Second-Hand Markets and Intrasupply Chain Competition

Journal of Retailing 87 (4, 2011) 489–501

Second-Hand Markets and Intrasupply Chain Competition Konstantin Kogan ∗ Department of Management, Bar-Ilan University, Israel

Abstract We consider a monopolistic supply chain consisting of a manufacturer and a retailer (service provider) who in addition to selling new durables, buy and resell used ones. The supply chain provides services for both new and used goods. Accordingly, consumers incur service charges for all types of goods. This study is motivated by the modern trend in cell phone businesses where retailers commence buying used phones from customers willing to upgrade their phones. The used phones are then refurbished and resold along with the services. The question that this trend gives rise to is how the interaction with the secondary market affects the performance of the supply chain in terms of its intracompetition and thereby its profit. We show that for a wide range of service rates, the second-hand market coordinates the supply chain by either reducing the double marginalization effect or by offsetting it with extra profits gained by servicing the used goods. This, however, does not imply that both parties always improve their profits. Furthermore, we find that when the service rates are low, the supply chain would be better off if the goods were not durable thereby precluding the very existence of the second-hand market. © 2011 New York University. Published by Elsevier Inc. All rights reserved. Keywords: Supply chain management; Coordination; Second-hand markets

Introduction Reuse and recycling of durables has recently gained significant attention in both theory and practice of management in the context of so-called closed loop supply chains. Due to the increasing popularity of remanufacturing, academic research into product recovery management has grown considerably (see, for example, extensive literature reviews by Fleischmann et al. (1997) and Guide and Van Wassenhove (2002)). Specifically, operations planning and organization of channel operations are studied in Dekker et al. (2004) while centralized network design, shop floor control, and inventory control are discussed in Krikke et al. (2003), Guide and Srivastava (1997), and Van der Laan et al. (2003), respectively. A large stream of literature considers decentralized closed loop supply chains to account for intracompetition. These studies employ game theory to model competition in relation to remanufacturing decisions. For example, Emmons and Gilbert (1998) and Donohue (2000) determined optimal product return while Padmanabhan and Png (1997) studied the retaillevel competition under buy-back contracts. Savaskan et al. (2004) focused on choosing the appropriate reverse channel

∗

Corresponding author. E-mail address: [email protected]

structure for collecting used products from customers. They found that the agent who is closer to the customers, that is, the retailer, is the most effective implementer of product collection activity; they suggest a simple coordination mechanism to overcome intrasupply chain competition. Guide et al. (2003) determined the optimal acquisition and selling price for used products of different quality, assuming that the demand and the return rate functions are known. Karakayali et al. (2007) consider a durable end-of-life product from which a particular part can be dismantled and remanufactured with the remainder of the product further processed for part, material recovery, or both. They developed models to determine the optimal acquisition price of end-of-life products and the selling price of the remanufactured parts in centralized as well as remanufacturer and collector-driven decentralized channels. They also discuss how the decentralized channels can be coordinated to attain an end-of-life product collection rate that can be achieved in the centralized channel with no intracompetition. The main feature of the above mentioned research is that it deals only with durables (mostly end-of-life) that can be resold for further reuse through a unique reverse channel making it possible to monopolistically price them and thereby to control the rate of their return. In contrast, we assume that the durables become obsolete well before their physical end-of-life. As a result, they remain functional and can be resold in a perfectly competitive, second-hand market without

0022-4359/$ – see front matter © 2011 New York University. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.jretai.2011.10.001

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K. Kogan / Journal of Retailing 87 (4, 2011) 489–501

remanufacturing. Specifically, this paper addresses the reuse of durables in a decentralized supply chain consisting of a manufacturer and a retailer or service provider. Used durables are collected by the retailer, refurbished (if needed) and then resold along with services for them. Therefore, even if the supply chain can price monopolistically the new goods, the second-hand market dictates the price of the used goods and, thus, the rate of their return. Our motivation for this study springs from the modern trend in cell phone businesses where the retailers buy used phones from customers willing to upgrade their phones. According to an INFORM estimate, about 130 million cell phones were retired and over 500 million cell phones were stockpiled in the US in 2005 (Sullivan 2006). Cell phones are retired and replaced primarily because of marketing factors and constant innovations in this area. Wireless service contracts typically last one year, and even users who renew with the same provider often have an incentive to upgrade their current phone and service. A number of programs in the US promote the refurbishment (along with recycling as a byproduct) and reuse of cell phones to extend the utility of products and prevent functional products from being disposed of as waste. Geyer and Blass (2010) estimate that over 90 percent of all resold cell phones collected in the USA receive no or minimal refurbishment, such as testing, basic cosmetic treatment, and software updates. Based on detailed primary data collected from reverse logistics, reuse and recycling operations in 2003 in the UK and in 2006 in the US, the authors show that the refurbishment costs are very small and suggest that very little reprocessing takes place. In contrast to other electronic products, end-of-use cell phones have a thriving reuse market. In the USA, 65 percent of all collected cell phones are reused rather than recycled (Doctori Blass et al. 2006). As a result, the service providers can no longer afford to ignore the cell phone second-hand market. Sprint USA, T-Mobile UK, and CellCom Israel are just a few examples of wireless service providers who have a buy-back program for used cell phones from their customers. The buy-back programs give the customer a credit on his/her account balance based on the return of an eligible handset and battery. The question arises as to how this recent trend affects the overall supply chain including both the manufacturers of new cell phones and the service providers. According to Rust (1986), “the conventional wisdom is that a secondary market provides close substitutes for new durable goods limiting profits of the monopolist in the primary market.” On the other hand, a second-hand market may serve to increase primary demand for a monopolist’s product if consumers anticipate a secondary resale value (Swan 1980). These arguments rely on the assumption that consumers have homogeneous preferences, that is, the representative consumer is indifferent about buying new, used or not buying at all. The size of the second-hand market is therefore indeterminate in such models. Accordingly, the impact of the second-hand market on the primary market is not fully identified. This is to say, although double marginalization is revealed when a manufacturer turns to independent intermediaries (dealers) to sell his products (see extensive retailing literature, for example, Cai (2010), Betancourt and Gautschi

(1998), Tsay (2001), and Wu et al. (2010)) the effect of the second-hand market on the magnitude of the double marginalization remains unclear. The assumption that the consumers constitute a homogeneous group underlies various models that study time-inconsistency – the problem which stems from the incentive to lower prices and sell more units after an initial period of sales is completed. Specifically, Purohit (1995) employs a two-period model in which the quantity that dealer sells in period 1 is potentially available for the used market in period 2. Purohit shows that when the monopolist must rely on intermediaries (unless he can commit to a set of prices), he prefers to go through an intermediary who sells rather her products than one who rents them. Desai et al. (2004) show that by precommitting to appropriate two-part contracts with dealers, a manufacturer can eliminate time-inconsistency. Arya and Mittendorf (2006) also consider the severity of the channels commitment problem in a similar two-period as well as three-period setting. Bhaskaran and Gilbert (2009) do not allow the manufacturer to precommit to future contract terms and assume that each intermediary can choose whether to lease or sell goods bought from the manufacturer. In particular, they show that when the manufacturer interacts with a single dealer, he would be better off selling instead of leasing to this dealer. Based on Mussa and Rosen (1978) and unlike the above-mentioned stream of literature assuming homogeneous consumers, Anderson and Ginsburgh (1994) suggested a two-period model in which consumers have heterogeneous preferences for new and used goods. Following Rust (1986) and Swan (1980) they assume that the monopolist sets his price once and for all to eliminate time inconsistency problems and to focus on interactions between the second-hand and primary markets. The second-hand price is determined by transaction costs and the interaction of demand and supply of used durables. They derive the conditions in which a monopoly seller may gain or lose from the existence of a second-hand market. Based on these conditions, the monopolist, in choosing his price, can determine the extent of the secondary market. Since they consider a monopoly, which does not resell goods and employs no intermediaries, they refer to this as a form of indirect second-degree price discrimination. Huang et al. (2001) extend this model to accommodate concurrent leasing and selling and show that price discrimination is the major motivation for a manufacturer to offer a leasing program to heterogeneous consumers. In this paper we adapt the Anderson and Ginsburgh (1994) model to study the interaction between a monopolistic supply chain and a second-hand market. Unlike Anderson and Ginsburgh (1994) and Huang et al. (2001), we assume that (i) there is no direct interaction between the manufacturer and the consumers, rather it is through the retailer (intermediary) who together with the manufacturer comprise a supply chain; (ii) the retailer buys and resells used goods and thus the supply chain may benefit directly not only from the primary market, but also from the secondary market; and (iii) although consumers incur no transaction (search) costs for the used goods, the retailer provides services for both new and used goods and thus the consumers incur service charges for all types of goods. Clearly,

K. Kogan / Journal of Retailing 87 (4, 2011) 489–501

for such a supply chain to be monopolistic with respect to a certain brand and price its new goods correspondingly, the manufacture should favor a selected agent (retailer) to sell his brand name device and the service rates for both used and new goods should be competitive. If not, even loyal consumers may switch to less attractive brands to get lower service rates. That is, we assume service prices are exogenously determined and there is a competitive market for services. In particular, the consumers preferring used goods will favor buying them from the supply chain if they get service for them and the service rate is competitive, the transaction costs are kept at zero, and that the price they get for their old goods is the price of the perfectly competitive used market. This implies that the retailer’s acquisition price for the used goods is identical to her selling price. Consequently, in terms of used goods, the retailer profits only from services rather than from resale. The basic model in this study is the classic channel system of a manufacturer and a retailer and thus there double marginalization. In such circumstances the question arises: Does the existence of a second-hand market induce one of the channel members to better align the channel so that total channel profits are increased? To answer this question, we must understand what would happen if there was no used market and compare this to what would happen if there was one. We show how the interaction with the secondary market affects the performance of the overall supply chain, in particular, its intracompetition when the supply chain handles not only new, but also used durables. Specifically, we find that the retailer coordinates the channel for a wide range of service rates by setting the retail price of the new goods to be in the region she finds best. When newness is low, the retailer wants to operate in the region where there is no market for the used good (since the new product is quite similar, albeit better than the used product). Accordingly, the retailer decides to hold down the retail price. This reduces the double marginalization and leads to Pareto-improving channel coordination since both the retailer and manufacturer gain higher profits. On the other hand, when service rates are low, the second-hand market may induce in the supply chain losses rather than coordinate it. Intrasupply chain competition Consider a supply chain, which is a monopoly in the primary market but faces perfect competition in the used market. The supply chain consists of a manufacturer who produces goods and a retailer who sells new and used goods as well as provides services for them. We assume that since the goods become obsolete much faster (during only two periods) than their durability, they rarely require any repairs. Therefore the refurbishment costs are negligible. In addition, to keep the number of parameters from becoming too large, we set the marginal production cost equal to zero and concentrate on the effect of the second-hand market on the supply chain performance. Consequently, employing the standard setting, let w be the wholesale price of the new goods set by the manufacturer and m be the retailer’s margin (the retailer does not get any margin from the sale of the used durable). The retail price is then pN = w + m. The parties are transparent and

491

make a decision simultaneously to maximize their own profits. The result of such a game can be affected by an upper bound imposed on the retail price. Such a bound, for example, can create a pricing barrier for the second-hand market driving it out of existence. If the retailer expects that she is better off with the barrier, then the bound would be announced before the parties make a decision and they will play a “constrained game” with the constraint burden equally shared (Rosen 1965). There are many reasons for the manufacturer to share the constraint burden. Gilbert and Cvsa (2003), for example, discuss ceiling wholesale price contracts, in which the supplier commits in advance to an upper bound on the wholesale price thereby reducing his margin. They show that these type of contracts, commonly used in practice, induce downstream cost reduction and mitigate the risk related to demand uncertainty. Consequently, they are preferred to full flexibility and full commitment wholesale price contracts. Note, that the manufacturer might suggest a retail price, the so-called manufacturer’s suggested retail price (MSRP; which is also referred to as the Monroney retail price). Since the retailer has no obligation to accept such a price, this will not affect the outcome of the game. The resultant profits of the parties are then due to the decisions made with respect to the corresponding margins, w and m; service rates; and demands for new DN and used DU goods. Accordingly, to study the impact of the resale on the profit of the supply chain, we first derive the demands for durables by segmenting the market into consumer type – those buying new and those buying used. Demands for durables Assuming consumers can buy from a retailer new, used, or no goods at all and keep the purchased durables for a period of time, let the price for the used goods be pS . The value of the service provided by a used product is v, and the value provided by a new product is v + k, where k is the improvement or extra benefit of newness and every improvement per period is the same. Specifically, the fact that newer devices might allow consumers to do more or different things is present in the added value of the new service k. Services are competitively priced and exogenously determined. Specifically, the retailer charges sN and sU , respectively for servicing new and used durables. That is, as a new device with new possibilities arrives to the market, the retailer reconsiders the service charges for the devices becoming one period old and thus providing already limited services. Following Anderson and Ginsburgh (1994) we assume that the life-span of each product is only two periods and that there are different valuations of these services according to a parameter θ. That is, θ is between zero and one, with higher θ denoting individuals with greater willingness to pay. The model The options available to the consumer are to buy new, used, or not at all. The utility V a consumer derives from each of these options, respectively, is

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K. Kogan / Journal of Retailing 87 (4, 2011) 489–501 VN = 2[(v + k)θ − pN − sN + pS ] VK = (2v + k)θ − pN − sN − sU , VU = 2[vθ − pS − sU ] VZ = 0.

Buy a new good for each period: Buy new and keep for two periods: Buy used good for each period: Do not buy at all:

The basic assumption of the model is that consumers will choose the utility-maximizing option. The point of indifference θ NK between buying new each period and buying new and then keeping it for two periods is defined by setting VN = VK . Then we have 2[(v + k)θ NK − pN − sN + pS ] = (2v + k)θ NK − pN − sN − sU thereby θ NK = [pN + sN − sU − 2pS ]/k, so that VN > VK when θ > θ NK and VN < VK when θ < θ NK . Similarly, the point of indifference θ KU is found from VK = VU , which leads to θ KU = [pN + sN − sU + 2pS ]/k, that is, θ NK = ␪KU . Since the consumer’s utilities are increasing with θ, we conclude that the consumers never buy new to keep for two periods. This result corresponds to the zero transaction cost in Anderson and Ginsburgh (1994), which implies that the service rates are not substitutes for the transaction costs. Consequently, the number of possible options reduces along with the points of indifference to, θNU =

pN − 2ps + SN − SU , k

(1)

ps + SU . v

(2)

Therefore, if 0 < θ UZ < θ NU < 1, then the consumers buying new goods are those with ␪ ≥ ␪NU , buying used, ␪UZ ≤ ␪ < ␪NU , and not buying at all, ␪ < ␪UZ . Then ␪NU = (pN − 2pS + sN − sU )/k < 1 implies pN < k − 2ps + SU − SN ,

(3)

otherwise nobody buys new goods and there are no used goods. Similarly, θ UZ = (pS + sU )/v < θ NU implies     2+k 1+k pN > ps + sU − SN , (4) v v otherwise the market for the second-hand goods does not exist. Finally, θ UZ > 0 always holds if sU > 0. Demands for new and used goods Let the demand for the new and second-hand goods exist, pS (2 + k/v) + sU (1 + k/v) − sN < pN < k + 2pS + sU − sN . Then assuming, that consumers are uniformly distributed on θ, the fractions of consumers buying new DN , used DU , and no goods DZ , are respectively: DN = 1 − θNU =

1 − (pN − 2ps + SN − SU ) , k

sN pN DU = θNU− θUZ = + − k k   2 1 − + ps , k v



1 1 + v k

(5)

 SU (6)

θUZ = (ps + sU ) . v

(7)

Eqs. (5)–(7) imply that the larger the price of the new units and the lower the price of the used units, the smaller the demand for new goods and the higher the demand for the used. That is, the two markets compete and the endogenous used price impacts both markets. Furthermore, high, used-product service rates, sU , make it more likely for the endogenous used prices to be driven to zero. We also observe that higher prices for the used goods result in a greater number of consumers who prefer not buying any goods at all. However, greater newness, k, implies less price sensitivity of the demand for the new and used goods to both pN and pS. . Moreover, the higher value of the service provided by a used product, v, also reduces the sensitivity of the demand for the used goods to their price, pS . The value of pS , is determined as the price that clears the second-hand market. Specifically, the supply per period is the number of consumers buying new each period, DN . The demand per period consists of those consumers who buy used goods, DU . Then, the price of the used goods is found from DN = DU . That is, ps =

and θUZ =

DZ =

(pN + sN − sU )2/k − sU (1/v) − 1 . (4/k) + (1/v)

(8)

From (8) we readily observe that the greater the newness, k, the lower the price of the second-hand goods while an increase in the price for a new good induces a higher price for the used good. Note that if the price for the new goods falls, it can drive the second-hand price to zero, that is, from (8) we derive that, if   pN ≤ k 1+k − sN + sU , (9) 2 2v then the consumers preferring new products dispose of the used for free, pS = 0. Consequently, conditions (3) and (4) transform into sU (1 + k/v) − sN < pN < k + sU − sN . This condition, when combined with (9) and assuming that the service rate cannot be higher than the value of the services, leads to the following proposition. Proposition 1. If sU (1 + k/v) − sN < pN ≤ (k/2) − sN + sU (1 + (k/2v)), the consumers preferring new products freely dispose of their used goods and the supply of the second-hand products exceeds the demand for them. Specifically, DN = 1 − (pN + sN − sU )/k, DU = (pN + sN − sU )/k − sU /v, DZ = sU /v and DN ≥ DU . Proposition 1 considers the case when the price for new goods is so low that the number of customers buying them (and thus willing to dispose from the used ones) exceeds those preferring the second-hand devices. That is, the supply for the used goods exceeds the demand for them. This drives down the market value of the used goods to zero. When the price for the new goods is even lower than that determined in Proposition 1, pN ≤ sU (1 + k/v) − sN , the new goods provide such an advantage compared to the used goods, that the second-hand market is simply priced out of existence.

K. Kogan / Journal of Retailing 87 (4, 2011) 489–501

A

B SU (1+ ) - SN

C

493

D

– SN + SU (1+ )

2V + K – SU - SN

Fig. 1. Pricing regions.

Proposition 2. If pN ≤ sU (1 + k/v) − sN , the market for the second-hand goods does not exist, DU = 0, DN = 1 − (sN + pN )/(v + k) and DZ = (sN + pN )/(v + k).

(a)

Substituting (8) into (3) and (4), we find that both (3) and (4) result into the same inequality, pN < 2v + k − sU − sN . This implies that either both primary and secondary markets exist or no market exist at all. Taking into account (8) and (9), we arrive, based on Eqs. (5)–(7), at Proposition 3. Proposition 3. If (k/2) − sN + sU (1 + (k/2v)) < pN < 2v + k − sU − sN , then both markets of new and used goods exist, pS > 0 and the demands for goods are: DN = DU = 1 − (pN + sN + sU + 2v)/(4v + k), Dz = (2(pN + sN + sU ) − k)/(4v + k). Otherwise, if pN ≥ 2v + k = sU − sN , then the goods are too expensive compared to the utility value they are endowed with and thereby no market exists, DN = DU = 0, DZ = 1. According to Propositions 1–3, the retailer faces two different kinked demand curves, one for new units and one for used units. Moreover these two markets are interrelated. This results in four different pricing regions illustrated in Fig. 1. Region A has only the new market, that is, there is no second hand market. Region B also has a second market, but used prices are zero, as DN > DU . Still the retailer gets revenue from this market from exogenously determined service charges, sU . Region C has a full-scale second market, here new and used sales are matched, DN = DU , and there is a positive price for the used units, and the retailer still gets service profits from these units (but not from the sale of the used units). Finally, in Region D there are no new or used sales and thus no service revenue, that is, DN = DU = 0. Comparing the results of Propositions 1–3, we conclude that the demand for new goods always drops when their price increases unless the price is so high that there is no consumer willing to buy the new goods (see Fig. 2). This is similar to the downward sloping linear demand frequently assumed for homogeneous consumers. The difference is that when the consumers are heterogeneous, the demand function becomes kinked, that is, the slope of the demand changes. Specifically, from Propositions 1 to 3 we find that the absolute value of the slope first increases when the second-hand market emerges. This trend, however, changes as the price for the used goods becomes strictly positive. In such a case, the absolute value of the slope drops to a level that is even below that when no second-hand market exists. This is to say, consumers are most sensitive to the price of new goods when the supply for the used goods exceeds the demand for them. On the other hand, demand for the used goods is not always characterized by a negative slope in the price of new goods (see Fig. 2). Specifically, if there is a second-hand market,

(b)

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

Du Dz Dn

0

2

4

6

8

10

PN

Du Dz Dn

0

2

4

6

8

10

12

PN

Fig. 2. Demand for new and used durables, as well as the fraction of consumers not buying any product at all, v = 4, k = 4, sN = 1 and (a) sU = 2 and (b) sU = 1.

that is, pN > sU (1 + k/v) − sN , then the demand for the used goods increases until the price for the new goods reaches pN = (k/2) − sN + sU (1 + k/2v). A further increase beyond that price, however, results in a decline in demand for the used goods. Thus, from Fig. 2, we observe that for a fixed sU , sN , v and k, increasing the retail price initially expands the used market (Region B), that is, steals away from the new durable market so that the number of consumers not buying any product does not change. However, at some point, higher retail prices reduce the available used units that can be sold. As a result, both markets are reduced and the number of consumers not buying any product increases (Region C). Entering this region, however, can be delayed if the consumers face higher, used-product service rates (compare Fig. 2(a) and (b)). Indeed, higher service rates defer consumers from buying used goods. Accordingly, Region C starts from higher retail prices. The impact on the demand for used goods as a result of the change in the price of the new goods is further elaborated in Propositions 4 and 5 (see Appendix A). In the next section we study equilibrium pricing by the manufacturer and retailer. Monopoly equilibrium pricing Given the demand for new and used goods, we now study the interaction between the supply chain which sells new and

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K. Kogan / Journal of Retailing 87 (4, 2011) 489–501

used goods along with services for them and the second-hand market. According to our assumptions, the manufacturer’s profit is only due to the new product sales, ΠM = wDN .

(10)

The retailer’s profit, on the other hand, depends on both new and used goods as well as the charges for the service provided, ΠR = (pN + SN − w − ps )DN + (ps + sU )DU .

(11)

Since both parties simultaneously maximize (10) and (11), the first order optimality conditions applied to (10) and (11) result in a Nash solution, which we discuss next in relation to different conditions. Note that the retailer has complete control of the retail price and thus can play in any of regions depicted in Fig. 1. Accordingly, the kinked demand curves illustrated in Fig. 2 imply that the parties may have multiple equilibria. These equilibria will correspond to interior points of the pricing regions of Fig. 1 as well as to the boundaries of these regions as the retailer may suggest a pricing barrier to induce a specific type of equilibrium. This is to say, the retailer has two options. 1. Charge the standard, bi-lateral, monopoly retail price (thus resulting in double marginalization) or 2. Alter the price to play either at a boundary of the same region or in a different region, possibly reducing the double marginalization effect. One main driver for deciding the extent to which the retailer alters price is the magnitude of the externally determined, second-hand market service fee. The reason for this is that the higher the service fee, the lower the price that can be charged for the used unit and also the smaller the market size for used units. The other major driver is the magnitude of the difference in value k of the new product versus the old product. In particular, the greater the difference between the two products, the easier it is for the retailer to sell into the two markets, that is, the retailer might be better off by pricing in Regions B or C. On the other hand, if there is little difference in the quality of the new and old units, then it is hard for the retailer to segment the two potential markets. (In other words, there is considerable “intrabrand” competition.) Thus the retailer might want to reduce this competition by eliminating the used market so that the retailer can operate in a different region of the kinked demand function. To decide which equilibrium will be adopted by the parties in the specific environment (sU , sN , v, and k), we compare the profits that the parties can gain under alternative equilibrium solutions. In particular, we first establish the specific conditions (which are a function of sU ) for when the retailer should choose the region in which to set prices and then examine them under different levels of k. No second-hand markets Consider first the case when the second-hand market is priced out of existence for whatever reason with pN ≤ sU (1 + k/v) − sN

(region A, Fig. 1). Then, with respect to Proposition 2, the objective functions (10) and (11) transform into   sN + w + m ΠM = w 1 − . (12) v+k   sN + w + m ΠR = (m + sN ) 1 − . (13) v+k Both functions are concave in the corresponding decision variables, w and m. Consequently, the equilibrium pair we and me is we =

v+k v+k and me = − sN , 3 3

(14)

which leads to the standard bi-lateral monopoly equilibrium price for the new goods peN =

(v/k)2 . 3 − sN

(15)

On the other hand, the system-wide optimal solution, that is, the optimal solution for a centralized  supply chain, pN *, which  maximizes the overall profit M + R is p∗N =

v+k . 2 − sN

(16)

The retailer’s margin m* and manufacturer’s wholesale price w* are then the supply chain internal transfers that can be chosen arbitrarily under the centralized approach so that m* + w* = p*. Consequently, the classical double marginalization effect is observed from an increased price peN > p∗N and reduced demand e < D∗ due to the intracompetition between the supply chain DN N parties, that is, due to the fact that each party accounts only for its margin thereby reducing the overall supply chain profit. Equilibrium pricing policy (15) is identified under the condition that the upper bound on the price for new goods is not violated, pN ≤ sU (1 + k/v) − sN (Region A) or, with respect to (15), when the charges for service of the used goods are high, sU ≥

2 v. 3

(17)

Otherwise, if (17) does not hold, the equilibrium price is set at the upper bound of Region A, peN = sU (1 + k/v) − sN , of the coupled constraint, m + w ≤ sU (1 + k/v) − sN . (A generalized Nash equilibrium, which is also referred to as a coupled constraints equilibrium can be determined by using the normalized equilibrium solution concept proposed by Rosen (1965)). Specifically, assuming the constraint burden is shared in solidarity (Contreras et al. 2007), the shadow prices associated with the coupled constraint become identical for both players, ∂ΠM /∂w = ∂ΠR /∂m This along with the binding coupled constraint results in the following solution:     1 + k/v 1 + k/v (18) and me = sU − sN . we = sU 2 2 Note that substituting equilibrium prices either (15) or (18) in the demand for the new goods, we discover that the equilibrium demand does not depend on newness of the goods. Indeed, when

K. Kogan / Journal of Retailing 87 (4, 2011) 489–501

consumers do not have the alternative of buying used goods, the benefit of newness does not affect their decision under a proper pricing approach. On the other hand, it is readily observed between (15) and (18) that the newness affects the price for the new goods – the lower the newness the lower the price, ensuring steady demand. The next proposition summarizes the pricing policies for Region A. Proposition 6. Let the price of new goods be bounded as pN ≤ sU (1 + k/v) − sN . If sU ≥ 2/3v, then (15) is the equilibrium price of the new goods, which is determined by Nash solution (14). Otherwise, if sU < 2/3v then the equilibrium price is peN = sU (1 + k/v) − sN , determined by Nash solution (18). Zero second-hand prices When sU < 2/3v and the upper bound on the price of new goods is extended, a new Nash solution can be found that makes use of the oversupplied second-hand market (Region B, Fig. 1). Specifically, assuming conditions of Proposition 1 and that the used goods are therefore being freely given away, pU = 0, the objective functions (10) and (11) transform into   m + w + s N − sU . (19) ΠM = w 1 − k 

 m + w + s N − sU ΠR = (m + sN ) 1 − k   m + w + s N − sU sU + sU − . k v

(20)

Functions (19) and (20) are concave and the Nash equilibrium pair we and me is we =

k k and me = − sN + SU , 3 3

(21)

and the standard bi-lateral monopoly retail price is peN =

2k − s N + sU . 3

(22)

Thus, if the feasible range of prices is (1 + k/v)sU − sN < pN ≤ (k/2) − sN + sU (1 + (k/2v)), (see Proposition 1), which with respect to (21) requires service charges for the used goods to be moderate, 1 2 v ≤ sU < v, 3 3

(23)

then the supply chain may encourage the oversupplied secondhand market (Region B) with an equilibrium price (22). This, however, is not the only pricing policy since one of the parties may suggest a pricing barrier to induce the equilibrium conditions determined in Proposition 6 thereby killing off the secondary market. Indeed, since the demand for the new goods is more sensitive to the price when an oversupplied secondhand market is introduced (see Proposition 4), the manufacturer expects reduced profits. Therefore he may suggest the retail price

495

that will eliminate the second-hand market (Region A). Specifically, comparing the manufacturer’s profit when constrained 1 , with that of Π 2 , for solution solution (18) is adopted, ΠM M 2 1 (21), we find that ΠM − ΠM < 0 (see Eq. (A1)). Proposition 7. Let the price of new goods be bounded as pN ≤ (k/2) − sN + sU (1 + (k/2v)) and (1/3)v ≤ sU < 23v. The manufacturer is always better off if the price of the new goods is bounded from above as pN ≤ sU (1 + k/v) − sN . Encouraging and discouraging the second-hand market To decide whether the retailer will adopt the manufacturer’s suggested retail price, we compare her profits due to equilibrium (18), ΠR1 , and equilibrium (21), ΠR2 (see Eq. (A2)). Consequently, if ΠR2 − ΠR2 > 0, that is, 9k(v − sU )(2vsN − sU (v + k)) + 18sU v2 (k − sU ) + 2v2 k2 > 0,

(24)

the retailer has an incentive to encourage the second-hand market (Region B) rather than adopt the manufacturer’s suggested pricing in Region A, as shown in the next proposition. Proposition 8. Let the price of new goods be bounded as pN ≤ (k/2) − sN + sU (1 + k/2v) and (1/3)v ≤ sU < 23v. If condition (24) holds, the supply chain makes use of the second-hand market with equilibrium price (22) determined by Nash solution (21). Otherwise, if (24) does not hold, the supply chain wipes out the second-hand market with equilibrium price peN = sU (1 + k/v) − sN determined by Nash solution (18). Although condition (24) appears awkward for understanding, the circumstances when the retailer takes advantage of the second-hand market are easy to unveil from (24). Specifically, by accounting for (23), feasibility condition of (21), that is, (k/3) − sN + sU ≥ 0, and sU ≥ 0, we have sN ≥ k/3. Then a sufficient condition for (24) to hold is v ≤ k. This condition implies that the supply chain makes use of the second-hand market when the new good is a model that allows for high value services. Proposition 8 does not consider two cases, which we discuss next. One case arises when the service rates are high, sU ≥ 2/3v According to (23), high service rates naturally drive out of existence the second-hand market with equilibrium price (15). The other case of low service rates, sU < 1/3v, has already been covered by Proposition 6. However, when sU < 1/3v, the retailer may want to impose the upper bound of Region B on the price of new goods by setting peN = (k/2) − sN + sU (1 + k/2v). Such a price will eliminate Region C, that is, the full-scale secondhand market. With this pricing policy, we derive an additional (coupled constraint) equilibrium, (1 + sU /v)k (1 + sU /v)k (25) and me = + sU − s N . 4 4 Substituting either (25) or (22) into the demand for new and used goods, we observe that when there is no full second-hand market, the demands for new and used goods are steady regardless of the benefit from newness that consumers obtain when buying new goods. This is because consumers can only give

we =

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their used goods away for free, rather than sell them. Similar to the case of no second-hand market, the steady demand is then ensured by adjusting the equilibrium prices. Since the retailer derives two equilibria (18) and (25) for the same service rates and different pricing barriers, her natural choice of a pricing policy is subject to the equilibrium, which provides her with a larger profit. Accordingly, we next compare the retailer’s profits ΠR1 and ΠR2 due to the upper bounds of Regions A and B, that is, equilibrium prices (18) and (25), respectively (see Eq. (A3)). Consequently, if ΠR3 − ΠR1 > 0, that is, 2 (3k2 + 4kv − 8v2 ) + 4kvsU (v − k) + sN kv(v − sU ) sU

+ v2 k2 > 0,

(26)

the retailer will not set an additional barrier to strangle the oversupplied second-hand market, as shown in the next proposition. Proposition 9. Let the price of new goods be bounded as pN ≤ (k/2) − sN + sU (1 + (k/2v)) and sU < (1/3)v. If condition (26) holds, the supply chain makes use of the second-hand market with equilibrium price peN = (k/2) − sN + sU (1 + (k/2v)) determined by Nash solution (25). Otherwise, if (26) does not hold, the supply chain wipes out the second-hand market with equilibrium price peN = sU (1 + k/v) − sN determined by Nash solution (18). Note that a sufficient condition for (26) to hold is v ≤ k. We thus observe again that the supply chain makes use of the secondhand market when the new good is characterized by a high value of newness. Henceforth, we refer to the level of newness k as low if both (24) and (26) do not hold, while k ≥ v will be viewed as a high level of newness. We also consider k > 2v to be unrealistically high. Positive second-hand prices We next study pricing policies emanating from Proposition 3. Specifically, if the price range is such that (k/2) − sN + sU (1 + (k/2v)) < pN < 2v + k − sU − sN (Region C, Fig. 1), then both markets of new and used goods exist and pS > 0. Consequently, the profit functions (10)–(11) take the following form ΠM

m + w + sN + sU + 2v = w(1 − ). 4v + k

ΠR = (m + sN + sU )(1 −

m + w + sN + sU + 2v ). 4v + k

(27) (28)

Both profit functions (27) and (28) are strictly concave in their decision variables and the corresponding Nash equilibrium pair we and me is me =

1 1 2 2 v + k − sU − sN and we = v + k, 3 3 3 3

(29)

while the equilibrium price is pN e =

4 2 v + k − s U − sN 3 3

(30)

Thus, when (k/2) − sN + sU (1 + (k/2v)) < pN < 2v + k − sU − sN , which with respect to (30) implies sU <

1 8v + k v, 3 4v + k

(31)

then (30) is the standard bi-lateral monopoly equilibrium price. This, however, is not the only equilibrium pricing policy and we again reveal multiple equilibria. Indeed, since (2/3)v > (1/3)(8v + k/4v + k) > (1/3)v, we derive two cases. One occurs when the service rates are low sU < (1/3)v. Then with respect to Proposition 9, if (26) holds, we need to compare the retailer’s profit due to the Region C (equilibrium (29)), ΠR4 , and due to the upper bound of B (equilibrium (25)), ΠR3 . Otherwise, if (26) does not hold, we compare the retailer’s profit under solution (29), ΠR4 with that under (18), ΠR1 . That is, the retailer chooses between Regions A and C. Specifically, from ΠR4 − ΠR3 (see Eq. (A4)) we find that ΠR4 − ΠR3 > 0 if 2 32v2 − 4kv3 − v2 k2 + (108kv + 288v2 + 9k2 )sU − (72kv2

+ 288v3 )sU > 0.

(32)

Condition (32) holds when the service rates constitute only a few percents of the value v of the used goods services. For example, when k = v, ΠR4 − ΠR3 > 0 holds for sU ≤ v/15. Let condition (32) transform into equality when sU = ε˜ v. Then when sU < ε˜ v, the retailer prefers balanced second-hand market to the oversupplied one. Interestingly, the manufacturer always gains 4 − Π 3 (see Eq. (A5)) is from the full used market since ΠM M positive for any realistic k. Thus we arrive at Proposition 10. Proposition 10. Let the benefit from newness be low. If sU < ε˜ v, then both the manufacturer and the retailer, by using the second-hand market (Nash solution (29)) with nonzero service charges, earn larger profits than from the oversupplied secondhand market (Nash solution (25)). Similarly, when (26) does not hold, we find from ΠR4 − ΠR1 = 1 (see Eq. (A6)) that if − ΠM

4 ΠM

2 8v4 + 8kv3 + 2v2 k + (36v2 + 45kv + 9k2 )sU − (368v3

+ 45v2 k + 9vk2 )sU ≥ 0

(33)

then the second-hand market is preferred. Indeed, it is preferred by both parties. Again we observe that this condition holds if sU is small, sU < εv, where sU = εv transforms (33) into equality. This also implies that in case of (1/3)v ≤ sU < (1/3)(8v + k/4v + k)v, both parties prefer equilibrium (18), which suppresses the second-hand market. Proposition 11. Let the benefit from newness be low. If sU < εv, then both the manufacturer and the retailer gain larger profits by using the second-hand market (Nash solution (29)) rather than by wiping it out (Nash solution (18)). From Propositions 10 and 11 we conclude that if the service charges are very low, the full-scale second-hand market increases the overall profit of the supply chain compared to an oversupplied second-hand market or no used market at all. This, however, does not imply that the supply chain is better off when

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the second-hand market does not exist regardless of the service rates and primary market prices as will be discussed later. When (1/3)v ≤ sU < (1/3)(8v + k/4v + k)v, we also determine two equilibrium pricing policies. One is derived in Proposition 11 (equilibrium (29)) and the other is from Proposition 8. This implies that if (24) holds, then we need to compare the retailer’s profit due to equilibrium (29), ΠR4 and equilibrium (21), ΠR2 . Otherwise, if (24) does not hold, we have found that equilibrium (18) is advantageous for both parties. Consequently, from A(7) we obtain that ΠR4 − ΠR2 < 0 for moderate service rates, (1/3)v ≤ sU < (1/3)(8v + k/4v + k)v, 4 − Π 2 = (4/9)(v2 /4v + k) > 0. Accordingly, while while ΠM M the manufacturer is better off with the full second-hand market (29) of Region C, the retailer is not. Therefore the retailer will set a barrier with price bound pN ≤ (k/2) − sN + sU (1 + (k/2v)) to encourage the oversupplied second-hand market (Region B) so that only Proposition 8 will be applicable when (1/3)v ≤ sU < (1/3)(8v + k/4v + k)v. Finally, we note that the effect of newness on the demand is different from that observed when the used market is wiped out or oversupplied. Substituting equilibrium price (30) into the demand, we get DN = DU = (2v + k/12v + 3k). This implies that if the benefit from newness shrinks, then the demand for both new and used goods shrinks.

Theorem 2. Let the benefit from newness be high. If sU < ε˜ v, then the supply chain uses the second-hand market with equilibrium price (30) as determined by Nash solution (29) and second-hand price (8). If ε˜ v ≤ sU < (2/3)v, the supply chain utilizes the oversupplied second-hand market with ps = 0. Specifically, if ε˜ v ≤ sU < (1/3)v, then Nash solution (25) determines the equilibrium price pN e = (k/2) − sN + sU (1 + (k/2v)). If (1/3)v ≤ sU < (2/3)v, then Nash solution (21) determines equilibrium price (22). Otherwise, if sU ≥ (2/3)v, then Nash solution (14) determines equilibrium price (15). Theorem 2 illustrates the fact that when the level of the benefit from newness of the goods is high, k ≥ v, the supply chain always makes use of the second-hand market unless the service of the used goods is very expensive, sU ≥ (2/3)v. Indeed, high newness implies a significant margin that the retailer gains from both new and used goods when making use of the second-hand market. Consequently, the retailer is interested in encouraging the second-hand market. Specifically, if sU is small, the retailer operates in Region C. As sU increases, the retailer wants to operate in Region B either at the boundary or unconstrained. In both cases, the retailer lowers the used price to zero thereby compensating for the high service fees. In contrast, very high values of sU imply that there is no substantial market for the second-hand product and thus the retail firm operates in Region A.

Global pricing policy: low newness Based on the pricing policies determined in Propositions 6–9 for specific price ranges, we now conclude with a global policy for any feasible range of prices for new goods. Theorem 1. Let the benefit from newness be low. If sU < εv, then the supply chain uses the second-hand market with an equilibrium price (30) for the new goods as determined by Nash solution (29) and second-hand price (8). Otherwise the secondhand market is wiped out. Specifically, if εv ≤ sU < (2/3)v, then Nash solution (18) determines peN = sU (1 + k/v) − sN as the equilibrium price of the new goods, while Nash solution (14) for sU ≥ (2/3)v, sets the equilibrium price of the new goods at (15). Theorem 1 defines the equilibrium prices of new goods for all possible charges for services for the used goods. Specifically, we observe that except for the case of low service rates, little newness always causes the supply chain to kill off the secondhand market. Theorem 1 is driven by the fact that when k is small, the second-hand market highly impacts the new market, thereby holding down margins. When sU is small, it pays to operate in Region C and sell in both markets. Otherwise, the size of the used market is small. In such cases, the firm finds it best to operate in Region A – either at the boundary or unconstrained. It does so by lowering the retail price. Global pricing policy: high newness We next summarize our result for the case when the benefit from newness is high, k ≥ v.

497

Implications We now contrast the supply chain’s performance when no second-hand market can exist (the base case), regardless of the monopoly pricing and service rates. If the second-hand market cannot exist, then equilibrium (14) is the solution for both parties under any service rates. This situation can occur, for example, when the used goods have a very limited technical durability and therefore become nonoperational after a single period. The manufacturer may also limit the quality improvements of his new versions thereby increasing his profits by reducing double marginalization. Low level of newness We start off using Theorem 1 to compare profits when the service rates are moderate, (1/3)v ≤ sU < (2/3)v, that is, we compare the supply chain profit under equilibrium solution (14) 1 − Π 0 (see and that under equilibrium (18), ΠR1 − ΠR0 = ΠM M Eq. (A8)). From (A8) we observe that both parties are better off with the pricing policy presented in Theorem 1 (equilibrium (18)). In other words, the fact that the new goods can serve more than one period and, hence, have the potential to be resold in the used market induces the retailer to set a barrier on the price of the new goods. With this barrier the retailer strangles the secondhand market and improves the overall supply chain profit. The improvement is due to the reduced price for the new goods p1N − p0N = −(2v2 + 2kv − 3sU (v + k))/3v < 0 and increased 1 − D0 = (2v − 3s /3v) > 0 for εv ≤ demand for them DN U N sU < (2/3)v. Note, in both cases there is no used market, but in the base case this is due to exogenous factors while in the

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analyzed case the retailer decides to price it out of existence. Furthermore, bearing in mind the optimal price (16) for the centralized supply chain, we find that the maximum effect is achieved when sU = (1/2)v in which case the double marginalization is fully eliminated, peN = p∗N . On the other hand, when 4 − Π 0 = −(kv/9(4v + k)) < sU < εv, from ΠR4 − ΠR0 = ΠM M 0, we find that the performance of the supply chain deteriorates. However, the deterioration reduces as the newness decreases. We can also estimate the worst case loss, by setting k = v. Then 4 − Π 0 is below 2.22 percent and the total supply chain loss ΠM M cannot exceed 4.44 percent. We thus conclude with the following result. Theorem 3. Let the benefit from newness be low. If sU ≥ (2/3)v, regardless of whether the second-hand market can exist or not, the supply chain is unaffected. If εv ≤ sU < (2/3)v, the second-hand market coordinates the supply chain. Moreover, not only the overall profit of the supply chain increases, but also the manufacturer and the retailer are better off. The coordination becomes perfect when sU = (1/2)v. Otherwise if sU < εv, then the second-hand market reduces the profits of the both parties in the supply chain.  From Theorem 3 we find that the second-hand market has a positive effect on the supply chain over a wide range of service rates when the level of newness is not high, k < v. This result is due to a barrier that the retailer sets on the price of new goods in order to discourage the second-hand market. Moreover, losses are only possible when the service charges are low. In such a case, the retailer uses the service for the used goods. As a result, the loss that each party incurs is limited to only 2.22 percent at most and the lower the newness, the lower the loss. To elaborate on the effectiveness of the current trend of buying and selling used phones by the retailers, let us assume the supply chain does not deal with used goods. Consider the case of (k/2) − sN + sU (1 + (k/2v)) < pN < 2v + k − sU − sN , which implies that both markets of new and used goods exist, pS > 0. Consequently, profit function (27) does not change while now (28) does not account for the service of the used goods and takes the following form   m + w + sN + sU + 2v . (36) ΠR = (m + sN ) 1 − 4v + k The corresponding Nash equilibrium pair me =

we

and

me

is

1 1 1 1 2 2 v + k − sU − sN and we = v + k − sU , (37) 3 3 3 3 3 3

and the equilibrium price is pN e =

2 2 4 v + k − sU − s N . 3 3 3

(38)

Thus, when (k/2) − sN + sU (1 + (k/2v)) < pN < 2v + k − sU − sN , which with respect to (38) implies sU <

8v + k v, 10v + 3k

(39)

the supply chain uses the second-hand market. Since (8v + k/10v + 3k)v > (1/3)v, we next consider sU < (1/3)v

comparing equilibrium (37) based profit, ΠR5 , with equilibrium (29) based profit, ΠR5 , where the retailer buys and services 4 − Π 5 = (4v + 2k − used goods. We find, ΠR4 − ΠR5 = ΠM M sU /4v + k)(SU /9), which is always positive. Furthermore, the relative improvement of the profit of each party is (4v + 2k − sU /(2v + k − sU ))sU . For example, if k = 1 and sU = (1/4)v (for which condition (33) holds inducing the supply chain to encourage the full second-hand market), then each party improves its profits by 19 percent if the retailer does not ignore the possibility of servicing used goods. The overall loss of the supply chain, compared to the case when no used market can exist, can thus reach up to 2*(19 percent + 2.22 percent) = 42.44 percent. We thus conclude that the current trend significantly improves the performance of the supply chain. High level of newness We next consider the conditions when the level of newness is high, k ≥ v (Theorem 2). Comparing profits due to solutions (21) and (14), we find that although the manufacturer’s profit decreases, the overall supply chain profit improves 2 0 ΠR2 + ΠM − ΠR0 − ΠM =

sU (2v − 3sU ) 2 − v 3v 9 1 1 2 + sU > 0, for v ≤ sU < v. 0 3 3

The manufacturer’s profit decreases because the demand for new goods remains the same while the price for new goods decreases, p2N − p0N = −(2/3)v + sU < 0. The retailer then earns extra profit from used goods. Accordingly, the improvement in the overall supply chain profit is due to offsetting the double marginalization effect. Consider now conditions of Theorem 2 corresponding to low service rates, ε˜ 0 ν ≤ sU < 1/3ν. Then comparing the profits under equilibrium (25) and (14), we detect that the manufacturer is better off when no second-hand market can exist while the retailer gains extra profits with the second-hand market. The 0 = overall supply chain profit is then ΠR3 + ΠR3 − ΠR0 − ΠM 2 2 2 3 (kν + 24sU ν (3 − sU /ν)/3ν) − 9ksU ν − 16ν , which is pos∨

∨

∨

itive for a service charge, sU > εν, ε < ε < 1/3 found solving 3 − Π 0 − Π 0 = 0 in s . Otherwise, the perequation ΠR3 + ΠM U R M ∨

formance of the supply chain deteriorates. For example, ε 0 = 1/4 is a sufficient charge in order for the supply chain to improve ∨ its profit with the second-hand market for ε 0 ν ≤ sU < 1/3ν. Note, that we observe again that due to the second-hand market, the price for the new goods drops, while the demand increases, kν − 3sU (k + 2ν) + 4ν2 3 0 < 0, DN − DN 6ν ν − 3sU > 0. = 6ν

p3N − p0N = −

Thus, in addition to the interval (1/3)ν ≤ sU < (2/3)ν, the second-hand market offsets the double marginalization of the

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supply chain in the primary market also on the interval of

∨ ε0 ν

≤ sU < (1/3)ν. Interestingly, in contrast to the low newness conditions (Theorem 3) where the coordination is due to the supply chain discouraging the second-hand market, the coordination in case of high newness is caused by the supply chain encouraging ∨ the second-hand market. Finally, the case of sU < εv is similar to that discussed in Theorem 3. We thus conclude with the following theorem.

Theorem 4. Let the benefit from newness be high. If sU ≥ 2/3␯, regardless of whether the second-hand market can exist or not, ∨ the supply chain is unaffected. If εν ≤ sU < 2/3ν, the secondhand market coordinates the supply chain. Although the overall profit of the supply chain increases, only the retailer gains extra profit with the second-hand market, while the manufacturer’s ∨ profit shrinks. Otherwise if sU < εv, then the second-hand market reduces the profits of the both parties in the supply chain. Conclusions We consider a monopolistic supply chain, consisting of a manufacturer and a retailer, which faces a perfectly competitive second-hand market. Assuming heterogeneous consumer tastes, we derive the demand for both new and used goods and study the impact of the second-hand market on the supply chain’s profits. We show that although the full-scale second-hand market increases the demand in the primary market, the intracompetition in the supply chain may wipe out this effect. Specifically, compared to the case when no used market can exist, both parties in the supply chain may incur significant losses, if the retailer does not commence reselling and servicing the used goods and the service rates are low. The losses drop, however, to only a few percents when the retailer handles the used goods. On the other hand, the used market has no impact on the supply chain when the service rates are very high. We show that the retailer coordinates the channel by setting the retail price of the new goods to be in the region she finds best. Furthermore, the level of the benefit from newness that the consumer gets when buying new durables is critical. When newness is low, the retailer wants to operate in the region where there is no market for the used good (since the new product is quite similar, albeit better than the used product). Accordingly, the retailer decides to price the second-hand market out of existence. This reduces the double marginalization and leads to profit-Pareto-improving channel coordination since both the retailer and manufacturer gain higher profits. Moreover, when the market service rates are half of the value the consumer gets from the used product, the coordination becomes perfect and the overall profit is equal to that of the centralized supply chain. When the newness is high, k ≥ v, the second-hand market also improves the performance of the supply chain for a wide range of service rates. The cause of the improvement is however different. The retailer’s pricing policy is to flood the secondhand market driving prices there to zero but still allowing some individuals to consume used goods by picking them up for free.

499

Although, the overall supply chain profit increases due to the service of the used goods, only the retailer benefits from the second-hand market. Importantly, the coordination by offsetting the double marginalization is achieved in this case by making use of the second-hand market rather than by driving it out of existence. We thus find that overall, unless the service rates are too low or too high, the second-hand market plays an essential role in improving the performance of the supply chain for a wide range of service rates. A negative impact on performance is observed only when the service rates are too low. Then the supply chain incurs losses compared to the case when the goods are not durable and, hence, no second-hand market can exist regardless of the price for the new goods. These losses, however, can be significantly reduced if the retailer resells and provides services for the used goods. The model we consider assumes that the devices are advancing very rapidly in terms of what they can do. Therefore, the service rates for new and used durables are different and the price for a new device takes into account both the value added by the new services and the charges for them. This is to say, pricing of the new devices is an essential aspect of the market modeled. On the other hand, the general picture is broader. There is a great variety of devices in the market. Some of them provide new services; some do not. In the latter case, the pricing of the new device is based on the vintage of the device and the service rate is no different for new and used durables. Then, the pricing of the services is essential rather than the pricing of the devices and is the subject of our future research. Furthermore, we assumed that if a price ceiling contract is employed by the parties, the burden associated with this constraint is shared equally by both channel parties. This approach is just an initial step in understanding the effect of a second-hand market on supply chain performance. More complex schemes of sharing the constraint burden, including bargaining, is an important research direction for further exploring the results presented in this paper. We also assumed that the interacting firms are of equal power, which is not always the case. Considering one of them, for example, the manufacturer as the Stackelberg leader, is an important research direction especially as the double marginalization effect commonly worsens under power asymmetry. Finally, we considered a monopolistic supply chain in terms of new goods as the manufacturer favors selling and servicing his brand name with a selected agent. A more general situation characterized by competition between supply chains, not only over used goods, but also over new ones, is an important issue to deal with. Appendix A. A.1. Interactions between the primary and secondary markets The first type of interaction is derived by considering the conditions when the second-hand market exists, but consumers voluntarily dispose of the used goods, pS = 0, (see Proposition 1). In this case of no resale value, we observe opposing impacts of the price of the new goods on demand in the two markets,

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(∂DN /∂pN ) = − (1/k), (∂DU /∂pN ) = (1/k), we thus observe that the higher the newness, k, the smaller both demands are affected and the effect of the second-hand market on the primary market is negative, (∂DN /∂DU ) = (∂DN /∂pN )(∂DU /∂pN )−1 = − 1. That is, any increase in the number of consumers buying used goods results in the identical loss in the number of consumers buying new, as shown below. Proposition 4. If SU (1 + k/v) − SN < pN ≤ (k/2) − SN + SU (1 + (k/2v)), when the price of the new goods increases, then sales of the new goods fall while the sales of the used goods rise by the same amount. Consequently the oversupply of the market with the used goods decreases. The number of those who do not buy any goods does not change. On the other hand, considering the conditions when both markets exist and the price for the used goods is positive (Proposition 3), that is, the used goods have high resale value, we find that if the price of the new goods rises, demand in both markets drops, (∂DN /∂pN ) = (∂DU /∂pN ) = −(1/4v + k) < 0. Then the number of those who do not buy at all increases, (∂DZ /∂pN ) = (2/4v + k) > 0. This implies a positive impact (the opposite of what is described in Proposition 4) of the second-hand market on the primary one, (∂DN /∂DU ) = (∂DN /∂pN )(∂DU /∂pN )−1 = 1. This effect is reduced by both an increased newness of the new goods and higher value of the used goods. Proposition 5. Let (k/2) − SN + SU (1 + (k/2v)) < pN < 2v + k − SU − SN , then an increase in the second-hand market sales results in a similar increase in primary market sales. Specifically, when the price of the new goods falls, both the sales of the new goods and used goods rise while the number of those who do not buy any goods decreases. Profit comparisons 2 1 ΠM − ΠM =

9sU k(v − sU )(2vsN − sU (v + k)) + 18sU v2 (k − SU ) + 2v2 k2 . 18kv2

(A1) ΠR2 − ΠR1 =

9sU k(v − sU )(2vsN − sU (v + k)) + 18sU 18kv2

v2 (k

− SU

) + 2v2 k2

.

(A2) 2 (3k2 + 4kv − 8v2 ) + 4kvsU (v − k) ΠR3 − ΠR1 = (sU

+ sN kv(v − sU ) + v2 k2 )

1 . 8kv2

(A3)

ΠR4 − ΠR3 +

2 − (72kv2 + 288v3 )s 32v4 − 4kv3 − v2 k2 + (108kv + 288v2 + 9k2 )sU U

4 3 − ΠM ΠM =

72(4v + k)2

2 32v4 − 4kv3 − v2 k2 + 9(4kv + k2 )sU . 72(4v + k)2

.

(A4) (A5)

4 3 ΠR4 − ΠR1 = ΠM − ΠM

=

2 − (36kv3 + 45v2 k + 9vk 2 )s 8v4 + 8kv3 + 2v2 k + (36v2 + 45kv + 9k2 )sU U . 2 18(4v+k)v

(A6)

ΠR4 − ΠR2 = =

2 − (36v + 9k)s 4v2 + (36v + (9k/v))sU U 9(4v + k)

4v2 + (36v + 9k)((sU /v) − 1)sU . 9(4v + k)

1 0 ΠR1 −ΠR0 = ΠM − ΠM =

(A7)

(9sU (v − sU ) − 2v2 )(v + k) . (A8) 18v2

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