The interaction between product rollover strategy and pricing scheme

Accepted Manuscript The interaction between product rollover strategy and pricing scheme Jingchen Liu, Xin Zhai, Lihua Chen PII:

S0925-5273(18)30152-X

DOI:

10.1016/j.ijpe.2018.03.027

Reference:

PROECO 6997

To appear in:

International Journal of Production Economics

Received Date: 25 October 2017 Revised Date:

26 March 2018

Accepted Date: 29 March 2018

Please cite this article as: Liu, J., Zhai, X., Chen, L., The interaction between product rollover strategy and pricing scheme, International Journal of Production Economics (2018), doi: 10.1016/ j.ijpe.2018.03.027. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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The Interaction between Product Rollover Strategy and Pricing Scheme Jingchen Liu a, Xin Zhai a, , Lihua Chen a a

Guanghua School of Management, Peking University, Beijing 100871, China

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Abstract: In high-tech and innovative industries, many firms make joint decisions on product rollover strategy and pricing scheme and offer trade-in programs under some circumstances to encourage repeated purchasing. This

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paper studies the interaction between product rollover strategy and pricing scheme with trade-in program offered, by proposing a two-period model incorporating market heterogeneity and consumers’ forward-looking behavior.

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The results show that for both single rollover and dual rollover, the firm is better off following price skimming when consumers are not strategic enough, and product salvage value is low compared to new product innovation level; otherwise, penetration pricing is preferable. For given pricing scheme, the firm’s optimal rollover strategy depends on product innovation level, salvage value, and how strategic the consumers are. Under either rollover

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strategy, the firm has no incentive to offer the trade-in program under the circumstances when product innovation

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level is low, product salvage value is extremely low or high, or consumers are not strategic enough.

heterogeneity

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1. Introduction

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Key Words: product rollover; trade-in program; strategic consumer; pricing scheme; sequential innovation; market

With the rapid development of technology and economy, manufacturers are launching new products more frequently than ever to expand their market shares and increase their profits, particularly in high-tech industry, e.g., smartphones, tablets, and wearable devices (Koca et al., 2010). With more new products available, some firms

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Corresponding author. Tel.: +86 10 62757460; Fax: +86 10 62753182; Postal Add.: Guanghua Sch Management Bldg 2, Peking Univ, 5 Summer Palace Rd, Beijing 100871, Peoples R China. E-mail addresses: [email protected] (J. Liu), [email protected] (X. Zhai), [email protected] (L. Chen). 1

ACCEPTED MANUSCRIPT phase out old products as soon as the new generation is released, which is called single rollover.1 On the other hand, some firms keep their older products in the market at a mark-down price after launching the new generation, known as dual rollover.2 The trade-off between the two rollover strategies has long been a subject of debate,

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especially when strategic consumer becomes more common in high-tech and innovative industries (Liang et al., 2014; Lobel et al, 2016). Among them the most important considerations are the postponement effect and cannibalization effect (Bala and Carr, 2009; Liang et al., 2014; Yin et al., 2015; Lobel et al., 2016). However, even

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though some extant studies compared the two rollover strategies under different circumstances, none has

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incorporated the trade-in program, a key attribute of the high-tech and innovated industries in recent years. In addition to product rollover strategy, pricing for different generations of products is also a critical decision to both practitioners and researchers. Different from Swinney (2011), Du and Chen (2014), and Whang (2015), who use price skimming and penetration pricing schemes to the same product in different sales periods, Krishnan and

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Ramachandran (2011) apply these two pricing schemes to the sequential introduction of innovative products. They

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use price skimming and penetration pricing to describe the relative positioning of the two generations of products,

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and thus two different demand profiles. Specifically, in price skimming, the initial version of the product is charged at a higher price compared with the new generation. Hence, the initial version is launched exclusively targeting

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high-end consumers, while the new generation is targeting more general consumers. By contrast, in penetration pricing, the initial version is attractive to a wider consumer base with a lower price than does the new generation of product (Besanko and Winston, 1990; Krishnan and Ramachandran, 2011). Penetration pricing seems to be more

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Concerning the single rollover strategy, Apple generally discontinued the old generations of MacBook, iMac, and iPad when introducing the new ones. Nikon superseded the older digital camera by the newer one, for instance, the D7200 was superseded by the D7500 in 2017. A wearables manufacturer Fitbit replaced the old version of fitness wristband Fitbit Charge and Fitbit Flex with Fitbit Charge 2 and Fitbit Flex 2, respectively. Last but not the least, Amazon usually phased out the old generations of portable reader such as Kindle Fire, Kindle Paperwhite, Kindle Oasis when upgrading to new version. Besides, Amazon also replaced the Amazon Echo, a smart home device, with its upgraded version Amazon Echo 2. 2 Concerning the single rollover strategy, Apple continued to sell the older version of Apple Watch, iPhone at a discounted price after the new version is released. Samsung officially sell both the current and former generations of Samsung Galaxy Gears and Galaxy Notes at the same time. In addition, many smartphone and laptop manufacturers such as Huawei, HTC, Dell, Lenovo also follows dual rollover when introducing new products. 2

ACCEPTED MANUSCRIPT common in practice, for example, the price of iPhone 8 is higher than iPhone 7. However, there are also many applications of price skimming in reality3, for instance, the second generation of Amazon Echo Dot is charged at a lower price.

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To encourage repeated purchase, many firms offer trade-in programs under which patrons can return the old-generation product to the firm and obtain a rebate when purchasing the new generation, especially the FMCG electronics. In many of the cases, firms leverage on combinations of different strategies to expand market size. In

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recent years, an increasing number of smartphone and laptop manufactures offer trade-in programs, e.g., Apple,

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Samsung, Huawei, Dell, Lenovo, etc. In addition, almost all of these manufacturers face the joint decision on product rollover and pricing strategies at the same time as well. Rollover strategy, pricing scheme, and trade-in program interact with each other. For example, GoPro, an action-camera maker, provides the trade-in program in 2017, but fails in new product launching due to unreasonable pricing and rollover decisions, and even has to sell the

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whole company now (The Motley Fool News, 2017; CNN Tech News, 2018). Apple sets another example for firms

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using different combinations of strategies under different situations. For instance, Apple uses single rollover for

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iPhone and Apple watch. Regarding pricing scheme, Apple follow price skimming for early models of iPhone, as the release price of iPhone remains $199 from iPhone 3GS to iPhone 6; and then follows penetration pricing for

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later models since the release price increases for each generation after iPhone 6s. Moreover, Apple launched the trade-in program in China in 2015 and restarted it in 2016, but met lukewarm response of Chinese consumers (ZDNet News, 2015; ZDNet News, 2016). To the best of our knowledge, no academic study has studied joint decisions on product rollover and pricing scheme, with trade-in program offered as well. To address this gap, this research studies firm’s joint decisions on product rollover strategy and pricing scheme by taking into consideration

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For example, Sony’s headphone MDR-1000x is priced at $399, while the upgraded version Sony MDR-1000xm2 costs only $349. The price of Sony’s game machine Playstation 4 (PS4) is $399, while the price of the new version Sony Playstation 4 Slim (PS4 slim) is only $299. Amazon upgrades the smart home device Amazon Echo Dot to the second generation in late 2016, which has improved voice recognition but also lower price. The fitness wristband Fitbit Charge 2 is sold at $149.95, also not higher than the last version Charge HR. 3

ACCEPTED MANUSCRIPT the impacts of the trade-in program and strategic customer behavior all together. In this paper, with different levels of strategic consumer taken into account, we explore the following three questions. (1) What is the optimal pricing scheme for a given rollover strategy with trade-in program? (2) What is

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the optimal product rollover strategy for the firm? (3) What is the value of the trade-in program for the firm given any rollover strategy? Our results show that, first, for either rollover strategy, the firm is better off following price skimming when consumers are not strategic enough, and the salvage value is low compared with the new product

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innovation; otherwise, penetration pricing is preferable. Second, for a given pricing scheme, the firm’s optimal

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rollover strategy depends on product innovation incremental value, product salvage value, and how strategic the consumers are. Specifically, if the firm follows price skimming, there is no difference between single rollover and dual rollover. If the firm follows penetration pricing, single rollover is more profitable when consumers are strategic enough, the product innovation increment is low, and the product salvage value is high; otherwise, dual

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rollover strategy is preferable. Third, under either rollover strategy, the firm has no incentive to offer the trade-in

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program when product innovation incremental value is low, the product salvage value is extremely low or high, and

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consumers are not strategic enough.

The rest of this paper is organized as follows. We briefly review the related literature in Section 2 and

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introduce model setting in Section 3. We then study the firm’s optimal pricing decisions in equilibrium for both single rollover and dual rollover strategies with trade-in program in Sections 4 and 5. In Section 6, we study the firm’s optimal rollover strategy. In Section 7, we numerically analyze the impact of the trade-in program under both rollover strategies and conclude the paper in Section 8.

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2. Literature Review 2.1. Research on Product Rollover Product rollover has drawn the attention of researchers for over a decade, but only a few studies compare rollover

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strategies using analytical models and explore the appropriate conditions for both strategies. In the context of durable goods, Levinthal and Purohit (1989) examine the effects of both cannibalization and postponement when introducing an improved version of a current product. Lim and Tang (2006), Ferguson and Koenigsberg (2007),

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Arslan et al. (2009), and Koca et al. (2010) study the optimal product rollover strategy by considering a firm’s

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decisions on pricing, timing of new product launches, and inventory, respectively. Liang et al. (2014) study the interplay between different product rollover strategies and strategic consumer behavior and find that single rollover is more valuable when the innovation level of new product is low and the number of strategic consumers is high. Zhou et al. (2015) focus on the fashion industry, where consumers may buy multiple products in different

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generations rather than only one durable product, and take the consumer’s mental book value of changing products

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into consideration. However, none of the above papers considers the trade-in program. In this paper, we incorporate

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not only the influence of the trade-in program on the optimal product rollover strategy and pricing scheme, but also the effect of consumers’ strategic purchasing behavior in a setting with sequential product innovations.

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2.2. Research on Trade-in Program

A trade-in program allows customers to obtain a new product at a discounted price if they return the old product. Ray et al. (2005) develop a single period model, in which the monopolist firm adopts price discrimination by offering a trade-in rebate and charges a higher price to first-time buyers, to study three pricing schemes. van Ackere and Reyniers (1995) consider a monopolist who sells the same product in two periods and divide consumers into holders and non-holders in the second period, to investigate the effect of the trade-in discount with different levels of consumer rationality. Chen and Hsu (2017) examine the market segmentation effect by considering trade-ins and

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ACCEPTED MANUSCRIPT certified pre-owned options for a durable good firm facing strategic consumers. The above papers focus on the durable goods and assume that the firm sells the same product. However, the following papers are more relevant to our study because they assume that the firm sells two generations of products, and the newer version has a higher

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level of quality and/or innovation (Fudenberg and Tirole, 1998). Bala and Carr (2009) investigate the role of product improvement and user upgrade costs on pricing decisions in the computer software industry. Heese et al. (2005) and Ferrer and Swaminathan (2006) consider duopoly competition and examine the effect of

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remanufacturing the take-back product. In view of market heterogeneity and uncertainty, Yin and Tang (2014) and

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Yin et al. (2015) analyze a two-period dynamic game model to determine the optimal pricing and trade-in decisions with forward-looking consumers in the presence and absence of an up-front fee. However, all the aforementioned studies focus on single rollover strategy with trade-in program. Actually, after introducing a new-generation product, many firms not only offer a trade-in price for customers buying the new product, but also sell the

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old-generation product to new consumers (especially lower-end consumers) at the same time. Therefore, we study

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the value of the trade-in program on both single rollover and dual rollover.

2.3. Research on Strategic Consumers

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“Strategic consumer” is a term widely used in literature on economics, marketing, and operations to describe

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rational consumers who take future purchase options into consideration when making decisions in the current status. A growing number of studies on how strategic consumer behavior influences firms’ pricing, inventory, new product launching, and timing decisions stem from the seminal works by Su (2007), Aviv and Pazgal (2008), and Su and Zhang (2008). Shen and Su (2007) provide a prominent review of strategic consumer behavior in revenue management and point out future research directions in this area. Aviv and Pazgal (2008), Su and Zhang (2009), Lai et al. (2010), Dasu and Tong (2010), and Cachon and Feldman (2015) investigate different pricing schemes including responsive pricing and preannounced pricing in the presence of farsighted consumers. Cachon and

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ACCEPTED MANUSCRIPT Swinney (2009, 2011) examine the impact of quick response capability and enhanced product design in the fast fashion industry with uncertain demand. Swinney (2011), Papanastasiou and Savva (2017), and Yu et al. (2016) examine the optimal pricing scheme when the product value is ex-ante uncertain and social learning about the

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product quality is possible. Yin et al. (2009) and Whang (2015) examine the effect of various inventory display format strategies and demand learning using an upfront price commitment scheme. Mersereau and Zhang (2012) study the firm’s pricing decision when facing an unknown fraction of strategic consumers. Besbes and Lobel (2015)

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and Lobel et al. (2016) investigate new product development and introduction decisions under pre-commitment and

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no-commitment strategies. Lobel et al. (2016) show the value of pre-commitment before the release of new product versions with alternating minor and major technology launch cycles.

Different from existing literature, we incorporate the trade-in program to explore its value on the joint decisions for product rollover strategy and pricing scheme given consumers are strategic. As far as we know, this is

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the first study that explore the optimal rollover strategy and pricing scheme jointly with trade-in program offered in

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the context of consumers’ forward-looking behavior, sequential innovation products, and market heterogeneity.

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Particularly, our research focuses on high-tech and innovative products, which have durability and perishability in the meanwhile, thus Bulow (1986) refers to them as the intermediate durable goods. To be more specific, on the one

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hand, products fall in this category can be used over a lengthy period rather than being completely consumed in one use, which is the main characteristic of durable goods. On the other hand, the relative value of current generation of product depreciates as the firm successively introduces new generations of product with higher quality and/or more functions.

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3. Model Description 3.1. The Firm’s Problem In the two-period model, the monopolistic firm with continuous innovation sells product V1 in period 1 and an

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improved generation V2 in period 2. Consumer purchased V1 in period 1 is allowed to exchange it for V2 with some rebate under the trade-in program provided by the firm. Two rollover strategies are available to the firm: single rollover and dual rollover. The firm must choose one rollover strategy before period 1 and make a credible

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announcement to the public (Liang et al., 2014; Zhou et al., 2015). In period 1, only V 1 is available for sale. In

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period 2, only V2 is available for sale under single rollover, while both V1 and V2 are available for sale under dual rollover.

We assume V1 and V2 are of the same marginal production cost, which is a common assumption for high-tech products (e.g., Liang et al., 2014; Ray et al., 2005). Without loss of generality, we set the marginal cost to zero,

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which is appropriate for a product with a high R&D cost but low production cost (e.g., Kornish, 2001;

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Ramachandran, 2007; Bala and Carr, 2009). The innovation levels of V1 and V2 are 1 and

, where

represents the innovation incremental value of V2 compared with V1 (Liang et al., 2014). Under

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both rollover strategies, the firm sets retail prices

and

for V1 and V2 respectively, and trade-in rebate

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.??Under dual rollover strategy, the firm also decides the discounted price V1. Since V1–holders are allowed to buy V2 at

via the trade-in program in period 2,

for guarantees

that even with the trade-in rebate, consumers still have to pay a positive price for V2. Otherwise, the firm will give the new product to V1–holders for free and even some cash back under the trade-in program. Each traded-in product has a salvage value of

to the firm. We assume

reasonability of our results and to eliminate the trivial results.4 Actually,

4

to guarantee the

implies that the salvage value of

makes sense from the perspective of practice. In order to limit the research scope on the comparison of different rollover strategies, we do not consider the refurbishment and resale of each returned old generation. Therefore, the salvage value of V1 to the firm mainly depends on the recycling core components (e.g., mainboard, screen, battery for smartphone, tablet computer, or laptop) 8

ACCEPTED MANUSCRIPT the old generation (i.e.,

) is lower than the maximum absolute incremental value of the new generation (i.e.,

). This assumption guarantees all prices and sales volumes in equilibrium to be both positive and reasonable. Otherwise, if

, the trade-in program shall not be offered in the second period, not only due to the negative

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prices of V1 and V2, but also because of the non-monetary value brought by the trade-in program. The firm is risk neutral with an objective to maximize his total profit over two periods. To simplify analysis, in the base model, we assume the firm is able to fulfill all the consumer demand for both generations of products, which is reasonable for

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high-tech industry, thus the stockout problem is out of the scope of this research (Bala and Carr, 2009; Yin and Tang, 2014; Yin et al., 2015).5

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3.2. The Consumer’s Problem

The consumer’s valuation is heterogeneous. In periods 1 and 2, the consumer’s valuation for V1 is

, which

follows the uniform distribution U[0, 1] (Bala and Carr, 2009; Zhou et al., 2015). In period 2, the consumer’s . All

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valuation for V2 depends on both her valuation for V1 and the innovation level of V2, which is

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consumers arrive in period 1, and without loss of generality, we normalize the potential market size to 1. We assume that consumers are strategic and take their anticipation on price (

in period 2 into

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consideration when making purchasing decisions in period 1 (e.g., Dhebar, 1994; Yin and Tang, 2014; and Yin et al.,

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2015). When making the buying-or-waiting decision, the strategic consumer maximizes her total surplus, with the second-period surplus discounted at rate

. A higher

implies a more strategic consumer and

means the consumer does not anticipate future purchasing opportunity (i.e., myopic consumer). Thus, in this sense, can be viewed as the level of how strategic the consumer is (e.g., Cachon and Swinney, 2011; Swinney, 2011; Yu

and their condition to be further used. However, due to the very fast technology development, product iteration in electronics industry is significantly accelerated, making the salvage value of the old generation very small. On the other hand, , the innovation incremental value, is evaluated from the consumer’s perspective. In this sense, can be interpreted as the incremental value of the new generation product perceived by the consumer, which is hardly to evaluate in an explicitly way and could be very high potentially. 5 According to a review by Gönsch et al. (2013) on strategic consumers, nearly 30% of research papers along this line assume infinite capacity, among which are some quite recent papers, including Shum et al. (2017), Papanastasiou and Savva (2017), Yu et al. (2016), Yin et al. (2015), Zhou et al. (2015), and Yin and Tang (2014). In this research, we study the interaction of product rollover strategy and pricing scheme by minimizing the influence of other factors. Thus, we assume the firm has ample capacity for both generations of products. This simplification is consistent with business practice in Apple, Samsung, and Huawei, etc., as inventory scarcity after the introduction of new product is rarely seen. 9

ACCEPTED MANUSCRIPT et al., 2016; Shum et al., 2017; Papanastasiou and Savva, 2017). Besides, some literature does not discount the second-period surplus, such as Yin and Tang (2014), Yin et al. (2015), which can be viewed as a special case of .

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We assume that if a consumer with V1 wants to purchase V2, she will trade-in V1 for V2 in period 2. We also assume the consumer cannot buy V1 in the secondhand market in period 2. In case of ties between purchasing V1 and V2 in period 2, a consumer buys V2. Similarly, if a consumer is indifferent between buying or not-buying, she

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chooses to buy.

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3.3. Structure of the Game

We model a two-period dynamic game between the firm and potential consumers. We assume that the information structure is complete (Liang et al., 2014; Yin and Tang, 2014; Yin et al., 2015), i.e., all of the preceding parameters are common knowledge, including the innovation incremental value of V2 over V1, the salvage value of V1, the

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level of consumer’s strategic behavior, the market size, and the marginal production cost of both V1 and V2.

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Sequence of events is illustrated in Figure 1. Before period 1, the firm announces his product rollover strategy.

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Based on the selected rollover strategy, the firm determines

in period 1. Strategic consumers decide whether to

purchase V1, considering their willingness to pay and future options. Then, in period 2, the firm determines

under dual rollover strategy. Consumers with V1 purchased in period 1

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under either rollover strategy and

and

decide whether to trade in V1 for V2 or continue using V1, while those who have bought nothing in period 1 decide to buy whether V1, V2, or still nothing.

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Figure 1 Sequence of Events , or

(Dhebar, 1994). Let

before the second period, but they develop rational expectations about

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, and

,

denote the set of consumers who buy V1 based on

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Consumers do not know

,

, and

, . A

subgame perfect equilibrium with rational expectations is a pair of pricing and purchasing decisions that satisfy the following conditions (e.g., Liang et al., 2014; Yin and Tang, 2014; Yin et al., 2015). (1) Given

, a consumer decides whether to purchase V1 to maximize her total surplus over two periods

maximize the second-period profit consumer’s

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(3) The

expectation

.

purchase V1 in period 1, the firm decides

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(2) Given that consumers with

, denoted as

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based on her rational expectation on

is

rational,

,

, and

, i.e., and

to .

equals

to

the

firm’s

optimal

prices,

i.e.,

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.

(4) The firm sets

to maximize his total profit over two periods, i.e.,

.

We then solve the subgame perfect equilibrium with rational expectations following backward induction. Notations are summarized in Table 1. We use superscripts “s” and “p” to denote price skimming and penetration pricing, respectively. Table 1 Summary of Notations Notation

Description

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ACCEPTED MANUSCRIPT Innovation incremental value of V2 over V1 Salvage value of V1 Level of consumers’ strategic behavior

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Consumers’ valuation on using V1 Price of V1 in period 1

,

Price of V2 in period 2

,

Trade-in rebate in period 2

,

Mark-down price of V1 in period 2

,

Demand for V1 in period 1

,

Demand for V2 from new consumers in period 2

,

Demand for V2 from trade-in consumers in period 2

,

Demand for V1 in period 2

D

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,

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4. Equilibrium Analysis under Single Rollover with Trade-in Program

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4.1. The Consumer’s Purchasing Decision

Under single rollover with trade-in program, consumers have four purchasing options, as specified in Table 2.

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Table 2 Consumer Options and Corresponding Total Surplus under Single Rollover with Trade-in Program Notation

NN

Purchasing Option

Consumer Surplus

Buy nothing in either period

NV2

Buy nothing in period 1 and buy V2 in period 2

V1N

Buy V1 in period 1 and still use V1 in period 2

V1V2

Buy V1 in period 1 and trade in for V2 in period 2

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ACCEPTED MANUSCRIPT A strategic consumer makes purchasing decision to maximize her total surplus in two periods at equilibrium, i.e., . Lemma 1 summarizes the strategic consumer’s optimal decision by segmentation. Lemma 1. The strategic consumer’s optimal purchasing decisions under single rollover with trade-in program are

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as follows. (1) If the firm follows price skimming,

(c) when

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, NV2 is optimal;

(b) when

, V1N is optimal;

(d) when

, V1V2 is optimal.

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(2) If the firm follows penetration pricing,

(a) when

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, NN is optimal;

, V1N is optimal;

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(b) when

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(c) when

The threshold value of skimming,

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, NN is optimal;

(a) when

, V1V2 is optimal.

is different in price skimming and penetration pricing (see Figure 2). Note that in price

; while in penetration pricing,

. The price of V2 is discounted by rate

because

strategic consumers discount the second-period surplus and the price paid in the second period. It is noteworthy that the definitions of price skimming and penetration pricing remain the same regardless of single rollover or dual rollover. Specifically, if the firm follows price skimming, all the four consumer segmentations exist, whereas only

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ACCEPTED MANUSCRIPT three of them exist if penetration pricing is used, because NV2 is weakly dominated by V1N as the price of V1 is

)

(b) Penetration Pricing (

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(a) Price Skimming (

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lower than that of V2.

)

Figure 2 Consumer Segmentations under Single Rollover with Trade-in Program

4.2. The Firm’s Pricing Problem as the demand for V1 in period 1,

as the demand for V2 from non-V1-holders in period 2, and

as

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Denote

as the firm’s second-period profit. The firm’s second-period pricing problem is

(1)

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perfect equilibrium. Denote

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the trade-in demand for V2 from V1-holders in period 2. We follow backward induction to obtain the subgame

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(2) (3) (4) (5)

Constraints (2), (3), and (4) ensure that the second-period quantities and prices are nonnegative and reasonable. Specifically, these three constraints guarantee that V1-holders can trade-in V1 for V2 in period 2 at price

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.

ACCEPTED MANUSCRIPT Non-V1-holders should buy V2 at

and the trade-in rebate

can never exceed

.

and

in constraint (5) represent price skimming and penetration pricing, respectively. as the firm’s total profit over two periods, then the firm’s first-period pricing problem is

where

(6)

(7) (8)

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Denote

is the firm’s equilibrium profit in period 2, and constraints (7) and (8) ensure that the first-period

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quantity and price are both nonnegative and reasonable.

Proposition 1. Under single rollover with trade-in program, there is a unique subgame perfect equilibrium for each pricing scheme.

,

,

,

,

,

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(a) when

D

(1) If the firm follows price skimming,

;

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, and

,

,

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(b) when

, and

, and

,

,

.

(2) If the firm follows penetration pricing,

,

,

,

,

,

.

Given Proposition 1, consumers who purchased V1 in period 1 will trade in V1 for V2 in period 2. Moreover, if the firm follows price skimming, he has no incentive to provide any trade-in rebate when the incremental innovation 15

ACCEPTED MANUSCRIPT value for new product is high enough. The main difference between these two pricing schemes lies in the choice of non-V1-holders in the second period. To be more specific, in price skimming, since the firm charges a higher price for V1 than for V2, non-V1-holders purchases V2 in period 2. In penetration pricing, since the firm charges a lower

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price for V1 than that for V2, non-V1-holders will purchase V1 at the discounted price in period 2.

(1)

,

,

.

(2)

,

,

.

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Corollary 1.

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It’s interesting that demand for V1 and demand for V2 from trade-in are the same under both price skimming and penetration pricing, while the equilibrium prices in price skimming are always lower than those in penetration pricing. The intuition is as follows: if the firm follows price skimming, low-end consumers tends to wait and buys V2, while they have no incentive to wait for V2 in penetration pricing because V2 is more expensive. Hence, the

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firm can charge higher prices in penetration pricing to capture more consumer surplus as there is no need to target

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non-V1-holders in period 2.

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Proposition 2. Under single rollover with trade-in program, there exists a threshold value optimal for the firm to choose price skimming, and when

.

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pricing, where

when

,

; when

it is

it is optimal for the firm to choose penetration

when

Proposition 2 implies that when the salvage value of V1 is sufficiently low, price skimming is optimal for the firm. Intuitively, in price skimming, when V1’s salvage value is low, demand for V2 is high; therefore, price skimming wins with “small profits but quick turnover”. In contrast, when the salvage value of V1 is high, the firm is in favor of penetration pricing due to higher profit margin. Furthermore, Figure 3 illustrates the impact of strategic

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ACCEPTED MANUSCRIPT consumers on the optimal pricing scheme. Specifically, when consumers are less strategic, either pricing scheme may be optimal; while, when consumers are strategic enough, the firm always chooses penetration pricing. To summarize, under single rollover with trade-in program, the firm has an incentive to follow price skimming when

(a) Less Strategic Consumer (

)

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consumers are not strategic enough and the salvage value is low.

(b) More Strategic Consumer (

)

D

Figure 3 Optimal Pricing under Single Rollover with Trade-in Program

TE

5. Equilibrium Analysis under Dual Rollover with Trade-in Program

EP

5.1. The Consumer’s Purchasing Decision

Under dual rollover strategy, V1 is still available at a mark-down price in the second period. Consumer’s purchasing

AC C

options are summarized in Table 3.

Table 3 Consumer Options and Corresponding Total Surplus under Dual Rollover with Trade-in Program Notation

Purchase Option

Consumer Surplus

NN

Buy nothing in either period

NV1

Buy nothing in period 1 and buy V1 in period 2

NV2

Buy nothing in period 1 and buy V2 in period 2

V1N

Buy V1 in period 1 and still use V1 in period 2

17

ACCEPTED MANUSCRIPT V1V2

Buy V1 in period 1 and trade in for V2 in period 2

A strategic consumer makes decisions to maximize her total surplus in two periods at equilibrium; i.e., . Lemma 2 summarizes the strategic consumer’s optimal decision by segmentation.

RI PT

Lemma 2. The strategic consumer’s optimal purchasing decisions under dual rollover with trade-in program are as follows. (1) If the firm follows price skimming, , NN is optimal;

(b) when

SC

(a) when

M AN U

, NV1 is optimal;

, NV2 is optimal;

(d) when

, V1N is optimal;

D

(c) when

(e) when

TE

, V1V2 is optimal.

(a) when

, NN is optimal; , NV1 is optimal;

AC C

(b) when

EP

(2) If the firm follows penetration pricing,

(c) when

(d) when

The threshold value of

, V1N is optimal;

, V1V2 is optimal.

is different in price skimming and penetration pricing (see Figure 4). Specifically, if the

firm follows price skimming, all the five consumer segmentations exist, whereas only four of them exist if

18

ACCEPTED MANUSCRIPT penetrating pricing is applied, because NV2 is weakly dominated by V1N since the price of V1 is lower than that of

)

(b) Penetration Pricing (

M AN U

(a) Price Skimming (

SC

RI PT

V2.

)

Figure 4 Consumer Segmentations under Dual Rollover with Trade-in Program

5.2. The Firm’s Pricing Problem

Again, we follow backward induction to obtain the subgame perfect equilibrium. Denote

as the firm’s

TE

D

second-period profit and the firm’s second-period pricing problem is

EP

(9)

(10)

AC C

(11) (12) (13) (14) (15) (16)

19

ACCEPTED MANUSCRIPT Constraints (11) and (12) guarantee that only non-V1-holders buy V2 at (15) ensures that the mark-down price

is no greater than the introductory price

in period 2; constraint

.

as the firm’s total profit over two periods, and the firm’s first-period pricing problem is

(18) (19)

is the firm’s equilibrium profit in period 2, and constraints (18) and (19) ensure the first-period quantity

and price are both nonnegative and reasonable.

M AN U

where

(17)

SC

RI PT

Denote

or buy V1 at

Proposition 3. Under dual rollover with trade-in program, there exists a unique subgame perfect equilibrium for each pricing scheme.

,

,

EP

,

,

AC C

(b) when

,

TE

(a) when

D

(1) If the firm follows price skimming:

,

,

,

,

,

;

,

,

, and

(2) If the firm follows penetration pricing:

,

, and

,

,

,

.

,

, and

,

,

,

.

Proposition 3 illustrates that if the firm follows price skimming, dual rollover will degenerate to single rollover because no one buys V1 at the mark-down price in period 2. However, if the firm follows penetration pricing, the 20

ACCEPTED MANUSCRIPT equilibrium is different from that under single rollover. It is obvious that under either pricing scheme, all V1-holders will trade in V1 for V2 in period 2. Moreover, by using price skimming, the firm has no incentive to provide trade-in rebate when the new product innovation is high enough.

(1)

,

,

,

.

(2)

,

,

,

.

RI PT

Corollary 2.

pricing,

where

; when

it is

it is optimal for the firm to choose penetration

M AN U

optimal for the firm to choose price skimming, and when

SC

Proposition 4. Under dual rollover with trade-in program, there exists a threshold value

when

,

when

.

D

Proposition 4 implies that the optimal pricing scheme under dual rollover stays almost invariant as that under single

TE

rollover. Furthermore, Figure 5 illustrate the impact of strategic consumer on pricing scheme. Specifically, when

EP

consumers are less strategic, either pricing scheme might be optimal; when consumers become more strategic, the

situations.

AC C

firm is better off following penetration pricing. Table 4 summarizes the optimal pricing scheme under different

21

ACCEPTED MANUSCRIPT (a) Less Strategic Consumer (

)

(b) More Strategic Consumer (

)

Figure 5 Optimal Pricing under Dual Rollover with Trade-in Program Table 4 Optimal Pricing under Different Rollover Strategies Single Rollover

Dual Rollover

RI PT

Range

Price skimming

Price skimming

Penetration pricing

,

Penetration pricing

Price skimming

Price skimming

Penetration pricing

Penetration pricing

Penetration pricing

,

,

.

TE

D

Note.

M AN U

Price skimming

Penetration pricing

SC

Price skimming

EP

6. Optimal Product Rollover Strategy With trade-in program offered, Proposition 5 presents the optimal product rollover strategy for given pricing

AC C

scheme. To make these results more distinct, we illustrate Proposition 5 (2) in Figure 6, where the innovation incremental value of V2 over V1 and the -axis is the salvage value of V1. Proposition 5. With trade-in program offered, the optimal product rollover strategy is as follows: (1) In price skimming, the firm is indifferent to dual rollover and single rollover. (2) In penetration pricing, (a) when

, the firm is better off following dual rollover;

22

-axis is the

ACCEPTED MANUSCRIPT (b) when

, there is a threshold

the firm is better off

, the firm is better off following dual rollover;

following single rollover; and when

, the firm is better off following single rollover.

)

(b) Less Strategic Consumer (

)

AC C

EP

TE

D

(a) Myopic Consumer (

M AN U

SC

RI PT

(c) when

; when

(c) Less Strategic Consumer (

) (d) More Strategic Consumer (

)

Figure 6 Optimal Rollover Strategy in Penetration Pricing

Proposition 5 concludes that for given pricing scheme, the firm’s optimal rollover strategy depends on product innovation incremental value, product salvage value, and how strategic the consumers are. In price skimming, the firm does not use dual rollover strategy because no one will buy V1 at the discounted price in period 2. The intuition is that due to the high price of V1, consumers who strategically delay purchasing in the first period have an incentive to wait for V2, instead of V1. In penetration pricing, the firm is better off following single rollover when 23

ACCEPTED MANUSCRIPT consumers are strategic enough and the product innovation incremental value is low. The rationale is as follows. The more strategic the consumers are, the more likely they will delay purchasing. Since dual rollover provides another reason for consumers to wait due to the price markdown of V1, especially when V2 is not innovative

RI PT

enough, the firm has to lower the price of V1 in period 1 to encourage the number of first-period purchases. The low profit margin leads to a weak performance of dual rollover under these conditions. To better understand the optimal product rollover strategy, in Corollary 3 we compare the prices and demands of single (denoted by

SC

subscript ‘S’) and dual (denoted by subscript ‘D’) rollover with trade-in program.

(1)

,

,

,

(2)

,

,

,

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Corollary 3. . .

The above results are instructively reasonable because no matter which rollover strategy the firm follows, he will

D

always adopt the same pricing scheme. To complete our analysis, we obtain the optimal rollover strategy without

TE

considering the constraint of the same pricing scheme using the numerical method. Figures 7, 8, and 9 illustrate the impacts of product innovation incremental value, product salvage value, and level of consumers’ strategic behavior

EP

on the firm’s total profit under different product rollover strategies with the best pricing scheme, respectively. We to represent situations where consumers are more strategic, less strategic, and myopic,

AC C

use respectively. We set

to make sure

to represent upgraded generation with high/low innovation incremental value. We .

24

(a) More Strategic Consumer (

) (b) Less Strategic Consumer (

RI PT

ACCEPTED MANUSCRIPT

) (c) Myopic Consumer (

on Profit under Single/Dual Rollover

TE

D

M AN U

SC

Figure 7 Impact of

EP

(a) High Innovation + More Strategic Consumer (b) High Innovation + Less Strategic Consumer ;

)

(

;

)

AC C

(

(c) Low Innovation + More Strategic Consumer (d) Low Innovation + Less Strategic Consumer (

;

)

( 25

;

)

)

ACCEPTED MANUSCRIPT on Profit under Single/Dual Rollover

(a) High Innovation (

)

(b) Low Innovation (

)

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Figure 9 Impact of

SC

RI PT

Figure 8 Impact of

on Profit under Single/Dual Rollover

It is interesting to note that single rollover is not worse off than dual rollover in almost all of these situations. Figure 7 shows that (1) the firm’s total profit increases as innovation incremental value increases, (2) the difference

D

in profit between single rollover and dual rollover increases as the innovation incremental value increases, and (3)

TE

the marginal effect of incremental innovation value on the firm’s profit becomes smaller. The result is the same as

EP

in Yin et al. (2015), who also find that the firm’s optimal profit under the trade-in program and single rollover invariably increases with product innovation incremental value. Liang et al. (2014) find that single rollover is more

AC C

valuable when new product innovation is low in the case without trade-in program, which is partly consistent with our finding. Figure 8 demonstrates the interaction between product innovation incremental value and product salvage value. In particular, the firm benefits from higher product salvage value when product innovation incremental value is high, but suffers from higher product salvage value when product innovation incremental value is low. Figure 9 illustrates that firm’s profit decreases first and then increases as consumers become more strategic. Both Figures 7 and 9 illustrate that profit difference between single rollover and dual rollover increases as consumers become more strategic.

26

ACCEPTED MANUSCRIPT

7. Value of Trade-in Program In this section, we quantify the value of the trade-in program, and then examine the conditions under which the firm to offer the trade-in program.

RI PT

7.1. Single Rollover without Trade-in Program

Proposition 6 elaborates the subgame perfect equilibria under single rollover without trade-in program.

for each pricing scheme.

(a) when

,

(b) when (c) when

,

,

,

,

,

,

,

,

,

TE

D

(2) If the firm follows penetration pricing:

,

such that:

, and

,

,

Note: Detailed expressions for

,

M AN U

(1) If the firm follows price skimming, there are two thresholds

SC

Proposition 6. Under single rollover without trade-in program, there exists a unique subgame perfect equilibrium

,

,

,

, and

;

, and

,

,

;

;

,

and

.

are provided in the appendix.

EP

Given Proposition 6, it is interesting to note that not all V1-holders will buy V2 in period 2, which is different from

AC C

the results with trade-in program. All V1-holders will buy V2 in period 2 only in price skimming and when new product innovation is moderate. In this regard, trade-in program is highly beneficial for sales growth of V2. Furthermore, if the firm follows price skimming, consumers will skip the first period and only buy V2 in period 2 when product innovation incremental value is sufficiently high. Another interesting observation is that the prices for both V1 and V2 are higher in price skimming than that in penetration pricing. Therefore, in a sense, the trade-in program also impacts firm’s pricing decision.

27

ACCEPTED MANUSCRIPT Proposition 7. Under single rollover without trade-in program, there exists a threshold it is optimal for the firm to choose price skimming, and when

such that when

it is optimal for the firm to choose

satisfies

.

M AN U

SC

RI PT

penetration pricing, where

Figure 10 Optimal Pricing under Single Rollover without Trade-in Program

7.2. Dual Rollover without Trade-in Program

D

Proposition 8. Under dual rollover without trade-in program, there exists a unique subgame perfect equilibrium for

TE

each pricing scheme:

EP

(1) If the firm follows price skimming, there are two thresholds (a) when

,

,

,

AC C

(b) when

,

,

,

,

such that:

,

,

,

,

, and

,

,

; , and

;

(c) when

,

,

,

,

(2) If the firm follows penetration pricing:

,

and

Note: Detailed expressions for

,

,

,

,

, and

,

.

,

,

,

,

28

,

are provided in the appendix.

;

,

ACCEPTED MANUSCRIPT Proposition 8 illustrates that if the firm follows price skimming, dual rollover will degenerate to single rollover. If the firm follows penetration pricing, the results are the same under the two rollover strategies, except that some consumers will wait until period 2 to purchase V1 under dual rollover. Other characteristics are consistent with the

RI PT

case of single rollover. Proposition 9. Under dual rollover without trade-in program, there is a threshold optimal for the firm to choose price skimming, and when satisfies

it is

it is optimal for the firm to choose penetration

SC

pricing, where

such that when

.

M AN U

The following proposition summarizes the firm’s optimal rollover strategy under different pricing schemes. Proposition 10. Without trade-in program, the optimal product rollover strategy is as follows: (1) In price skimming, the firm is indifferent to dual rollover and single rollover. (2) In penetration pricing, when

, the firm is better off following single rollover, and when

,

D

the firm is better off following dual rollover.

TE

Comparing results in Proposition 5 & 10, we see that with trade-in program, all three parameters (i.e., product innovation incremental value, product salvage value, and level of consumers’ strategic behavior) influence the

AC C

makes the difference.

EP

optimal rollover strategy. However, without trade-in program, only the level of consumers’ strategic behavior

7.3. Value of Trade-in Program In what follows, we study the condition under which the firm is better off with trade-in program by quantifying value of the trade-in program, which is defined as the difference in the maximum profit between the case with and without trade-in program, under either rollover strategy. We also study the influence of product innovation incremental value, product salvage value, and level of consumers’ strategic behavior by numerical study. Consequently, the firm has an incentive to offer trade-in program if and only if the value is positive.

29

(a) More Strategic Consumer (

) (b) Less Strategic Consumer (

) (c) Myopic Consumer (

)

SC

on Value of Trade-in Program

TE

D

M AN U

Figure 11 Impact of

RI PT

ACCEPTED MANUSCRIPT

(a) High Innovation + More Strategic Consumer (b) High Innovation + Less Strategic Consumer ;

)

(

;

)

AC C

EP

(

(c) Low Innovation + More Strategic Consumer (d) Low Innovation + Less Strategic Consumer (

;

)

(

30

;

)

ACCEPTED MANUSCRIPT Figure 12 Impact of

(a) High Innovation (

SC

RI PT

on Value of Trade-in Program

)

)

on Value of Trade-in Program

M AN U

Figure 13 Impact of

(b) Low Innovation (

Figures 11, 12, and 13 illustrate the impacts of product innovation incremental value, product salvage value, and level of consumers’ strategic behavior on the value of the trade-in program. It’s interesting to note that the trade-in

D

program cannot always guarantee a profit increase for the firm. Specifically, under either rollover strategy, the firm

TE

has no incentive to offer the trade-in program under the situations when the product innovation incremental value is low, the product salvage value is extremely low or high, or consumers are not strategic enough. Intuitively, when

EP

consumers are shortsighted, they think less about future options and the corresponding surplus; thus, the trade-in

AC C

program doesn’t have much influence on their purchasing behavior. Consequently, the firm’s profit declines because he cannot obtain enough profit from the trade-in buyers. Yin and Tang (2014) and Yin et al. (2015) examine the optimal pricing decisions under single rollover with trade-in program and find that it is beneficial for the firm to offer a trade-in program when the product innovation incremental value is high, which is in accordance with our findings. Similarly, Bala and Carr (2009) find that offering upgrade prices is not always optimal. In addition, the trade-in program is more valuable to the firm when he adopts single rollover, compared with dual rollover, in most cases. From Figure 11, we see that as product innovation incremental value increases, the value of the trade-in program increases when consumers are strategic enough; when consumers are myopic, the 31

ACCEPTED MANUSCRIPT value of the trade-in program increases first and then decreases. Figure 12 illustrates the interaction between product innovation incremental value and product salvage value. Specifically, with a high level of product innovation, the higher the product salvage value is, the higher is the value of the trade-in program. However, with a

RI PT

low level of product innovation, the higher the product salvage value is, the lower is the value of the trade-in program. The firm has no incentive to offer the trade-in program when the product innovation level is low while the product salvage value is high6. This finding differs significantly from Yin and Tang (2014), who find that the

SC

product salvage value invariably has a positive effect on the trade-in program. That is because the firm cannot

M AN U

charge a high enough price when the new product is not attractive enough due to the low innovation level, especially from the non-trade-in buyers. Moreover, profit margin from the trade-in buyers decreases as product salvage value increases because the firm is willing to offer more discount for trade-in. These two effects together lead to a total profit loss in that situation. Furthermore, as shown in Figure 13, when consumers are more farsighted,

D

the value of the trade-in program first decreases and then increases. With a high level of new product innovation,

TE

the value of the trade-in program decreases a little when consumers are sufficiently forward-looking, which cannot

8. Conclusion

EP

happen when product innovation level is low.

AC C

In this paper, we investigate the firm’s optimal product rollover strategy pricing scheme when trade-in program is offered to strategic consumers by proposing a two-period dynamic game model in which a monopolist firm determines his rollover strategy and pricing scheme, while strategic consumers decide whether to purchase immediately or wait for a newer generation. The firm can choose from single rollover and dual rollover. For either rollover strategy, both price skimming and penetration pricing are applicable to the firm. We derive the optimal product rollover strategy and the corresponding pricing scheme. Our results are summarized as follows. First, for

6

This finding verifies the legitimacy of assumption

. 32

ACCEPTED MANUSCRIPT either rollover strategy with trade-in program, the firm is better off following price skimming when consumers are not strategic enough, and the salvage value is low; otherwise, penetration pricing is preferable. Second, for a given pricing scheme, the firm’s optimal rollover strategy depends on product innovation incremental value, product

RI PT

salvage value, and how strategic the consumers are. Specifically, if the firm follows price skimming, there is no difference between single rollover and dual rollover. If the firm follows penetration pricing, single rollover is more profitable when consumers are strategic enough, the product innovation increment is low, and the product salvage

SC

value is high; otherwise, dual rollover strategy is preferable. Third, under either rollover strategy, the firm has no

M AN U

incentive to offer the trade-in program when the product innovation incremental value is low, the product salvage value is extremely low or high, and consumers are not strategic enough.

This paper contributes to the existing literature by bringing together three streams of research on product rollover strategy, trade-in program, and strategic consumer behavior. To the best of our knowledge, no extant study

D

has considered how the existence of the trade-in program influences the optimal product rollover strategy in the

TE

presence of forward-looking consumers. Our study is closely related to Liang et al. (2014), who explore the pricing and inventory issues under each rollover strategy and find the condition under which single rollover strategy can

EP

improve a firm’s profit. However, the difference between our paper and Liang et al. is significant. First, our study

AC C

considers the trade-in program and its effect on rollover strategies, while that of Liang et al. (2014) does not. Second, we explore different pricing schemes under both rollover strategies, while Liang et al. (2014) do not incorporate a variety of pricing decisions. Third, we study a deterministic market and regard dual rollover as a way to segment consumers, while in Liang et al. (2014) firms use dual rollover to clear the leftovers because the market size is a random variable. Fourth, Liang et al. (2014) assume the market consists of high-end customers (strategic and myopic) and bargain hunters who are unbounded in number. Note that the valuation of consumers in each segment is homogenous, while we assume customers are all strategic but value the initial generation of product

33

ACCEPTED MANUSCRIPT heterogeneously. The above distinctions enable us to examine the performance of different rollover strategies in a different market structure. Furthermore, our study provides managerial insights for when to adopt the trade-in program and with which rollover strategy for the high-tech and innovative markets.

RI PT

This research can be extended in several ways. First, in considering strategic consumer behavior, we assume consumers are equally strategic in the market. It would be interesting to investigate a situation in which consumers are heterogeneously strategic, which is common in practice. Second, our model could be extended to incorporate

SC

duopoly competition, in which firms are forced to use dual rollover strategy to enlarge their total market share.

M AN U

Third, we assume that the product innovation incremental value is exogenous and deterministic. However, in practice, firms’ investments in R&D and their product innovation levels are closely. Therefore, the interplay between firms’ R&D investment and product rollover decisions would be an interesting direction for future research.

D

Acknowledgement

TE

This work was supported by the National Nature Science Foundation of China (NSFC) [Grant No. 71772006].

EP

Reference

Arslan, H., Kachani, S., Shmatov, K., 2008. Optimal product introduction and life cycle pricing policies for

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multiple product generations under competition. Journal of Revenue and Pricing Management, 8(5), 438-451. Aviv, Y., Pazgal, A., 2008. Optimal pricing of seasonal products in the presence of forward-looking consumers. Manuf. Serv. Oper. Manag. 10(3), 339-359. Bala, R., Carr, S., 2009. Pricing software upgrades: The role of product improvement and user costs. Prod. Oper. Manag. 18(5), 560-580. Besanko, D., Winston, W.L., 1990. Optimal price skimming by a monopolist facing rational consumers. Manag. Sci. 36(5), 555-567. 34

ACCEPTED MANUSCRIPT Besbes, O., Lobel, I., 2015. Intertemporal price discrimination: Structure and computation of optimal policies. Manag. Sci. 61(1), 92-110. Bulow, J., 1986. An economic theory of planned obsolescence. Q. J. Econ. 101(4), 729-250.

RI PT

Cachon, G.P., Feldman, P., 2015. Price commitments with strategic consumers: Why it can be optimal to discount more frequently than optimal. Manuf. Serv. Oper. Manag. 17(3), 399-410.

Cachon, G.P., Swinney, R., 2009. Purchasing, pricing, and quick response in the presence of strategic consumers.

SC

Manag. Sci. 55(3), 497-511.

M AN U

Cachon, G.P., Swinney, R., 2011. The value of fast fashion: Quick response, enhanced design, and strategic consumer behavior. Manag. Sci. 57(4), 778-795.

Chen, J.M., Hsu, Y.T., 2017. Revenue management for durable goods using trade-ins with certified pre-owned options. Int. J. Prod. Econ. 186, 55-70.

D

CNN Tech News, 2018. GoPro CEO: We’re ‘absolutely’ open to selling company. Jan. 11, 2018.

TE

http://money.cnn.com/2018/01/10/technology/business/gopro-sale/index.html.

EP

Dasu, S., Tong, C., 2010. Dynamic pricing when consumers are strategic: Analysis of posted and contingent pricing schemes. Eur. J. Oper. Res. 204(3), 662-671.

AC C

Dhebar, A., 1994. Durable-goods monopolists, rational consumers, and improving products. Mark. Sci. 13(1), 100-120.

Du, P., Chen, Q., 2014. Skimming or penetration: Optimal pricing of new fashion products in the presence of strategic consumers. Ann. Oper. Res. 1-21. doi:10.1007/s10479-014-1717-0. Ferguson, M., Koenigsberg, O., 2007. How should a firm manage deteriorating inventory. Prod. Oper. Manag. 16(3), 306-321. Ferrer, G., Swaminathan, J.M., 2006. Managing new and remanufactured products. Manag. Sci. 52(1), 15-26.

35

ACCEPTED MANUSCRIPT Fudenberg, D., Tirole, J., 1998. Upgrades, tradeins, and buybacks. Rand. J. E. 29(2), 235-258. Gönsch, J., Klein, R., Neugebauer, M., Steinhardt, C., 2013. Dynamic pricing with strategic customers. J. Bus. Econ. 83(5), 505-549.

RI PT

Heese, H.S., Cattani, K., Ferrer, G., Gilland, W., Roth, A.V., 2005. Competitive advantage through take-back of used products. Eur. J. Oper. Res. 164(1), 143-157.

Koca, E., Souza, G.C., Druehl, C.T., 2010. Managing product rollovers. Decis. Sci. 41(2), 403-423.

SC

Kornish, L.J., 2001. Pricing for a durable-goods monopolist under rapid sequential innovation. Manag. Sci. 47(11),

M AN U

1552-1561.

Krishnan, V., Ramachandran, K., 2011. Integrated product architecture and pricing for managing sequential innovation. Manag. Sci. 57(11), 2040-2053.

Lai, G., Debo, L.G., Sycara, K., 2010. Buy now and match later: Impact of posterior price matching on profit with

D

strategic consumers. Manuf. Serv. Oper. Manag. 12(1), 33-55.

TE

Levinthal, D.A., Purohit, D., 1989. Durable goods and product obsolescence. Mark. Sci. 8(1), 35-56.

EP

Liang, C., Cakanyildirim, M., Sethi, S., 2014. Analysis of product rollover strategies in the presence of strategic customers. Manag. Sci. 60(4), 1033-1056.

AC C

Lim, W.S., Tang, C.S., 2006. Optimal product rollover strategies. Eur. J. Oper. Res. 174(2), 905-922. Lobel, I., Patel, J., Vulcano, G., Zhang, J., 2016. Optimizing product launches in the presence of strategic consumers. Manag. Sci. 62(6), 1778-1799. Mersereau, A.J., Zhang, D., 2012. Markdown pricing with unknown fraction of strategic customers. Manuf. Serv. Oper. Manag. 14(3), 355-370. Okada, E.M., 2001. Trade-ins, mental accounting, and product replacement decisions. J. Consum. Res. 27(4), 423-446.

36

ACCEPTED MANUSCRIPT Papanastasiou, Y., Savva, N., 2017. Dynamic pricing in the presence of social learning and strategic consumers. Manag. Sci. 63(4), 919-939. Ramachandran, K., 2007. Design architecture and introduction timing for rapidly improving industrial products.

RI PT

Manuf. Serv. Oper. Manag. 10(1), 149-171. Ray, S., Boyaci, T., Aras, N., 2005. Optimal prices and trade-in rebates for durable, remanufacturable products. Manuf. Serv. Oper. Manag. 7(3), 208-228.

M AN U

research opportunities. Prod. Oper. Manag. 16(6), 713-728.

SC

Shen, Z.M., Su, X., 2007. Customer behavior modeling in revenue management and auctions: A review and new

Shum, S., Tong, S., Xiao, T., 2017. On the impact of uncertain cost reduction when selling to strategic customers. Manag. Sci. 62(3), 843-860.

Su, X., 2007. Intertemporal pricing with strategic customer behavior. Manag. Sci. 53(5), 726-741.

D

Su, X., Zhang, F., 2008. Strategic customer behavior, commitment, and supply chain performance. Manag. Sci.

TE

54(10), 1759-1773.

EP

Su, X., Zhang, F., 2009. On the value of commitment and availability guarantees when selling to strategic consumers. Manag. Sci. 55(5), 713-726.

AC C

Swinney, R., 2011. Selling to strategic consumers when product value is uncertain: The value of matching supply and demand. Manag. Sci. 57(10), 1737-1751. The Motley Fool News, 2017. GoPro’s new products are too much, too late. Sep.29, 2017. https://www.fool.com/investing/2017/09/29/gopros-new-products-are-too-much-too-late.aspx. van Ackere, A., Reyniers, D.J., 1995. Trade-ins and introductory offers in a monopoly. Rand. J. E. 26(1), 58-74. Whang, S., 2015. Demand uncertainty and the Bayesian effect in mark-down pricing with strategic customers. Manuf. Serv. Oper. Manag. 17(1), 66-77.

37

ACCEPTED MANUSCRIPT Yin, R., Aviv, Y., Pazgal, A., Tang, C.S., 2009. Optimal mark-down pricing: Implications of inventory display formats in the presence of strategic customers. Manag. Sci. 55(8), 1391-1408. Yin, R., Li, H., Tang, C.S., 2015. Optimal pricing of two successive-generation products with trade-in options

RI PT

under uncertainty. Decis. Sci. 46(3), 565-595. Yin, R., Tang, C.S., 2014. Optimal temporal customer purchasing decisions under trade-in programs with up-front fees. Decis. Sci. 45(3), 373-400.

M AN U

pricing of new experience goods. Manag. Sci. 62(2), 410-435.

SC

Yu, M., Debo, L.G., Kapuscinski, R., 2016. Strategic waiting for consumer-generated quality information: Dynamic

ZDNet News, 2015. Apple’s trade-in program meets lukewarm response in China. Apr. 1, 2015. http://www.zdnet.com/article/apples-trade-in-program-meets-lukewarm-responses-in-china/#. ZDNet

News,

2016.

Apple

resumes

trade-in

program

in

China.

Feb.

3,

2016.

D

http://www.zdnet.com/article/apple-resumes-trade-in-program-in-china/.

TE

Zhou, E., Zhang, J., Gou, Q., Liang, L., 2015. A two period pricing model for new fashion style launching strategy.

Appendix

EP

Int. J. Prod. Econ. 160, 144-156.

AC C

Proof of Lemma 1. Figure 2 compares the slopes and intercepts of consumer surpluses corresponding to the four alternatives. It is easy to obtain the optimal purchasing decisions with respect to consumer’s valuation

from

Figure 2. There are three indifferent conditions in price skimming:

, and

,

. In penetration pricing, there are two indifferent conditions: . We get the threshold values by solving these indifferent conditions.

and

□

Proof of Proposition 1. Under single rollover with trade-in program, there are two pricing schemes available to the firm. 38

ACCEPTED MANUSCRIPT (1) If the firm follows price skimming, his second-period pricing problem is

(A1)

SC

RI PT

(A2)

(A4) (A5)

M AN U

The unconstrained solution is

,

should satisfy

. To meet the second-period constraints,

. We add those constraints to the first-period problem, which

D

is

TE

(A6)

EP

(A7)

AC C

(A8)

(A9)

The unconstrained solution is

. Since the upper bound from (A9) is lower

than the unconstrained solution and the first-period profit is concave in

upper bound. Thus, we have

, and

(A3)

, the optimal solution is to set

,

. As

,

if and only if 39

, when

,

,

.

to its

,

ACCEPTED MANUSCRIPT (2) If the firm follows penetration pricing, his second-period pricing problem is

(A10)

SC

RI PT

(A11)

The unconstrained solution is

(A13) (A14)

should satisfy

M AN U

. To meet the second-period constraints,

(A12)

. We add those constraints to the first-period problem, which is

D

(A15)

TE

(A16)

AC C

EP

(A17)

The unconstrained solution is

(A18)

. Since the upper bound from (A18) is lower than the

unconstrained solution and the first-period profit is concave in

bound. Thus, we have

.

,

,

□

40

, the optimal solution is to set

,

,

to its upper

, and

ACCEPTED MANUSCRIPT Proof of Corollary 1. After comparing the equilibria on price, demand, and total profit in price skimming and penetration pricing, we can obtain Corollary 1.

□

Proof of Proposition 2. It is straightforward to obtain the optimal pricing scheme under single rollover with □

RI PT

trade-in program from Corollary 1.

Proof of Lemma 2. Figure 4 compares the slopes and intercepts of consumer surpluses corresponding to these five alternatives. We can obtain the optimal purchasing decisions with respect to consumers’ valuation ,

,

. There are three indifferent conditions in penetration pricing:

M AN U

and

,

SC

4. There are four indifferent conditions in price skimming:

from Figure

, and

. We get the threshold values by solving these indifferent conditions.

, □

Proof of Proposition 3. Under dual rollover with trade-in program, there are two pricing schemes available to the firm.

TE

D

(1) If the firm follows price skimming, his second-period pricing problem is

(A19)

EP

(A20)

AC C

(A21)

(A22)

(A23)

(A24) (A25) (A26) 41

ACCEPTED MANUSCRIPT The unconstrained solution is

second-period constraints,

,

,

should satisfy

. To meet the

. We add those constraints to the

M AN U

SC

RI PT

first-period problem, which is

The unconstrained solution is

,

Thus,

, when

AC C

and only if

(A29)

(A30)

we

,

have

,

,

, the optimal solution is to set

D

bound.

TE

upper

EP

its

(A28)

. Since the upper bound from (A30) is

lower than the unconstrained solution and the first-period profit is concave in

to

(A27)

,

,

, and

,

. As

if

.

(2) If the firm follows penetration pricing, his second-period pricing problem is

(A31)

(A32) (A33) (A34)

42

ACCEPTED MANUSCRIPT (A35)

(A36)

,

. To meet the second-period constraints,

. We add those constraints to the first-period problem, which is

M AN U

should satisfy

(A39)

(A40)

D

(A41)

TE

(A42)

. Since the upper bound from (A42) is lower than the

EP

The unconstrained solution is

AC C

unconstrained solution and the first-period profit is concave in

bound. Thus, we have

,

(A38)

SC

The unconstrained solution is

RI PT

(A37)

,

,

, the optimal solution is to set

,

, and

,

to its upper

,

□

.

Proof of Corollary 2. After comparing the equilibria on price, demand, and total profit in price skimming and penetration pricing, we can obtain Corollary 2.

□

Proof of Proposition 4. It is straightforward to obtain the optimal pricing scheme under dual rollover with trade-in program from Corollary 2.

□ 43

ACCEPTED MANUSCRIPT Proof of Proposition 5. Comparing the equilibria in Propositions 1 and 3, we can obtain the optimal product rollover strategy with trade-in program under the constraint of the same pricing scheme.

□

Proof of Corollary 3. After comparing the equilibria on price and demand under the single rollover and dual □

RI PT

rollover strategy with trade-in program, we can obtain Corollary 3.

Proof of Proposition 6. Under single rollover without trade-in program, there are two pricing schemes available to the firm.

TE

D

M AN U

SC

(1) If the firm follows price skimming, his second-period pricing problem is

. To meet the second-period constraints,

(A44)

(A45)

(A46)

should satisfy

EP

The unconstrained solution is

(A43)

AC C

. We add those constraints to the first-period problem, which is

(A47)

(A48)

(A49)

(A50)

44

ACCEPTED MANUSCRIPT . As the lower constraint

The unconstrained solution is

always

holds,

while

the

upper

constraint

holds

,

which

if

only

if

, then we denote the threshold value of

as

if

and

satisfy

SC

and

only

and

following equilibrium: ,

(b) when

,

, ,

,

,

, and

,

,

,

,

,

where

and

. Thus, we have the

;

, and

, and

D

(c) when

,

M AN U

, and we have

(a) when

and

RI PT

,

if

TE

,

;

,

,

EP

,

;

AC C

.

(2) If the firm follows penetration pricing, his second-period pricing problem is

(A51)

(A52)

(A53)

(A54)

45

ACCEPTED MANUSCRIPT . To meet the second-period constraints,

The unconstrained solution is

should satisfy

. We

add those constraints to the first-period problem, which is

M AN U

SC

RI PT

(A55)

unconstrained solution and the first-period profit is concave in

(A58)

,

,

, the optimal solution is to set

and

.

to its upper

□

D

,

(A57)

. Since the upper bound from (A58) is lower than the

The unconstrained solution is

bound. Thus, we have

(A56)

TE

Proof of Proposition 7. After comparing the equilibria profits in price skimming and penetration pricing, it is □

EP

straightforward to obtain the optimal pricing scheme under single rollover without trade-in program.

the firm.

AC C

Proof of Proposition 8. Under dual rollover without trade-in program, there are two pricing schemes available to

(1) If the firm follows price skimming, his second-period pricing problem is

(A59)

(A60)

(A61)

46

ACCEPTED MANUSCRIPT (A62)

(A63)

,

. To meet the second-period constraints,

. We add those constraints to the first-period problem, which is

M AN U

should satisfy

(A66)

(A67)

D

(A68)

TE

(A69)

and

while

the

AC C

holds,

EP

The unconstrained solution is

always

,

(A65)

SC

The unconstrained solution is

RI PT

(A64)

which

upper

. As the lower constraint

constraint

holds

,

only

if

only

if

, then we denote the threshold value of

as

and

satisfy

if

if

and

and

and

, and we have

following equilibrium:

47

. Thus, we have the

ACCEPTED MANUSCRIPT , ,

(b) when (c) when

,

,

,

,

,

,

,

,

,

,

,

,

where

,

,

,

,

,

,

; , and

, and

SC

,

, and

; ;

RI PT

(a) when

,

,

.

M AN U

(2) If the firm follows penetration pricing, his second-period pricing problem is

(A70)

(A71)

D

(A72)

TE

(A73)

AC C

EP

(A74)

The unconstrained solution is

(A75) (A76)

. To meet the second-period constraints,

should satisfy

. We

add those constraints to the first-period problem, which is

(A77)

(A78)

48

ACCEPTED MANUSCRIPT (A79)

(A80)

. Since the upper bound from (A80) is lower than the

unconstrained solution and the first-period profit is concave in

,

,

,

, the optimal solution is to set

,

,

to its upper

and

SC

bound. Thus, we have

RI PT

The unconstrained solution is

□

M AN U

Proof of Proposition 9. After comparing the equilibria profits in price skimming and penetration pricing, it is straightforward to obtain the optimal pricing scheme under single rollover without trade-in program.

□

Proof of Proposition 10. Comparing the equilibria in Propositions 6 and 8, we can obtain the optimal product

AC C

EP

TE

D

rollover strategy without trade-in program under the constraint of the same pricing scheme.

49

□

.