty and Li (2000) further investigate how consumers, who learn their valuation over time, can be screened via the introduction of refunds. Dana (1998) also investigates market segmentation under advance booking made by price-taking firms. Macskasi (2003) analyzes a differentiated products duopoly in which each consumer receives an ex ante signal of his own preferred location and only then learns about the true location. Rochet and Stole (2003) survey the broad topic of multidimensional screening. From a methodological point of view, we follow one of Rochet and Stole’s (2003) suggestions which is to model competitive screening in an extended Hotelling framework. Ringbom and Shy (2004) analyze partial refunds set by price-taking firms.

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The present paper adds to the above literature by focusing on the incentive to semicollude on a joint industry-wide refund policy. Finally, on this line, Davis et al. (1995), Che (1996) and Matthews and Persico (2005) analyze refunds on experience goods. Clearly, our analysis is different from theirs as we focus on services which cannot be returned after being experienced. Although the present paper focuses on services (as opposed to products) a natural question to ask is whether, for the case of products, refunds and warranties can function as similar instruments by which firms can enlarge the surplus extracted from their customers. Clearly, both refunds and warranties provide some insurance against some uncertainties related to consumption. However, we argue that these two instruments “insure” against completely different types of uncertainties. By definition, warranties insure consumers against low-quality products, by offering a product replacement or a monetary refund on defective items. Thus, in the literature on warranties, see for example earlier papers by Spence (1977) and Grossman (1980), the source of uncertainty is always on the firms’ side. For this reason, warranties may serve as a signalling device on products’ quality. In contrast, refunds insure against uncertainties on the consumer side. These uncertainties are generated by no shows as reflected by the showup probabilities assumed in the present paper. Thus, a firm may be able to signal its products’ quality by offering a warranty, but refunds cannot be used as a signalling device. The paper is organized as follows. Section 2 sets up a model of service providers who select prices and refunds on no-shows. Section 3 analyzes monopolistic price and refund settings under joint ownership. Section 4 analyzes service providers who compete in prices and on the amount of refunds given to consumers who do not show up at the time when the service is scheduled to be delivered. Section 5 analyzes semicollusion on refund levels only. Section 7 further extends the model by investigating the incentives to collude on an industry-wide refund policy when consumer behavior exhibits moral hazard. Section 8 summarizes and discusses the findings of this paper. 2. A model of refunds Consider two service providers, indexed by j = A, B. Service providers set their service price pA and pB , and their refund level rA and rB . These refunds are given to those consumers who either cancel or do not show up at the service delivery time. Clearly, we assume that the decision variables satisfy pj ≥ 0 and rj ≥ 0, however, notice that at this stage we do not make any further restrictions on their relative magnitudes. That is, at this stage we do not rule out the possibility that the promised refund level may exceed the price paid by consumers, i.e., rj > pj , in which case refunds serve as a kind of an insurance subsidy to consumers. However, as we show below, the introduction of speculators will induce service providers to avoid such a strategy. 2.1. Consumers Consumers are differentiated along two dimensions: The basic benefit they derive from this service, and the probability of showing up for the reserved service. There are nH consumers who show up for the delivery of the service with probability σH . Similarly there are nL consumers whose probability of showing up is σL , where 0 < σL < σH < 1.1 Consumers are also indexed by x (0 ≤ x ≤ 1) that measures the distance (disutility) from service provider A, whereas (1 − x) 1 The introduction of two consumer types is crucial for this analysis since refund and price constitute two actions by which firms extract surplus. With only one consumer type, there exist a continuum of refund and price pairs by which a monopoly can extract the entire consumer surplus. With two consumer types, the solution is unique.

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measures the distance from B. Thus, x serves as the standard Hotelling index of differentiation. The (expected) utility of a consumer indexed by (σi , x) ∈ {σH , σL } × [0, 1] is given by ⎧ buying service A ⎪ ⎨ σi (β − τx) − pA + (1 − σi ) rA def U(σi , x) = σi [β − τ(1 − x)] − pB + (1 − σi ) rB buying service B (1) ⎪ ⎩ 0 not buying any service. The parameter β measures consumers’ basic utility from the service, and τ measures the degree of service differentiation, which is inversely related to the degree of competition between the two service providers. That is, competition becomes more intense when τ takes lower values. The utility function (1) reveals that the net benefit, β − τx or β − τ(1 − x), is obtained only if the consumer shows up (with probability σi ). The utility function (1) assumes that the consumers are heterogenous with respect to the actual consumption of the service. We would like to propose an alternative formulation of (1) where the consumers are heterogeneous with respect to the disutility inflicted by having to reserve the service in advance. Under this interpretation, the utility function could be written as ⎧ buying service A ⎪ ⎨ σi β − τx − pA + (1 − σi ) rA def U(σi , x) = σi β − τ(1 − x) − pB + (1 − σi ) rB buying service B (2) ⎪ ⎩ 0 not buying any service. From a technical perspective, the only difference between (1) and (2) is whether the disutility components −τx and −τ(1 − x) are multiplied by the show-up probability σi or not. The “sure” dissatisfaction from making the reservation (as opposed to the actual consumption of the service) should be attributed to the cost of making a reservation which may be subjected to transportation and value of time costs. Obviously, the utility function (2) is more appealing for cases where customers bear the disutility cost τ · min{x, 1 − x} regardless of whether they end up consuming the service or whether they end up claiming a refund. Throughout this paper we will be assuming that the utility function (1) holds. To save on space, we will not display our computations of equilibria under the alternative utility function (2), and will only briefly comment on some qualitative differences in the results. We initially abstract from moral hazard issues by treating the show up probabilities σi as constant parameters. Section 7 extends the model by making σi dependent on the amount of refund on cancellations and no shows given by service providers. 2.2. Speculators The consumers described in Section 2.1 make reservations with the “serious intention” of consuming the service, unless prevented from doing so by, say, force majeure which occurs with probability 1 − σi . In contrast to the above consumers, speculators make reservations and buy tickets with no intention of consuming the service. The only reason why they purchase tickets is to obtain refunds, and this can happen only if the refund levels are sufficiently high. Most importantly, since speculators never end up consuming the service, they are not constrained into purchasing only a single ticket. This is in contrast to the consumers described in Section 2.1, where each consumer was assumed to purchase at most one unit (say a single ticket on a specific flight). Let qjs denote the number of tickets purchased by speculators from service provider j. The utility (in fact profit function) of a representative speculator is given by

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⎧ s ⎪ ⎨ (rA − pA )qj def U s (pA , pB , rA , rB ) = (rB − pB )qjs ⎪ ⎩ 0

buying and obtaining refund from A buying and obtaining refund from B

(3)

not buying any service.

It is straightforward to infer from (3) that if a service provider j sets rj > pj , speculators will purchase the largest possible number of tickets (in fact, from a technical sense, the demand by speculators satisfies qjs = +∞) which would generate a loss to this service provider. Thus, we can state the following consequence. Result 1. In the presence of speculators, a profit-maximizing service provider will never set the refund level strictly above the service price. Formally, service providers A and B are constrained into setting rA ≤ pA and rB ≤ pB , respectively. One immediate application of Result 1 is that we do not need to explicitly model the speculators in this paper, since service providers will limit their refund levels to make any arbitrage unprofitable to speculators or to anyone else. Therefore, in what follows we will model only consumers who buy tickets with the intention of consuming the service at the time of service. 2.3. Costs Each service provider bears two types of per-customer costs. Let k ≥ 0 denote a service provider’s capacity cost or the cost of making a reservation for one customer. Note that this cost could be significant if the provider does not have any alternative use (no salvage value) for an unused capacity. Alternatively, it may not exist if capacity has an immediate alternative use upon no shows of consumers. Regardless of its magnitude, we view the parameter k as a sunk cost associated with any booking.2 In addition, service providers bear a per-customer cost of operation which we denote by c ≥ 0. The difference between the capacity cost and the operating cost is that the latter is borne only if the customer actually shows up for the service, whereas the capacity/reservation cost is borne regardless of whether the customer shows up. Finally, we assume that service providers always buy a sufficient amount of capacity to accommodate all reservations. That is, we deliberately abstract from overbooking as we view it as a completely different strategy, that should be separated from collusion on refunds, at least at this stage of preliminary research. 2.4. Profits of service providers Let qA and qB denote the endogenously determined number of consumers who each book (buy) one unit of service from providers A and B, respectively. Since not all consumers end up showing up at the service delivery time, we denote by sA and sB the expected number of consumers who show up at the service delivery time. Clearly, 0 ≤ sj ≤ qj for all j = A, B. Therefore, the

2 In this paper we do not distinguish between a cancellation and a no-show. Formally, service providers must sink k each time a reservation is made, since no salvage value is assumed. Clearly, a cancellation has the potential of recouping some of the sunk cost. In this respect, a natural extension to the present model would be to allow for three stages: Reservation stage, cancellation stage, and a no show stage. Since a cancellation is done prior to the service delivery time, the possibility of recouping some of this sunk cost (in the form of salvage value) is higher than that of a last minute cancellation. Finally, in this two-stage model, a canceled service with a salvage value can be accounted for by reducing the capacity cost k and by increasing the operating cost c with the salvage value.

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(expected) profit of each service provider j is given by πj (pj , rj ) = (pj − k)qj − c sj − rj (qj − sj ),

j = A, B.

(4)

The first term measures the revenue net of the reservation cost. The second term measures the operating cost borne only if consumers actually show up to be served. The last term is the expected total refunds to consumers who do not show up for the service they have paid for. 3. Single ownership We capture the monopoly market structure by assuming a single owner of the two service providers, who sets both prices and refund levels for both service providers. Thus, the owner sets a uniform refund level r = rA = rB and a price p = pA = pB to maximize πA + πB , where πA and πB are defined in (4). In order to be able to compare the single-ownership analysis with other market structures to be analyzed in subsequent sections, we solve only for the outcome where the single owner serves all consumers, see Assumption 1 below. It then follows that all consumers indexed by x = 0.5 must have U(σi , 0.5) ≥ 0, where U(σH , 0.5) and U(σL , 0.5) are defined in (1). Moreover, a single owner would raise prices and/or lower the refund levels to make these consumers indifferent between buying the service and not buying at all. Hence, U(σH , 0.5) = U(σL , 0.5) = 0 implies that σH (2β − τ) σL (2β − τ) and p = r(1 − σL ) + . (5) 2 2 Solving (5), and then substituting into (4), we conclude that the profit-maximizing price and refund levels as well as joint-ownership monopoly profit, under full market coverage, are given by   τ τ p = r = β − , hence πA + πB = (σH nH + σL nL ) β − − c − (nH + nL )k, 2 2 (6) p = r(1 − σH ) +

The following assumption ensures full market participation under the three market structures analyzed in this paper (joint ownership, competition, and semicollusion). Assumption 1. Consumers’ basic valuation for the service is sufficiently high relative to capacity and operating costs. Formally, β≥c+

k 3 + τ. σL 2

Intuitively, Assumption 1 states that a consumer’s basic valuation for this service exceeds the sum of the operating cost, the capacity cost (borne even if the consumer does not show up), and the markup. The following result is proved in Appendix A. Result 2. Under Assumption 1, the monopoly’s profit maximizing refund strategy is to provide full refunds on no-shows and cancellations. The unique price, refund and joint profit levels are given by (6). The result is important since it is shown later in Result 4 that providing full refunds is also the collusive joint industry-wide refund policy. Result 2 is crucially dependent on full market coverage (ensured by Assumption 1). Appendix A implies that it is optimal to exclude at least a part of the type-L market segment when k/σL + c + τ > β. This is the case when the showing-up probability of the type-L consumers

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is small. Obviously, an exclusion of only type-L customers is possible only if the price is strictly higher than the refund. We define consumer surplus as the sum of consumers’ utilities (1) evaluated at the equilibrium prices and refund levels. Formally,  1  0.5 def CS = [σi (β − τx) − pA + (1 − σi )rA ] dx + ni {σi [β − τ(1 − x)] ni i=H,L

0

− pB + (1 − σi )rB } dx =

i=H,L

0.5

(σH nH + σL nL )τ . 4

(7)

Notice that β does not appear in the computed aggregate consumer surplus (7) since under monopoly this surplus is extracted by the monopoly price (6). Thus, the non-extracted surplus is attributed to the reduction in price needed to attract consumers indexed by x = 0.5. 4. Competition in prices and refunds Consider a single-stage game where each service provider j = A, B determines both the service booking price, pj and the refund level rj . We look for a Nash equilibrium in pA , rA  and pB , rB , where all consumers are served. We will show that the fully-served market equilibrium is unique under Assumption 1.3 The utility function (1) implies that a type i consumer who is indifferent between booking service A and B is determined by σi (β − τ xˆ i ) − pA + (1 − σi )rA = σi [β − τ(1 − xˆ i )] − pB + (1 − σi )rB . Hence, xˆ i =

1 pB − pA + (1 − σi )(rA − rB ) + 2 2σi τ

for each type i = H, L.

(8)

Thus, the fractions of A and B buyers increase with the amount of refunds rA and rB , respectively. Clearly, the difference between the proportions xˆ H and xˆ L disappears when σL → 1 and σH → 1 since in this case all buyers always show up meaning that no one asks for any refund. In fact, setting σH = σL = 1 in (8) implies that consumers’ decision on which brand to buy becomes independent of the refund levels simply because the refund option is never utilized when all consumers always show up. From (8) we can compute the number of bookings (number of customers) made with each provider, and the expected number of show-ups: qA = nH xˆ H + nL xˆ L qB = nH (1 − xˆ H ) + nL (1 − xˆ L ) sA = nH σH xˆ H + nL σL xˆ L

(9)

sB = nH σH (1 − xˆ H ) + nL σL (1 − xˆ L ). Substituting (8) into (9), and then into (4), maximizing πA with respect to pA and rA , and πB with respect to pB and rB , and then solving the four first-order conditions yield

3 It turns out that this equilibrium outcome is identical to the outcome of the corresponding two-stage game where firms first compete on refund levels and then in prices. Therefore the comparison of these prices to the semicollusive prices solved in Section 5 is valid.

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rA = rB = c + τ,

pA = pB = c + k + τ,

π A = πB =

τ(nH σH + nL σL ) . 2

509

(10)

Thus, equilibrium profit levels consist of the markup τ multiplied by the expected number of show-ups per firm. Second-order conditions are satisfied since ∂2 πj /∂(pj )2 = −(nH σL + nL σH )/(σH σL τ) < 0, ∂2 πj /∂(rj )2 = −[nH σL (1 − σH )2 + nL σH (1 − σL )2 ]/(σH σL τ) < 0, and the determinant of the Hessian equals −nH nL (σH − σL )2 /(σH σL τ 2 ) > 0. Finally, substituting the equilibrium prices and refund levels (10) into the utility function of a type L consumer indexed by x = 0.5 defined by (1), implies that U(σL , 0.5) ≥ 0 by Assumption 1. Hence, the entire market is served. The equilibrium values (10) generate the following result. Result 3. The competitive refund given to customers who do not show up consists of the entire price less than the capacity cost. Formally, rA = pA − k and rB = pB − k. In other words, competitive refunds consist of the operating cost saving on a no-show, c, plus the duopoly price markup τ. This implies that service providers do not make any profit on customers who cancel. Hence, all profits are extracted only from consumers who do show up for the service.4 Intuitively, under full market coverage, competition on refunds focuses on type L consumers. Since type L consumers are less likely to show up, competition on refunds leads to a full insurance for those who cancel. Here, the appropriate expected marginal cost of a reservation made with service provider i is k + csi /qi ; or more precisely, k + c for those showing up and k for the no-shows. In a duopoly Hotelling model the Nash-equilibrium price is commonly characterized by the marginal cost, plus a service differentiation markup which can be extracted from the consumer. In our model the pricing takes the form of p = k + c + τ for those who show up, and p = k for those who do not show up. To compute aggregate consumer surplus, substituting the equilibrium prices and refund levels (10) into (7) yields

 5τ CS = β − c − (11) (nH σH + nL σL ) − k(nH + nL ). 4 Comparing consumer welfare under full competition (11) with consumer welfare under the single ownership equilibrium (7) reveals, as expected, that consumers are better off under competition. Comparing (6) with (10) reveals, as expected, that competition leads to lower prices and much lower refund levels compared with single ownership. 5. Collusion on refund levels In this section we approach our main investigation which is how the profit of service providers is enhanced when service providers coordinate on a joint industry-wide refund policy. We then compare the collusive refund levels to the competitive levels characterized in Section 4 and to the fully-collusive level analyzed in Section 3. We model semicollusion as a two-stage game. In Stage I, both service providers determine their refund levels rA and rB as to maximize joint profit πA + πB . In Stage II, refunds levels are taken as given, and each service provider chooses a price to maximize her own profit,

4 Under the alternative utility representation (2), the firms extract the price markup τ from all customers, including those who do not show up.

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taking the price of the other provider as given. We now solve for a subgame-perfect equilibrium. Our main result shows that the firms can achieve the same profit as under single ownership by colluding on refunds only while competing on prices. To be able to reach this profit levels, the firms set a uniform refund level rA = rB = r. The following result, is proved in Appendix B. Result 4. (a) The collusive industry-wide refund policy is to provide full refunds. (b) The collusive refund level and the implied competitive prices are identical to the levels set by a fully-colluding industry given by (6), where firms operate under a single ownership. Result 4 predicts that semicollusion involving an industry-wide commitment on a joint refund level while maintaining price competition between firms, yields the same outcome as under full collusion where a single owner sets both refunds and price levels noncompetitively. Therefore, this result implies that a regulator who is concerned with price collusion should be equally concerned with a joint decision on agreeing to refund at a certain level. Intuitively, Result 4 demonstrates that by raising the collusive refund level to the level set by monopoly, firms commit on high expected costs, which are then rolled over to the consumers in the form of higher “competitivelydetermined” prices. Finally, note that we assume that the firms collude on the level of refunds. Since no firm has an incentive to price below the refund level, a collusion on refund levels enforces a tacit collusion on price. Thus, colluding on a refund which is proportional to the price is less profitable for the firms, since the firms cannot use the refund level as a future commitment for a pricefloor. 6. Collusion on refunds when prices are fixed Consider a situation where firms must charge a fixed price p = pA = pB but are free to collude on a common refund level r = rA = rB . Substituting (8) and (9) into (4), setting r = rA = rB yields ∂(πA + πB )/∂r = nH (σH − 1) + nL (σL − 1) < 0. Hence, Result 5. In a market where prices are fixed, the firms have incentives to collude on lower refund levels than the competitively-determined levels. If all customers choose to buy the service under zero refunds, then giving no refunds constitutes the industry’s collusive refund policy. This result can be deducted logically considering the fact that once prices are fixed (say, during the first stage of the game), service providers minimize costs by refusing to give any refund on no-shows. Thus, once prices are fixed, strictly positive refunds can be realized only as an outcome of competition. 7. Collusion on refunds under moral hazard We say that consumer behavior exhibits moral hazard if an increase in the refund level offered by a service provider results in an increase in the probability of realizing no-shows and cancellations. Clearly, our analysis has so far abstracted from any moral hazard behavior by assuming that the showing-up probabilities σH and σL were exogenously-given constants.

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In this section we develop a moral hazard model in which consumers’ show-up probabilities decline with an increase in the promised refund levels. Formally, let us assume that the show-up probabilities are now modified to take the form of def

σH (rA ) =

σH , 1 + γrA

def

σL (rA ) =

σL , 1 + γrA

def

σH (rB ) =

σH , 1 + γrB

def

σL (rB ) =

σL . 1 + γrB (12)

We continue to assume that 0 < σi < 1. The parameter γ ≥ 0 measures the intensity of how the refund level affects consumers’ show-up probabilities. Clearly, unless γ = 0, σi (rA ) and σi (rB ) decline with rA and rB , respectively. Substituting the modified probabilities (12) into the utility functions (1), type i, i = H, L, “indifferent” consumers are now indexed by5 xˆ i =

(1 + γrA )(1 + γrB )(pB − pA ) + (rA − rB )(rA rB γ 2 − βγσi ) τσi (2 + γrA + γrB ) +

2 − r 2 ) − σ (r − r − τ) + r − r γ(rA σi τ + rA B A B i A B . τσi (2 + γrA + γrB )

(13)

Observe that if γ = 0 is substituted into (13), we obtain the indifferent consumers indexed by (8) as a special case. Therefore, the present formulation constitutes a generalization of our model. We examine the same two-stage game as in Section 5, where the two service providers first determine a joint refund level r = rA = rB , and then compete in prices, pA and pB . The following result which is proved in Appendix C. Result 6. In a semicollusive equilibrium under moral hazard, either both firms provide full refunds or they provide no refund. Formally, there does not exist an equilibrium where pj > rj > 0 for each firm j = A, B. From Result 6 and Appendix D we derive the following result for the extension of the model to include moral hazard behavior. Result 7. There exists a unique threshold level of the moral hazard parameter γ¯ beyond which service providers collude on providing no refund. Otherwise, the collusive refund policy is to provide maximum (full) refund. Thus, Result 7 obtains Result 4 as a special case when the moral hazard effects become insignificant (γ → 0). We also showed that partial refund cannot be a semicollusive outcome in the present model, as the the joint profit function is not concave with respect to the collusive refund level r. When moral hazard becomes significant, the collusive refund policy shifts from a full refund to no refund. To demonstrate that the threshold level defined by (18) is meaningful, we simulate one example where nH = nL = 1000, σH (0) = 0.8, σL (0) = 0.6, β = 40, τ = 1, and k = c = 10. In this example, γ¯ =

1415 ≈ 0.049, and, 58302

5 As before, our analysis is confined to full participation in which case Assumption 1 may need to be slightly modified to incorporate a higher lower bound on the basic valuation parameter β.

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p A = pB =

⎧ ⎪ ⎨ 39.5

  τ highest refund r = β − = 39.5 2

⎪ ⎩ 614 ≈ 17.5 35

no refund (r = 0).

(14)

The resulting joint profit level, evaluated either under the highest refund and under no refund (the ¯ = (7600/7) ≈ 1085. Therefore, ¯ is (πA + πB )(γ) profits are the same when evaluated at γ = γ), as expected, equilibrium prices under full refund clearly exceed the equilibrium prices under no refund since the collusion on a high refund generates a commitment for a higher expected cost. Finally, it is instructive to check how the show-up probabilities are affected by the provision of full refunds. Substituting the highest refund level r = 39.5, and γ¯ = 1415/58302 from (14) into the show-up probabilities (12) yields ¯ = σH (r; γ) =

0.8 ≈ 0.363 and 1 + (1415/58302)39.5 0.6 ≈ 0.272. 1 + (1415/58302)39.5

¯ σL (r; γ) (15)

Thus, the introduction of full refund reduces the show-up probabilities by 55%, relative to their levels under no refund. This implies that the difference between the two types, as measured by σH (r) − σL (r), diminishes when the firms provide full refunds compared with a no refund policy. 8. Conclusion The purpose of this research is to identify situations in which industry-wide explicit or implicit agreements on joint refund policies weaken price competition and reduce consumer welfare. If service providers can commit on a joint industry-wide refund policy before they compete in prices, they will raise refund levels above the competitively-determined refund levels. In this case, collusion on refunds reduces consumer welfare. It should be mentioned that the present setup can also be applied to some non-service industries where refunds are commonly observed. The showup probabilities may be replaced by some utility shocks that can be realized only after consumers pay for the products or services. The abovementioned results imply that high refund levels should be a major concern for regulators and consumer-rights organization. However, in practice consumer-rights organizations and regulators tend to be concerned that firms do not refund their customers enough. This “puzzle” can be explained by the fact that consumer organizations tend to focus more on sellers’ liability to replace faulty products (as opposed to services which is the focus of the present paper) and therefore are less concerned with the price increase implications associated with providing refunds for functioning products and services. There may be good reasons why firms do not always offer full refund, or even any refund. Moral hazard, which is partially modeled in this paper, is one reason. In addition, firms may bear high costs of administrating refunds to consumers who cancel or do not show up at the service delivery time. This paper has abstracted from the cost of administrating refunds. This cost could be high considering the fact that the service provider must fully identify the customer. Even if the service provider keeps a full record of all customers, including their credit cards, reversing a credit card transaction is highly costly in some service industries depending on the fees charged by the acquirers of credit and debit card transactions.

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Finally, consumers’ moral hazard behavior is an important issue for any firm providing refunds in the service industries, and for firms providing warranties in the market for products. Thus, a natural extension of the present framework would be to model consumer choice as to whether or not to book a service by introducing a stochastic shock to their consumption utility which can be observed only after the booking is made. In our view, however, the moral hazard effect is more accentuated in the market for products as the customer has a stronger legal right to be dissatisfied after they have tried the product which is not necessarily the case in markets for services. Acknowledgements We thank an anonymous referee, an editor, Fabio Manenti, Rune Stenbacka, Lixin Ye, as well as seminar participants at the University of Dortmund, Dresden University of Technology, University of Freiburg, University of Heildelberg, Helsinki Center for Economic Research, University of Magdeburg, University of Padova, CERGE-EI, Prague, and the January 2006 Winter Meetings of the Econometrics Society held in Boston, for most valuable suggestions and comments on earlier drafts. Appendix A. Proof of Result 2 Market of type i ∈ {L, H} consumers is fully covered if the utility of participation at x = 0.5 exceeds the reservation utility 0. It follows from utility function (1) that this occurs at a single pair of price and refund if

 1 σi β − τ − p + (1 − σi )r ≥ 0. 2 Otherwise, the participation rate of type i consumers is 2ˆxi = 2 argx {σi (β − τx) − p + (1 − σi )r = 0} = 2

σi β − p + (1 − σi )r . σi τ

Under joint ownership, the restricted maximum of the profit function (4) can be solve from the following Lagrangian ⎧ ⎪ ⎨  L(p, r, λL , λH ) = 2 · (p − k − r) ni ((σi β − p + (1 − σi )r)/σi τ) + (r − c)

  ⎪ ⎩ i=H,L ×



xˆ i

ni ((σi β − p + (1 − σi )r)/τ)

 

i=H,L

+

 i=H,L

σi xˆ i

 λi

⎫ ⎪ ⎬

1 σi β − p + (1 − σi )r − . ⎪ 2 σi τ ⎭

As the unrestricted profit function is concave (∂2 π/∂p2 < 0, ∂2 π/∂r 2 < 0, det ∇ 2 π > 0) and the restrictions are linear in p and r, the optimization problem is straight forward. Thus, when all

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consumers of both types are served, profit is maximized at τ p=β− , 2

τ r=β− , 2

and

λi = σi (β − c − τ) − k > 0, ni

for i = H, L,

which holds true if β > (k/σL ) + c + τ. If (k/σL ) + c + τ > β the type-L market is not covered under joint ownership. Under competition the market is fully covered if the reservation utility for a type-L consumer at x = 0.5, for p = c + k + τ and r = c + τ, (10) is non-negative, so that

 1 σL β − τ − (c + k + τ) + (1 − σL )(c + τ) ≥ 0.     2 p

r

That is when β>

k 3 + c + τ. σL 2

Appendix B. Proof of Result 4 A semicollusive industry cannot earn a strictly higher profit than the profit earned under single ownership given by (6) with pA = pB = r = β − τ/2. Obviously, the firms are allowed in the initial stage to jointly fix the refund level to r = β − τ/2. But then pA = pB = β − τ/2 is a unique Nash-equilibrium, as  



 1 1 nH nL 3 ∂πi  lim <− = − · β − c − τ (nL + nH ) − k + pi ↓r ∂pi p =r=β−τ/2 2τ 2 σL σH 2τ j

 k 3 · β− / j, − c − τ (nL + nH ) < 0, i, j = H, L; i = σL 2 πi is concave in pi (when pi ≥ r),6 and as pi < r = β − τ/2 is ruled out by Result 1. Appendix C. Proof of Result 6 By substituting the showing up probabilities (12) and p = r into the profit function (4) we immediately conclude that the joint-profit function is increasing with r. Therefore, it is sufficient to establish that the first-stage joint profit function is strictly convex with respect to the jointlydecided refund level r for the case where pj > rj > 0. Substituting (13) into (9), and then into (4), maximizing πA with respect to pA , and πB with respect to pB , and then adding the equilibrium profit levels yields (πA + πB )(r) =

nH nL (σH − σL )2 (γr 2 + r − γcr − c) + σH σL τ(nH + nL )2 (σL nH + σH nL )(rγ + 1)

for 0 < r < pA = pB .

6

∂2 πi /(∂psi )2 |pi >r = −(nL /σL + nH /σH )/τ < 0.

(16)

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515

Differentiating(16) twice with respect to r yields d 2 (πA + πB )(r)/dr 2 = 2γ 2 σH σL τ(nH + nL )2 / [(σL nH + σH nL )(rγ + 1)3 ] > 0. Hence, the profit function (16) is strictly convex with respect to the collusive refund level r. Appendix D. Proof of Result 7 Result 6 implies that the only candidate collusive refund levels are r = 0 (no refund), and r = β − τ/2 (the fully-collusive refund level derived in Section 3). Slightly modifying the equilibrium collusive profit level (6) for the case of moral hazard, and evaluating the joint profit (16) at r = 0, yields that a semicollusive industry chooses the refund policy which maximizes. maxr ∈ {0,β−(τ/2)} (πA + πB )(r)  ⎧n σ +n σ  τ H H L L ⎪ β − − c − (nH + nL )k ⎪ ⎪ 2 ⎨ 1 + γ(β − τ ) 2 = ⎪ 2 2 ⎪ + σ (n σ ⎪ H L H nL ) τ − nH nL (σH − σL ) c ⎩ nH σL + n L σH

if r = β −

τ 2 (17)

if r = 0.

Comparing the two profit levels in (17), reveals that colluding on the maximum refund level is ¯ more profitable than colluding on no refund if γ ≤ γwhere def

γ¯ =

2cσH σL (nH + nL )2 + 2k(nH + nL )(nH σL + nL σH ) + (n2H + n2L )σH σL (3τ − 2β) (2β − τ){cnH nL (σH − σL )2 − (nH + nL )[k(nH σL + nL σH ) + σH σL τ(nH + nL )]} +

2 +4σ σ σ 2 )−2β(σ 2 +σ 2 )] nH nL [τ(σH H L L L h . 2 (2β−τ){cnH nL (σH −σL ) −(nH +nL )[k(nH σL +nL σH )+σH σL τ(nH +nL )]}

(18) References Che, Y. (1996). Consumer return policies for experience goods. Journal of Industrial Economics, 44, 17–24. Courty, P., & Li, H. (2000). Sequential screening. Review of Economic Studies, 67, 697–717. Dana, J. (1998). Advanced purchase discounts and price discrimination in competitive markets. Journal of Political Economy, 106, 395–422. Davis, S., Gerstner, E., & Hagerty, M. (1995). Money back guarantees in retailing: Matching products to consumer tastes. Journal of Retailing, 71, 7–22. Gale, I. (1993). Price dispersion in a market with advance-purchases. Review of Industrial Organization, 8, 451– 464. Gale, I., & Holmes, T. (1992). The efficiency of advance-purchase discounts in the presence of aggregate demand uncertainty. International Journal of Industrial Organization, 10, 413–437. Gale, I., & Holmes, T. (1993). Advance-purchase discounts and monopoly allocation of capacity. American Economic Review, 83, 135–146. Grossman, S. (1980). The role of warranties and private disclosure about product quality. Journal of Law and Economics, 24, 461–483. Macskasi, Z. (2003). Horizontal Differentiation with Consumer Uncertainty. Northwestern University. Matthews, S., & Persico, N. (2005). Information acquisition and the excess refund puzzle. PIER Working Paper Archive 05–015, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. Miravete, E. (1996). Screening consumers through alternative pricing mechanisms. Journal of Regulatory Economics, 9, 111–132.

516

S. Ringbom, O. Shy / Journal of Economics and Business 60 (2008) 502–516

Ringbom, S., & Shy, O. (2004). Advance booking, cancellations, and partial refunds. Economics Bulletin, 13(1), 1–7. Rochet, J-C., & Stole, L. (2003). The Economics of Multidimensional Screening. In M. Dewatripont, L. Hansen, & S. Turnovsky (Eds.), Advances in Economic Theory (pp. 150–197). Cambridge University Press. Spence, M. (1977). Consumer misperceptions, product failure, and producer liability. Review of Economic Studies, 44, 561–572.