Pitch It Now or Pitch It Later? Extended Warranty Sales Strategies and the Impact on Manufacturer Warranties
H. Sebastian Heese Kelley School of Business Indiana University 1309 E 10th Street Bloomington, IN 47405
[email protected] Phone (812) 855-2729 Fax (812) 856-5222
February 2008
Pitch It Now or Pitch It Later? Extended Warranty Sales Strategies and the Impact on Manufacturer Warranties
Abstract Consider two competing manufacturers selling their products through the same retailer. If this retailer derives profits from extended warranty sales, the manufacturers face a dilemma in setting their base warranties. While they have incentive to increase their warranties to make their products attractive to consumers, the retailer might prefer selling lower-warranty products to enhance sales of extended warranties. We develop a stylized model to determine and analyze optimal manufacturer and retailer strategies in this setting. Consistent with the ongoing decline in warranties for products that are sold through independent retailers, we show that these dynamics exert downward pressure on manufacturer warranties. Rather than pitching the extended warranty at the checkout after customers have selected a certain product, we show that retailers can often benefit from inducing simultaneous consideration of product and extended warranty characteristics, for example by posting extended warranty information right on the product shelf. The supply chain dynamics under such simultaneous consideration harm the customers, who suffer from further reduction of the manufacturers’ free base warranties.
Keywords: extended warranties, sales strategies, supply chains, channel conflict, competition, product design, game theory
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Introduction
Would you like an extended warranty with that flat-panel TV? When Best Buy charges $400 for a four-year service contract on a $3,000 flat-panel TV, it passes on $160 to the insurers, with the remaining $240 going straight to the bottom line. Extended warranties have profit margins of 5060%, nearly 18 times the margin on product sales. Extended warranty sales account for about half of Best Buy’s operating profit and for all of Circuit City’s (Berner 2004). Because of their high profitability, shoppers today are increasingly likely to hear the above or a similar sales pitch for an extended warranty, and not only in the market for consumer electronics. Estimates are that about 30% of Dell’s and about 43% of Apple’s net income stem from extended warranty sales (Warranty Week 2004). The percentage of consumers purchasing extended warranties range from 30% for products such as automobiles to over 75% on products such as home electronics and appliances (Desai and Padmanabhan 2004). While most extended warranties are sold for automobiles, appliances, and consumer electronics, extended warranties are being offered for virtually any product “from bicycles to wedding jewelry” (O’Hara 2006). In 2005, the extended warranty market was about $16 billion, a 6.5% increase over 2004 (Warranty Week 2006). An extended warranty (service contract, protection plan) is a contract under which the provider offers to service, repair, or replace the product over a limited time period (usually 2-5 years), either for free or at reduced cost. Different from free base warranties that come bundled with the product, extended warranties offer optional additional coverage at a price to the consumer. While most extended warranties extend the duration of warranty coverage, their value often lies in offering additional service options or more flexible terms. Extended warranty contracts can be offered by the product manufacturers, by retailers, or by third-parties. In product categories where retailers control the point of purchase, the direct customer contact has enabled retailers to grow a significant revenue stream from extended warranties, underwritten either by themselves or by independent third-party providers. Given the substantially higher profitability of extended warranties, the primary role of product sales in many product categories is gradually shifting from generating revenue towards enabling warranty sales. An interesting point in case are the markets for appliances and consumer electronics, where most sales are generated by retailers that are independent from the different brand manufacturers. (This is in contrast to most car manufacturers’ supply chains, which are usually more exclusive or vertically integrated.)
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This article considers the dynamics that arise in settings where competing manufacturers sell their products through the same retailer, who derives profits from sales of extended warranties. In this case the manufacturers face an interesting dilemma in setting their base warranties. If customers value warranty coverage, manufacturers have incentive to offer good base warranties to make their products attractive to customers. However, while increasing a product’s base warranty improves its positioning vis-à-vis the competitor’s product, other things being equal, buyers of this product also have less interest in the retailer’s extended warranty, which now offers less incremental benefit.1 Hence, if the retailer has a means to affect sales of the manufacturers’ products (e.g., through sales effort or retail pricing), her interest in extended warranty sales creates a quandary for the manufacturers. How should the manufacturers adjust their base warranties and their products’ profitability to the retailer? Clearly, these dynamics are substantially affected by how customers make their purchase decisions regarding products and extended warranties. Observations of most retail environments suggest a sequential shopping pattern, where customers first make their product purchase decisions based on how the products’ characteristics, base warranties, and retail prices match their preferences, before they proceed to the checkout, where they are confronted with the retailer’s extended warranty pitch. However, some retailers have started posting information regarding their extended warranty offerings right next to the products on the shelf, supporting simultaneous consideration of product and extended warranty characteristics by the consumers. How does either choice pattern affect the supply chain dynamics and retailer profits? Hence, this research is guided by the following research questions: 1) How should manufacturers adjust their products’ warranties and sales commissions if retailers sell extended warranties? 2) What is the impact of the customers’ purchase pattern? Should a retailer support sequential choice (product decision before extended warranty decision) or simultaneous choice? To address these questions, we develop a stylized model of two manufacturers selling through a single retailer, who offers extended warranties. We use standard game-theoretic analysis to gain insights into the dynamics that result from the different parties’ individual
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The extended warranties offered by most retailers (e.g., Best Buy, Circuit City, CompUSA/Good Guys) overlap with the manufacturer’s warranty period (Berner 2005).
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incentives. The manufacturers competitively set their levels of base-warranty coverage as well as the retailer’s commissions associated with sales of their products. Given these base warranties and product profit margins, the retailer determines which product to push via sales effort, balancing profits from product sales against those from extended warranty sales. We compare the equilibrium outcomes under the two alternative models regarding the consumers’ shopping pattern (sequential vs. simultaneous) to gain insights into optimal extended warranty sales strategies for the retailer. This paper is structured as follows. We review the related literature in the following section 2, and we introduce our mathematical model in section 3. In section 4, we consider a base case without extended warranty sales to illustrate the impact of extended warranty sales on the retailer’s sales incentives. We derive and analyze the equilibrium solutions under the sequential and the simultaneous model in sections 5.1 and 5.2, respectively. In section 5.3, we investigate how the purchase pattern affects the different constituents and which purchase pattern the retailer should induce. We conclude with a discussion of our results in section 6. Additional technical results and all proofs are relegated to the Appendix. 2
Literature Review
There is wide research on product warranties that suggests they have three primary functions. One function is that of insurance against product failure, allowing customers to shift risk to sellers, who are usually less risk-averse (cf. Heal 1977). The work of Spence (1977) laid the foundations of what often has been referred to as the signaling function of warranties, which proposes that warranties can signal product reliability to consumers (e.g., Grossmann 1981, Wiener 1985, Kelley 1988, Gal-Or 1989, Lutz 1989, Welling 1989, Boulding and Kirmani 1993, Agrawal et al. 1996, DeCroix 1999, Kirmani and Rao 2000, Balachander 2001, Soberman 2003). Manufacturers can also use warranties as screening tools to extract additional profitability from heterogeneous customers (e.g., Braverman et al. 1983, Kubo 1986, Matthews and Moore 1987, Padmanabhan and Rao 1993, Lutz and Padmanabhan 1995, Soberman 2003). Much of the above mentioned research relates to the problem of (double) moral hazard, which arises when the seller’s and/or the buyer’s actions are unobservable (and thus non-contractible), and when these actions interact through warranty contracts. While the seller’s product quality choice is private information, the buyer affects the likelihood of warranty execution through product usage and care (e.g., Cooper and Ross 1985, Mann and Wissink 1988, Dybvig and Lutz 1993, Lutz and 4
Padmanabhan 1998, Balachandran and Radhakrishnan 2005). There has also been wide research on the costs associated with warranty execution, its interdependencies with product reliability, and on the provider’s optimal warranty reserve (Menke 1969, Blischke and Scheuer 1975, Mamer 1982, Nguyen and Murthy 1984a/b, Balcer and Sahin 1986, Mamer 1987, Frees and Nam 1988, Thomas 1989, Kao and Smith 1993, Murthy et al. 1995, Padmanabhan 1995, Patankar and Mitra 1995, Chen et al. 1998). Blischke (1990), Murthy and Blischke (1992), Blischke and Murthy (1992), Djamaludin et al. (1996), Thomas and Rao (1999) and Murthy and Djamaludin (2002) provide extensive reviews of these different streams of warranty research. More recently, there has been increasing research interest in extended warranties (or service contracts) that, unlike standard base warranties, do not come bundled with the product, but are available to customers at an additional cost (cf. Padmanabhan 1996). Chen and Ross (1994) show that if the usage pattern of some customers is more likely to result in product failure, selling extended warranties at a price above expected cost allows manufacturers to recuperate the extra cost of servicing intense users during the period the base warranty coverage. Lutz and Padmanabhan (1995) demonstrate that consumer moral hazard in the presence of a competitive warranty market creates a negative externality on the warranty redemption cost of the manufacturer, leading the manufacturer to offer only minimal warranty coverage to begin with. In this article, we demonstrate that the retailer’s interest in extended warranty sales might exert downward pressure on manufacturer warranties, thus providing a possible alternative explanation for low warranties. Lutz and Padmanabhan (1998) study how the presence of an independent extended warranty provider affects a manufacturer’s optimal product and warranty offerings. They show that competition in the warranty market might at times increase manufacturer profits, as the availability of extended warranties increases the attractiveness of the product and thus relaxes the participation constraint in the manufacturer’s product line design problem. Generally, the research on the functions and the design of (extended) warranties has primarily studied the interactions that arise between a (most often monopolist) seller and customers. In contrast, the focus of this article lies on the interest conflict that arises in a supply chain where two competing manufacturers provide base warranties that have a negative externality on the retailer’s sales of extended warranties. Given this focus on the dynamics between the supply chain partners, our description of the customer demand for warranties is kept
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simple. Kelley (1996) provides a discussion of how warranties can affect consumers’ product choice. Padmanabhan (1996) suggests there is “little understanding at present of the role of channel intermediaries in warranty policies” (p. 450). To the best of our knowledge, there are only two articles that explicitly consider the implications of supply chain interactions in this context. Desai and Padmanabhan (2004) consider a manufacturer (monopolist), who sells a product and an extended warranty to customers, who differ in terms of their valuation of warranties (riskaversion). While the product is always sold through the retailer, they consider three different distribution channel choices for the extended warranty: direct, through the retailer, or through both channels. They contrast the negative implications of double marginalization in a decentralized supply chain with the beneficial complementary goods effect that arises as an attractive warranty offering increases product demand. They show that selling the extended warranty alongside the product induces the retailer to internalize this positive externality, mitigating the double marginalization effect and leading to improved channel coordination. Consistent with this notion, Desai and Padmanabhan (2004) find that, if the extended warranty is provided by a third party provider, this provider should always sell through the retailer to benefit from this complementary goods effect. Similar to Desai and Padmanabhan (2004), Li et al. (2005) model a supply chain, where a single manufacturer sells a product through a retailer, and they study how optimal extended warranty terms change depending on whether the extended warranty is sold by the manufacturer or the retailer. They show that offering extended warranties through the retailer leads to longer warranty coverage and higher system profit than offering it through the manufacturer. They also consider a fully integrated supply chain as a benchmark and suggest possible channel coordination mechanisms. Our work differs from that of Desai and Padmanabhan (2004) and Li et al. (2005) in several important aspects. While Desai and Padmanabhan and Li et al. consider a single manufacturer (monopolist) and focus on optimal terms and distribution arrangements for the extended warranty itself, we assume a given supply chain structure with two manufacturers selling their product-warranty-bundles through a single independent retailer. In our model the retailer offers an extended warranty of exogenous coverage and price that can be purchased jointly with either product, on top of the manufacturer warranty. While we assume that the terms of the extended
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warranty are given, both manufacturers adjust their base warranty levels, competing for product sales. (Both Desai and Padmanabhan (2004) and Li et al. (2005) suggest modeling competition as an important avenue for future research.) Hence, while either manufacturer’s productwarranty-bundle exhibits a complementary goods property as in Desai and Padmanabhan and Li et al., the retailer’s interest in extended warranty sales adds a negative externality between manufacturer warranties and product sales, due to the retailer’s incentive to support the lowerwarranty product to increases her profits from extended warranty sales. The impact of extended warranty sales on the retailer’s sales incentives and the optimal adjustments of the manufacturers’ decisions are the key focus of our research. Finally, Desai and Padmanabhan and Li et al. assume that customers consider product and extended warranty offerings simultaneously. However, in many purchase environments customers are confronted with the extended warranty offering only after having made their purchase decision. We compare equilibrium solutions under both product purchase patterns to address the question whether (or when) the retailer benefits from inducing customers to consider extended warranties already when selecting the product. 3
The Model
Assume there are two manufacturers ( i = 1,2 ) who sell two competing products through the same retailer. We first consider the case where customers make decisions regarding the purchase of manufacturer-offered products and retailer-offered extended warranties in a sequential manner. Specifically, customers first compare the two manufacturers’ products and purchase the product they prefer; they then proceed to the checkout, where they are offered an extended warranty by the retailer. Differences that arise under the alternative setup with simultaneous choice of product and extended warranty are considered in section 5.2. From the customers’ perspective, the two products differ in three characteristics. Each product’s intrinsic value, not including warranty valuation, is reflected in its reservation price Ri which is the maximum price a customer would be willing to pay for the product with no warranty. Customers compare this reservation price to the product’s retail price Pi to derive their
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net valuation of the product (without warranty). Finally, customers consider each product’s base warranty of length wi .2 Rather than on pricing, our focus lies on how the retailer’s interest in extended warranty sales affects the base warranties and sales of the manufacturers’ competing products, and on the impact of different customer purchase patterns. In line with this focus, we assume that retail prices for the two products are fixed, and in the following we consider only those customers that are willing to purchase one of the two products, given those exogenous retail prices. Defining the relevant population of customers this way allows us to use a model with fixed market size and full market coverage, such that the effects of competition between the two manufacturers manifest directly in their respective market shares. For given retail prices, the two manufacturers determine how much of their per-unit profit margin to pass on to the retailer in terms of sales commissions. Individual customers differ with respect to their taste preferences for either manufacturer’s product and with respect to their willingness to pay for warranty coverage. Let d denote a customer’s type with respect to manufacturer (or product) taste preferences and let r denote a customer’s type with respect to warranty valuation. We use a Hotelling-type model to account for differences in product taste preferences, and we assume that customer types are uniformly distributed along a line of unity length, where the two products exactly meet the preferences of the customers at the extremes of that line. We use the parameter t to capture the strength of customer taste preferences, such that a customer of type d associates a disutility of td with the consumption of product 1 and a disutility of t (1 − d ) with product 2. Customer types regarding warranty valuations are also uniformly distributed. A customer of type r ∈ [0,1] derives an extra utility (in monetary terms) of θ w r per unit of warranty coverage. To keep our model analytically tractable, we assume these two dimensions of customer heterogeneity are independent. Finally, the customers’ product choice is affected by the retailer’s sales effort for either product ei . Let
θ e denote the effectiveness of such effort, such that sales effort of magnitude ei increases a customer’s valuation of product i (in monetary terms) by θ e ei .
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We assume the customers’ valuation for a product is independent of the product’s warranty, i.e. we do not capture signaling aspects of product warranties. However, our model can be easily adjusted to a scenario where customers interpret (base) warranty coverage as a signal of product quality.
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Using d1 = d and d 2 = 1 − d , the utility that a customer of type ( d , r ) associates with the purchase of product i is U i ( d , r ) = Ri − Pi + θ e ei − td i + θ w rwi . For a given warranty valuation type r , define the customer taste type d (r ) as the one that is indifferent between the two products and thus solves the equality U 1 (d (r ), r ) = U 2 (d (r ), r ) . Throughout the paper, we focus on market sharing equilibria with positive sales and profits for both manufacturers. For simplicity of exposition, we assume that no manufacturer captures all sales to customers of a given warranty valuation, i.e. we assume 0 < d ( r ) < 1 for all r ∈ [0,1] . While the location of d (0) is independent of the two manufacturers’ warranty offerings, the location of d (1) is a function of their warranties. d ( 0) =
1 ( R1 − P1 ) − ( R2 − P2 ) + θ e (e1 − e2 ) + 2 2t d (1) = d (0) +
θw 2t
(1)
( w1 − w2 )
(2)
Figure 1 illustrates our demand model and market shares for the two products for the case where the product of manufacturer 1 is less liked by customers that do not value warranties (i.e. d (0) < 1 / 2 ), but comes with a better warranty than product 2 ( w1 > w2 , so d (1) > d (0) ). In the
coming illustrations, customer taste types are distributed horizontally and warranty valuation types are drawn vertically. d (1) r =1 B
•
Manufacturer 1
Manufacturer 2
A
•
r =0 d =0
d ( 0)
d =1
Figure 1: Illustration of the Demand Model – Decision 1: Product Choice
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Consider two individual customers A and B. In the example illustrated in Figure 1, customer A with (d A , rA ) = (0.8,0.2) has a strong preference for product 2, but does not care much about warranty coverage, whereas customer B with (d B , rB ) = (0.5,0.8) is indifferent between the two products per se, but values warranty coverage. While customer A would prefer product 2, customer B would decide for product 1 with its superior manufacturer warranty. Using the indifferent customers, sales of the two products can be derived as S1 =
d (0) + d (1) , and 2
(3)
S 2 = 1 − S1 .
(4)
Manufacturer i ’s per-unit production cost depends on the warranty coverage associated with his product. Specifically, we assume that the per-unit cost is quadratic (increasing) in the manufacturer warranty with C i ( wi ) = ci + k i wi2 . (While product reliability is exogenous to our model, differences between the two products in that dimension could be captured through differences in their warranty cost parameters.) With fixed retail prices, the manufacturers’ warranty decisions determine the products’ total profit margins. We assume that each manufacturer can determine how much of this per-unit profit margin to pass on to the retailer. (Recall that the two manufacturers have incentive to keep their products attractive to the retailer, as they compete for the retailer’s sales effort.) Let mi denote the profit that the retailer derives from the sale of a unit of product i . Then the profit of manufacturer i equals
π i = ( Pi − C i ( wi ) − mi ) S i .
(5)
After the product purchase decision, buyers of either product approach the checkout point, where they are offered the retailer’s extended warranty, which offers coverage we > wi at price Pe . Consistent with prevalent industry practice, we assume that the extended warranty coverage
and price are set by an external insurer (whose considerations are exogenous to our model), and that the coverage of the extended warranty begins at the moment of purchase, rather than at the expiration of the manufacturer’s base warranty (cf. Berner 2005). Clearly, customers with low valuation of warranty coverage will not be interested in the retailer’s offer. However, even customers with substantial interest in warranty coverage might decide against the extended
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warranty offering, if it adds little on top of the manufacturer’s warranty. Customers will buy the retailer’s extended warranty if and only if their valuation of the added coverage θ w r ( we − wi ) exceeds the price of the extended warranty Pe . Hence, customers of product i will purchase the extended warranty only if they have a warranty valuation type higher than
ri =
Pe . θ w (we − wi )
(6)
We focus on equilibria where 0 < ri < 1 , such that at least some (but not all) customers of a product decide to purchase the extended warranty. Building on the example used in Figure 1, Figure 2 illustrates the customer segments that purchase the extended warranty. In this case, customer B would purchase the extended warranty ( rB > r1 ), whereas customer A would decide against it ( rA < r2 ).
d (r1 )
B
Manufacturer 1
d (1)
•
r1 C
•
•
Manufacturer 2
D
r2 A
d ( 0)
•
d (r2 )
Figure 2: Illustration of the Demand Model – Decision 2: Extended Warranty Purchase
Note that w1 > w2 implies r1 > r2 , since customers of product 2 buy a product with less warranty coverage and stand to gain more from the purchase of the extended warranty. Consider two customers C and D with the same warranty valuation, but with different product taste preferences ( d C , rC ) = (0.4,0.5) and (d D , rD ) = (0.6,0.5) . In this case, customer D would purchase the extended warranty, while customer C would not find the benefit on top of the coverage offered by manufacturer 1 worth its price Pe . As the retailer profits from sales of
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extended warranties, in this case she has incentive to use her sales effort to affect the customers’ decisions in favor of product 2. Knowing that customers of product i buy the extended warranty if their warranty valuation type is higher than ri , Figure 2 can be used to derive extended warranty sales as d (1) − d (r1 ) ⎞ d (1) − d (r2 ) ⎞ ⎛ ⎛ S e = (1 − r1 )⎜ d (r1 ) + ⎟ + (1 − r2 )⎜ (1 − d (1)) + ⎟, 2 2 ⎝ ⎠ ⎝ ⎠ where
d (ri ) = d (0) +
Pe ( w1 − w2 ) . 2t ( we − wi )
(7)
(8)
The extended warranty is provided by an non-strategic third-party provider, who grants the retailer a sales commission me on each extended warranty sold. Comparing her product sales commissions ( mi ) and the possible sales of extended warranties to customers of either product, the retailer determines which product she should “push” in order to maximize her profit. Consistent with our assumption of full market coverage (i.e. total demand is inelastic with respect to sales effort), we assume that there is a base amount of sales effort which is fixed, and we focus on additional sales effort that the retailer can exert to shift sales between the two products. Clearly, under these assumptions, the retailer would never want to exert (additional) positive sales effort for both products, but she would rather want to push one product, while advising customers against the purchase of the alternative. To model the decreasing marginal effect of such effort and to capture the cost associated with effort of either sign, we assume a quadratic cost function. For notational convenience3, we focus on the difference between the sales efforts ε = e1 − e2 , and assume that the retailer’s cost for sales effort is C e (ε ) = k e ε 2 . Intuitively, if ε > 0 , the retailer tends to support sales of product 1, while impeding sales of product 2, and if ε < 0 , she supports sales of product 2, to the detriment of product 1. With these assumptions, the retailer’s profits are given as follows:
π R = m1 S1 + m 2 S 2 + m e S e − C e (ε )
(9)
We assume the following sequence of events. The manufacturers first simultaneously set their base warranties ( wi ) and then decide, how much of their profit margin to pass on to the 3
Assuming a quadratic cost function of the same shape for individual efforts, the convexity of this function (with minimum at zero) implies a focus of the difference function is without loss of generality.
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retailer ( mi ), maximizing their respective profits (cf. equation 5). We assume that all parameters are common knowledge, such that optimal decisions of other (rational) players can be inferred. The manufacturers set their warranties ( wi ) and sales commissions ( mi ) in correct anticipation of the retailer’s optimal (maximizing profit as in equation 9) decision with respect to sales effort ( ε ). 4
Base Case: No Extended Warranty Sales
To illustrate the impact that the retailer’s extended warranty sales have on the incentives of the retailer and the two manufacturers, we first consider a benchmark scenario where the retailer does not engage in such sales. We use a bar (“ ”) to denote equilibrium outcomes for this base case without extended warranties. Proposition 1: Under both the sequential and the simultaneous customer choice pattern, if the retailer does not sell extended warranties, the equilibrium manufacturer warranties, sales commissions, and retailer sales effort are as determined by equations (10)-(12). k e tθ w θ e2 k i
(10)
2(Pi − C i ( wi ) ) + (P3−i − C 3−i ( w3−i ) ) 3 4k t 2 k tθ − e2 (( Ri − Pi ) − ( R3−i − P3−i ) + 3t ) − e 2 w (wi − w3-i ) 3θ e 3θ e
(11)
wi =
mi =
ε =
θe 4k e t
(m1 − m2 )
(12)
We see that in the absence of extended warranties, the retailer always supports the product of the manufacturer that grants the higher sales commission ( mi ). Each manufacturer sets its base warranty level to balance the cost of providing coverage ( k i ) against the amount to which additional coverage increases the customers’ valuation of the product ( θ w ). This optimal warranty level is independent of the competitor’s warranty terms, and the two manufacturers vary their products’ sales commissions to reflect all other competitive deliberations. While the manufacturers’ warranty terms do not have a direct effect on the retailer’s incentives, they affect the retailer’s sales effort indirectly by influencing the relative attractiveness of the two products
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to the customers, and thus product sales, which drive retailer profits through the associated sales commissions. Interestingly, the manufacturers’ optimal warranties decrease in the effectiveness of the retailer’s sales effort ( θ e2 /( k e t ) ); as the effect of sales effort on product sales becomes stronger compared to the effect of warranties, the manufacturers reduce their base warranties and instead use higher commissions to achieve supportive sales effort. It can be shown that, as a manufacturer’s cost of providing warranty coverage ( k i ) increases, he reduces his product’s base warranty coverage ( wi ) and increases the retailer’s sales commission ( mi ). In response, the retailer raises the support for his product through sales effort (
ε ), but this increase is not sufficient to prevent the sales of the manufacturer’s product ( S i ) from declining. Since identical manufacturers would set identical sales commissions and warranties, this implies that if the two manufacturers’ differed only in their cost of providing warranty, the higher warranty cost manufacturer would offer the lower warranty coverage and grant the retailer the higher sales commission to compensate her for providing the less attractive product. In reaction to this increase in her profit margin, the retailer actively promotes the lower warranty product through additional sales effort. However, sales of the lower warranty product are still lower than those of the product with better warranty coverage. We stress this intuitive insight at this point to highlight the significant shift in dynamics that occurs once the retailer derives a substantial part of her profits from selling extended warranties. She then might actually prefer selling a product with lower warranty coverage, as it is more likely to lead to an extended warranty sale. 5
Channel Dynamics under Extended Warranty Sales
In this section, we derive the equilibrium solutions for the case where the retailer engages in extended warranty sales. We first, in section 5.1 determine the equilibrium levels of retail sales effort, base warranties and sales commissions for the scenario, where customers make their product and extended warranty purchase decisions sequentially. We consider the alternative setup with sequential purchase decisions in section 5.2. In section 5.3, we compare the equilibria under these two scenarios to determine the impact of the retailer’s extended warranty sales strategy on manufacturer and retailer profits, and on customer surplus.
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5.1 Sequential Selection In this section we focus on the case where customers make their purchase decisions regarding products and extended warranties sequentially, i.e. they first choose which of the two manufacturers’ products to purchase, and then decide whether to buy the retailer’s extended warranty coverage. We derive the equilibrium using backward induction, and we use the asterisk (“*”) to denote equilibrium solutions for this scenario. Given the two manufacturers’ decisions with respect to warranty coverage w = {w1 , w2 } and sales commissions m = {m1 , m2 } , the retailer determines how much sales effort ε to exert in order to maximize her profits, as given in (9). Retailer profits are strictly concave in sales effort and solving the necessary and sufficient first-order condition yields her optimal sales effort
ε * ( w , m) =
θe ⎛
⎞ Pe me ( w2 − w1 ) ⎜⎜ m1 − m2 + ⎟. 4k e t ⎝ θ w (we − w1 )(we − w2 ) ⎟⎠
(13)
Inspection of (13) reveals the fundamental trade-off that the retailer faces when determining which product to support via sales effort. In the presence of extended warranty sales, there are two main drivers of her decision: the relative profitability of the two products in terms of their associated sales commissions and the likelihood that either product’s customers purchase the extended warranty, which decreases in this product’s base warranty. If the retailer does not engage in extended warranty sales, the second term in the bracket vanishes ( m e = 0 ), and she always supports the product with higher profit margin (cf. results in section 4). Substituting the retailer’s optimal response (as in equation 13), it can be easily confirmed that either manufacturer’s profit function is strictly concave in his respective retailer sales commission. Simultaneously solving the first-order conditions yields the manufacturers’ optimal sales commissions, given their earlier decisions regarding their base warranties w = {w1 , w2 } .
mi* (w) = mi (w) +
me Pe ( wi − w3−i ) 3θ w ( we − w1 )(we − w2 )
(14)
The structure of the manufacturers’ sales commissions again illustrates the dynamics that arise because of the retailer’s interest in selling extended warranty contracts, and yields the following interesting insight.
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Proposition 2: Anticipating the retailer’s interest in extended warranty sales, the manufacturer of the product with the better base warranty increases his sales commission to compensate her for impeding extended warranty sales. Proposition 2 illustrates one of the key insights of this research, as it illustrates the (ex ante) counterintuitive implications that extended warranty sales can have on channel dynamics. Compared to the scenario without extended warranty sales, the lower-warranty manufacturer now decreases the retailer’s sales commission, whereas the manufacturer with the higherwarranty product reimburses the retailer for making sales of the extended warranty more difficult. The competitive disadvantage of the lower warranty producer is mitigated, as the weaker warranty makes his product (relatively) more attractive to the retailer. The suggestion that the manufacturer with the better product might need to reimburse the retailer for selling this product seems bizarre. However, the rationale of such behavior becomes more intuitive once the profitability of extended warranty sales is factored in. While equation (14) shows that, for the same base warranty levels, consideration of extended warranty sales induces the manufacturer of the better-warranty product to grant a higher sales commission, the dynamics discussed above are likely to exert downward pressure on the base warranties, so the final effect on retailer profits originating from product sales is not immediately clear. Substituting the retailer’s sales effort from (13) and the sales commissions from (14), one can derive manufacturer profits as a function of the base warranties w = {w1 , w2 } . While closedform expressions for the optimal manufacturer warranties are complex and do not lend themselves for insightful analysis, it can be shown that there is at most one interior solution to the necessary first-order condition, and that either manufacturer’s profit function π i ( w ) is quasiconcave over the area of interest, such that any solution to the first-order condition must be a maximum (cf. Lemmas A1-A3 in Appendix A). Using the implicit function theorem with a simplified expression of the first-order condition (cf. equation (A1) in Appendix A), it is possible to determine how the different parameters affect the optimal manufacturer warranties. Each manufacturer sets his warranty terms at the individually most efficient level, balancing the impact of better warranties on customer perceptions of his product (the customers’ valuation of warranty θ w vis-à-vis the attractiveness of the retailer’s extended warranty in terms of coverage we and price Pe ) against the associated costs of providing warranty ( k i ) and the negative
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implications on the retailer’s sales incentives, weighted by the profitability of extended warranty sales to the retailer ( me ) and by the effectiveness of such effort (increasing in θ e and decreasing in k e and t ). Interestingly, the manufacturers consider their own cost of providing warranty coverage ( k i ) in determining their optimal warranty coverage, but not the competitor’s warranty cost ( k3−i ). The optimal warranty is also independent of all product-related characteristics of both manufacturers ( C i , Pi , and Ri ). The manufacturers consider differences in their products’ characteristics and warranty terms explicitly only when setting the retailer’s sales commissions, a result that resembles the findings of DeCroix (1999) that optimal warranty-reliability combinations of a firm are independent of the competitors’ warranty-reliability combinations and prices. Proposition 3: If the retailer profits from extended warranty sales, it is optimal for the manufacturers to reduce their base warranties compared to the base case without extended warranty sales (i.e. wi* < wi ). Proposition 3 confirms that the retailer’s extended warranty sales provides an incentive to the manufacturers to reduce the base warranty coverage of their products in order to support the products’ attractiveness to the retailer, who now is more likely to profit from the sales of extended warranties. 5.2 Simultaneous Selection In the previous section, we assumed customers made their product purchase decision before they considered the retailer’s extended warranty offering. In this section, we study how the different parties (manufacturers, retailer, and customers) are affected if customers make their purchase decisions regarding products and warranties at the same instance. Under such simultaneous product and warranty choice, the consumers’ decision process is more complicated, as four different options need to be considered (product 1 only, product 2 only, product 1 with extended warranty, or product 2 with extended warranty). Similar to Figure 2, the following Figure 3 illustrates the case with simultaneous product and extended warranty choice when w1 > w2 . We use the same notation as before (cf. section 3), and we use solid lines to define the relevant indifference lines.
17
d (1)
B
Manufacturer 1
•
E
• D
r1 F C
•
Manufacturer 2
•
r2 A
d ( 0)
•
•
d (r2 )
Figure 3: Illustration of the Demand Model – Simultaneous Choice
In this illustration customer C (customer A) would purchase product 1 (product 2) without the extended warranty, whereas customer B (customers D, E, and F) would decide to bundle product 1 (product 2) with the retailer’s extended warranty. As before, customers who decide for the higher warranty product of manufacturer 1 are less likely to purchase the retailer’s extended warranty (i.e. r1 > r2 ). However, comparing the slopes of the solid lines, we notice that if customers simultaneously chose between the different product-warranty bundles, the positive impact of manufacturer 1’s better warranty offering on the customers’ choice is unchanged only for the set of customer with low warranty valuations (below r2 ). The impact of the better warranty of product 1 is reduced for customers with intermediate warranty valuations (between
r2 and r1 ), some of which now prefer to buy product 2 with the extended warranty compared to buying product 2 without the extended warranty. Interestingly, in this case a higher warranty valuation benefits sales of the lower warranty product, as it is bought together with the extended warranty, which provides better coverage than the base warranty of product 1 ( we > w1 ). Clearly, differences in the products’ base warranties do not figure into the decision making of customers with high warranty valuation (above r1 ). All these customers decide to bundle their product with the retailer’s extended warranty and consequently compare the two products solely based on their non-warranty characteristics and the retailer’s sales effort, i.e. in the simultaneous case we have d (0) = d (r1 ) = d (1) . As before, the retailer has incentive to support the lower-warranty
18
product in order to support sales of the profitable extended warranty, increasing sales of this product, ceteris paribus. It is interesting to compare Figure 3 to Figure 2, assuming (for a moment) the same retailer sales effort and manufacturer base warranties in both scenarios. We see the number of customers that purchase product 2 without the retailer’s extended warranty remains unchanged. These customers do not value warranty coverage enough and thus are not affected by the extended warranty or the higher warranty of the competitor’s product. However, the number of customers that bundle the lower-warranty product (product 2) with the retailer’s extended warranty increases compared to the scenario with sequential choice. Considered jointly with the retailer’s extended warranty, many customers with high valuation of warranty coverage (above r1 ) now decide against the product with the higher base warranty and instead purchase the extended warranty (cf. customer E and the horizontally striped area in Figure 3). In addition to these customers with high valuation of warranty coverage, the bundle consisting of the lower-warranty product and the retailer’s extended warranty also becomes attractive to some intermediate warranty valuation customers (between r2 and r1 ), who would have purchased the higherwarranty product without the extended warranty, if their purchase pattern was sequential (cf. customer F and the vertically striped area). Overall, simultaneous rather than sequential consideration of product and (extended) warranty options by the customers leads to increased sales of the lower-warranty product (both striped areas), and it augments the retailer’s sales of extended warranties (vertically striped area). These observations suggest that simultaneous customer choice benefits the retailer, increasing extended warranty sales and the pressure on the manufacturer with the higher warranty product to compensate her for lowering the likelihood of extended warranty sales. However, recall that this illustrative comparison implicitly assumes that base warranties remain unchanged; in the following we investigate the impact of simultaneous choice on the manufacturer’s warranty choices. We use a tilde (“ ~ ”) to denote quantities associated with this scenario, where customers make their purchase decisions regarding products and warranties at the same time. With the definitions of d (0) , ri , and d ( ri ) as in the previous scenario (cf. equations 1, 6 and 8), sales of the two products and of the extended warranty can be derived from Figure 3 as
19
r (d (r2 ) − d (0)) ~ ~ and S 1 = 1 − S 2 = d ( 0) + 1 2
(15)
d (r2 ) − d (0) ⎞ ~ ⎛ S e = (1 − r1 ) + (r1 − r2 )⎜ (1 − d (r2 )) + ⎟. 2 ⎝ ⎠
(16)
With these adjusted sales quantities, the expressions for retailer profits ( π~R ) and manufacturer profits ( π~i ) are as in (5) and (9), respectively. We again use backward induction. Given the two manufacturers’ decisions with respect to warranty coverage w = {w1 , w2 } and sales commissions m = {m1 , m2 } , the retailer’s profit function is strictly concave in her sales effort, and solving the first-order condition reveals her optimal sales effort reflects the same reaction to sales commissions and base warranties, no matter if customer pattern is simultaneous or sequential, i.e.
ε~ ( w , m ) = ε * ( w , m ) .
(17)
Substituting the retailer’s optimal sales effort, it is easy to show that each manufacturer’s profit function is strictly concave in his respective sales commission, and simultaneously solving the first-order conditions, the manufacturers’ optimal sales commissions for given base warranties w = {w1 , w2 } are 2k e tPe2 ( wi − w3−i ) ~ (w ) = m * (w ) + 2k e tθ w ( wi − w3−i ) − m . i i 3θ e2 3θ wθ e2 ( we − wi )( we − w3−i )
(18)
These results in Proposition 2 suggested that for given warranties the retailer’s extended warranty sales induce the higher-warranty manufacturer to increase the sales commission to compensate her for the reduced likelihood of extended warranty sales, whereas the producer of the lower warranty product can actually reduce his sales commission, since his product’s liability makes the product more attractive in the retailer’s eyes. Comparing the manufacturers optimal sales commissions under the sequential and simultaneous shopping pattern for the same base warranties, it can be shown that this impact of the retailer’s extended warranty sales on the manufacturers’ optimal sales commissions is exacerbated, if customers make their purchase decisions regarding products and extended warranties simultaneously (see Lemma A4 in Appendix A). While it is interesting to derive such insights for given warranty levels, thus
20
controlling for eventual differences in manufacturer warranties, the arising dynamics will affect the manufacturers’ equilibrium warranty choices under the two induced shopping patterns, such that the true ranking of sales commissions and overall retailer profitability can not immediately be determined. With the retailer’s sales effort from (13) and the sales commissions from (18) it is possible to derive manufacturer profits as a function of the base warranties w = {w1 , w2 } . As in the scenario with sequential choice, it can again be shown that there is at most one interior solution to the necessary first-order condition, and that either manufacturer’s profit function π i ( w ) is quasiconcave over the area of interest, such that any such solution must be a maximum (cf. Lemmas A5-A7 in Appendix A). Using a simplified expression of the first-order condition (cf. equation (A2) in Appendix A), it then is possible to determine how the customers’ shopping pattern affects the manufacturers’ base warranty choices: Proposition 4: If customers make their purchase decisions regarding products and extended warranties simultaneously rather than sequentially, it is optimal for the manufacturers to further ~ < w * ). reduce their base warranties (i.e. w i
i
The findings of Proposition 4 suggest that simultaneous product and warranty choice by consumers increases the downward pressure on manufacturer warranties, as it reduces the positive impact of higher warranties on the product purchase decision. 5.3 Pitch Now or Pitch Later? Impact of the Induced Purchase Pattern on Profitability In the previous sections we analyzed the equilibria under sequential and simultaneous customer choice, respectively. In this section we compare these equilibria to see how the customers’ purchase pattern affects the different supply chain constituents and when it is in the retailer’s interest to induce simultaneous consideration. Such behavior could be supported for example through adjustments in the product price labels on the shelf, providing prices for the product both with and without an extended warranty. The retailer’s profit is affected by three components: profit from product sales, profit from sales of extended warranties, and cost of sales effort (cf. equation 9). While simultaneous choice benefits the retailer through increased extended warranty sales, it is not obvious how it affects her revenues from product sales; compared to sequential choice, under simultaneous consideration of products and extended warranties, the manufacturer of the higher-warranty 21
product increases his sales commission, but the lower-warranty manufacturer reduces the sales commission on his product (cf. Lemma A4 in Appendix A). Given the manufacturers’ adjustments in their base warranties (Proposition 4), the impact of simultaneous choice on the retailer’s sales effort and the associated costs is also unclear. While we focus on the question which customer purchase pattern the retailer should support, we are also interested in how the two manufacturers and the customers are affected by the way in which customers make their product and warranty purchase decisions. Given the lack of mathematical tractability of the expressions for optimal manufacturer warranties, we are not able to obtain insightful structural results for the general case. We therefore first present some insights based on a numeric experiment, before deriving additional analytical results for an interesting special case. Details on the numeric study are provided in Appendix C. Observations from a Numeric Study: (a) The retailer might prefer sequential choice or simultaneous choice. (b) The retailer is better off under simultaneous customer choice, unless the product of the lower-warranty manufacturer is substantially more attractive to the customers, i.e. unless both k i > k 3−i and Ri − Pi > R3−i − P3−i . (c) The lower-warranty manufacturer prefers simultaneous product choice, while the higherwarranty manufacturer is better off under sequential product choice. Observation (a) shows (and proves by example) that there is no dominant strategy for the retailer; it depends on the specific characteristics of the two products and manufacturers, whether she prefers customers to make their purchase decisions sequentially or simultaneously. Observation (b) identifies settings where the sequential purchase pattern might be preferable as (exclusively) those where the manufacturer with the more attractive product offers the lower warranty. We know that compared to sequential customer choice, the manufacturer of the lowerwarranty product decreases his sales commission if customers make their purchase decisions simultaneously (Lemma A4 in Appendix A). Clearly, this decrease in sales commissions is most detrimental to the retailer, if this manufacturer’s product is very attractive to customers (larger differential between reservation price and retail price), and thus captures a larger share of the market. While the higher-warranty manufacturer raises the sales commission on his product as the value of warranty-based differentiation decreases under the simultaneous purchase pattern,
22
this increase only affects a smaller portion of the market, as the characteristics of his product are less attractive to customers. Consistent with expectation, we find the retailer is better off under the simultaneous purchase pattern in 89.9% of the studied scenarios. Observation (c) lends further support to the notion that simultaneous choice benefits the lower-warranty producer, and that it harms the manufacturer with the better warranty; we find this qualitative insight to be true in all studied scenarios. It is interesting to note that, compared to the retailer’s profit, manufacturer profits seem rather insensitive with respect to the customer choice pattern. While the retailer’s profit on average increases by 20.6%, if the customers’ purchasing pattern is simultaneous rather than sequential, the profit of the lower-warranty manufacturer increases by only 2.8% and the profit of the higher-warranty manufacturer decreases by only 2.5%. One conclusion of this brief numeric study is that simultaneous customer purchase pattern is preferred by the retailer, unless the two products are extremely different and diametrically opposed in terms of manufacturer warranties and general attractiveness to customers. This notion finds further support in the following analytical result for the special case, where the two manufacturers have the same cost of providing warranty coverage (i.e. k i = k ). Let ~ ~ ~ = S~ m ~ m * = S1* m1* + S 2* m 2* and m 1 1 + S 2 m 2 denote the retailer’s average sales commission in the
scenarios with sequential and simultaneous choice, respectively. Proposition 5: If the manufacturers have the same warranty cost ( k i = k ), then: (a) The retailer is better off, if customers consider the purchase of product and extended warranty simultaneously ( π~R > π R* ). (b) If customers consider the retailer’s extended warranty when choosing their product, the ~ > m * ). manufacturers increase their sales commissions ( m (c) The manufacturers are indifferent between sequential and simultaneous customer decision making ( π~i = π i* ). (d) Customers are better off, if they make their decisions sequentially rather than simultaneously. If the two manufacturers have the same cost of providing product warranty coverage, the retailer is always better off, when customers consider the purchase of product and extended warranty simultaneously, no matter how the two products compare in terms of attractiveness to
23
customers (Proposition 5a). On the one hand, the retailer profits from increased extended warranty sales; not only are customers more likely to purchase the lower warranty product in anticipation of the retailer’s extended warranty offering (see Figures 2 and 3), extended warranty sales are also supported by the reduction in manufacturer warranties (cf. Proposition 4). The retailer’s interest in extended warranty sales induces manufacturers to lower their warranties to make their products more attractive to the retailer and to induce her to exert favorable sales effort (cf. Proposition 3). As the customers anticipate the availability of the retailer’s extended warranty offering in making their product purchase decisions, the value of providing better warranty coverage in supporting sales is further reduced, and the manufacturers increase their sales commissions in pursuit of retailer sales effort (Proposition 5b), providing a second source of increased profitability to the retailer. Interestingly, the manufacturers increase the average sales commission exactly by the amount they save due to the reduction in base warranties (cf. proof of Proposition 5b), leaving them indifferent between the two possible customer choice patterns (Propositions 5c). Proposition 5d provides a surprising finding regarding consumer well-being. Intuition suggests it is in the customers’ interest to consider products and warranties simultaneously rather than sequentially. While it is true that, ceteris paribus, customers can not be worse off if considering all options simultaneously, the assumption of ceteris paribus does not apply in this case, as the two manufacturers (and the retailer in reaction) adjust their decisions to the changed circumstances. Under simultaneous product choice, the two manufacturers opt for a strategy of lower warranty coverage and higher retailer sales commissions, in order to increase the attractiveness of their products to the retailer and induce favorable sales effort. The manufacturers’ per-unit savings from lower warranty costs are identical to the increase in the retailer sales commission, so that manufacturer profits do not change and the retailer is actually better off. However, the customers pay the same retail prices for products with lower base warranties, leaving them worse off than under the sequential choice scenario. The retailer’s extended warranty sales and the manufacturers’ dependence on the retailer’s sales effort thus pose the retailer’s interests in direct conflict with the objectives of the customers, who are negatively affected by the manufacturers’ and the retailer’s strategy to offer products with lower base warranty coverage.
24
6
Discussion & Conclusion
We consider the dynamics that arise when competing manufacturers sell their products through the same retailer, who derives profits from sales of extended warranties. If customers value warranty coverage, manufacturers have incentive to offer good base warranties to increase their products’ attractiveness to customers. However, while increasing a product’s base warranty improves its positioning vis-à-vis the competitor’s product, other things being equal, buyers of this product also have less interest in the retailer’s extended warranty, which now offers reduced incremental benefit. We find that these dynamics give the retailer incentive to adjust her sales effort in favor of the product with the lower base warranty, as buyers of this product are more likely to purchase the extended warranty. Considering the retailer’s preference for sales of the lower-warranty product, it is in the best interest of the manufacturer with the higher-warranty product to increase his sales commission to the retailer to compensate her for impeding extended warranty sales, so the retailer’s extended warranty sales decrease the value of a manufacturer’s potential warrantycost advantage. Clearly, these interactions exert downward pressure on the manufacturers base warranties, and we find it optimal for the manufacturers to reduce their warranties compared to the base case without extended warranty sales. Interestingly, most manufacturers of appliances and consumer electronics have cut back their base warranties over the last years, often to just 90 days. This stands in direct contrast to the automobile industry, where quality improvements and simultaneous increases in manufacturer warranties often obviate the need for extra coverage (Buss 2006). While there clearly are many alternate determinants of base warranty coverage that we controlled for in this research, the results obtained in this article provide a consistent rationalization for these apparently conflicting observations. While appliances and consumer electronics are mostly sold through independent retailers, who carry products from various competing providers, the typical car dealership is exclusive to products of one manufacturer, mitigating the need for manufacturers to compete for their dealers’ sales effort. We show that the impact of a retailer’s extended warranty sales can be substantially affected by how customers make their purchase decisions regarding products and extended warranties. If customers consider products and extended warranties simultaneously rather than sequentially, we find the above described effects become even more pronounced, giving the higher-warranty manufacturer even stronger incentive to increase his sales commissions, and exacerbating the
25
downward pressure on manufacturer warranties. Regarding the question of what customer shopping pattern the retailer should induce, our results suggest that she will be better off under simultaneous consumer choice, unless the product of the lower-warranty manufacturer is substantially more attractive to consumers in terms of other product characteristics and its retail price. Hence, we find that in most cases the retailer can increase profits by inducing a simultaneous customer shopping pattern, for example by posting information regarding the extended warranty offering next to the products on the shelf. It is interesting to note that, while most retail environments can still be characterized as inducing a sequential shopping pattern, where customers are confronted with the extended warranty sales pitch only after they have chosen a product, many retailers have now started to more aggressively prompt customers to take extended warranty offerings into consideration when making their product choice. For example, at Best Buy price labels contain a section labeled “Don’t Forget” which explicitly recommends customers to consider extended warranties, a recommendation which is also often supported by interventions of customer sales representatives. How does a push for simultaneous choice affect manufacturers and consumers? Our results suggest that manufacturer profitability is relatively insensitive with respect to the way customers make their purchase decisions, though simultaneous product choice slightly benefits the lowerwarranty manufacturer and harms the higher-warranty manufacturer. With respect to consumer welfare, intuition suggests that consumers should be better off if they considered products and warranties simultaneously rather than sequentially. However, under simultaneous product choice the two manufacturers opt for a strategy of lower warranty coverage and increased sales commissions in order to make their products more attractive to the retailer and induce favorable sales effort. Since customers pay the same retail prices for products with reduced base warranties, they are worse off than under sequential choice. The retailer’s interest in extended warranty sales and the manufacturers’ dependence on the retailer’s sales effort thus pit the retailer’s interests against the objectives of the customers. In order to maintain analytical tractability in our model with endogenous manufacturer warranties, endogenous commissions and endogenous sales effort, we made several simplifying assumptions. Our representation of costs associated with providing warranty coverage is kept very concise, ignoring any aspects of uncertainty and focusing on a single-period model. A richer representation of warranty cost, considering the dynamics emerging in a multi-period setting
26
with stochastic product failure in this context might be a promising area for future research. Considering the complications arising from product returns or exploring optimal decisions regarding product quality or extended warranty terms could be interesting extensions along this line. Focusing on the aspects that arise due to the retailer’s interest in extended warranty sales, we defined our market as the population of customers that associate a positive utility with at least one product, given fixed retail prices. Consistent with this view, we defined the retailers’ sales effort as distorting sales effort, which does not affect aggregate product sales, but rather the two products’ market shares. While we believe that this focus is consistent with the ensuing modeling assumptions and that it allows an elegant structural analysis of this problem, the associated assumption of full-market coverage implies that the population of customers that purchase one of the two products is not affected by the manufacturers’ base warranties. We believe that this is a reasonable approximation of many markets, where base warranty coverage has only a negligible effect on the customers’ decision to buy a product; our model does not adequately capture the dynamics that arise when base warranties have a substantial effect on aggregate product sales. One important prerequisite for the dynamics suggested in this article is the retailer’s ability to affect product sales. Most electronics retailers pay their sales representatives based on performance, often including a premium for sales of extended warranties. For example, postings to retailworker.com suggest sales representatives at Office Max receive a 10% bonus on warranty plan sales. Due to the associated premiums, salespeople refer to a good product sale as “hot dog”, while a good sale with a warranty plan is called “chili dog with cheese” (Stafford 2006). While several retailers have moved to commission-free contracts, their salespeople are trained to offer extended warranties wherever applicable, and often there are indirect benefits such as a team bonus for the shift with highest extended warranty sales (cf. Stafford 2006, Circuit City 2006). We modeled the retailer’s influence through sales effort to capture the resulting dynamics, but we expect the very same trade-off and dynamics to emerge, if her influence on sales was through retail pricing. A more detailed study of optimal incentive schemes, considering the effects on customer perceptions as well as the dynamics studied in this research, is beyond the scope of this article, but might be a valuable avenue for future research.
27
Appendix A – Additional Results (with Proofs) Lemma A1: Each manufacturer’s optimal warranty wi* is implicitly defined by 2 ⎛ me Pe * ⎞ θe ⎜ ⎟ + 2 = θw . k w i i ⎟ ⎜ θ ( w − w* ) 2 i ⎝ w e ⎠ 2k e t
(A1)
Proof: The manufacturer profit functions can be written as π i ( w ) = g i ( w ) 2 /( 72 k e ) , where g i ( w ) = m e Peθ e ( wi − w3−i ) / (tθ w ( we − wi )( we − w3−i ) ) − 2k eθ w ( wi − w3−i ) / θ e + θ e (( P3−i − C 3−i ( wi )) − ( Pi − C i ( wi )) ) / t − 4 k e (( Ri − Pi ) − ( R3−i − P3−i ) + 3t ) / θ e . The necessary
first-order condition to the manufacturers’ warranty coverage problem is ∂π i ( w * ) / ∂wi = g i ( w * ) /(36 k e ) * ∂g i ( w * ) / ∂wi = 0 , which is equivalent to ∂g i ( w * ) / ∂wi = 0 , since the
assumption of (strictly) positive firm profits in equilibrium implies g i ( w * ) ≠ 0 . This condition can be written explicitly as (A1). ■ Lemma A2: There is one positive solution to (A1), if m e Peθ e2 < 2k e tθ w2 we2 , and none otherwise. Proof: Since the left-hand side L( wi ) of (A1) is strictly increasing in wi , there is no positive solution if L (0) ≥ θ w , and there is exactly one solution if L (0) < θ w , which is equivalent to the given condition. ■ Lemma A3: Over the area of interest, each manufacturer’s profit π i (w ) is quasi-concave in wi . Proof: We prove quasi-concavity of π 1 (w) in w1 . (The same proof applies to the profit function of manufacturer 2.) The first derivative can be written as ∂π 1 (w) / ∂w1 = U (V + W ) / Z , where
(
)
U = θ w − m e Pe /(θ w ( we − w1 ) 2 ) + 2k1 w1 θ e2 /( 2k e t ) , V = 2d (1) / 3 , W = θ w ( w2 − w1 ) / 6t , and Z = θ e2 /( 2k e t ) > 0 . The conditions d (1) = 0 and d (1) = 1 provide implicit lower and upper
bounds on w1 , respectively. At d (1) = 0 we have V = 0 and W > 0 , since w1 > w2 would imply d (0) < 0 . Inspection of (A1) and the condition in Lemma A2 shows that U > 0 for all w1 < w1* ,
where w1* is interior by assumption. Hence, ∂π i ( w ) / ∂wi > 0 at d (1) = 0 . At d (1) = 1 we have
V + W > 0 ⇔ θ w ( w1 − w2 ) / 4t < 1 ⇔ S1 − d 0 < 1 , which is true since both variables on the lefthand side of this inequality take values strictly between 0 and 1. Inspection of (A1) and the condition in Lemma A2 shows that U < 0 for all w1 > w1* , where w1* is interior by assumption. 28
Hence, ∂π i ( w ) / ∂wi < 0 at d (1) = 1 . Since manufacturer profits are continuous (in the region of interest), and since by Lemma A2 there can be at most one extreme point with w1 ≥ 0 , π 1 (w) is quasi-concave in w1 . ■ Lemma A4: For warranty levels
w = {wi , w j }
with
wi > w j :
~ (w ) > m * (w ) m i i
and
~ (w ) < m * (w ) . m j j ~ (w ) ≥ m* (w ) Proof: Using (18): m i i ⇔ 2 k e tθ w ( wi − w3−i ) /(3θ e2 ) − 2k e tPe2 ( wi − w3−i ) /(3θ wθ e2 ( we − wi )( we − w3−i )) ≥ 0
(
(
))
⇔ 1 − Pe2 / θ w2 ( we − wi )( we − w3−i ) (wi − w3−i ) ≥ 0 ⇔ wi > w3−i , since
(
)
Pe2 / θ w2 ( we − wi )( we − w3−i ) < (Pe /(θ w ( we − max{wi })) ) = (max{ri }) < 1 . ■ 2
2
~ is implicitly defined by Lemma A5: The optimal manufacturer warranty w i 2 ⎛ me Pe Pe2 ~ ⎞⎟ θ e = ⎜ + 2 k w i i⎟ ~ )2 ~ 2 ⎜ θ (w − w i ⎝ w e ⎠ 2k e t θ w ( we − wi )
(A2)
Proof: The manufacturer profit functions can be written as π i ( w ) = hi ( w ) 2 /( 72 k e ) , where hi ( w ) = Pe ( wi − w3−i )( 2k e Pe t − m eθ e2 ) / (tθ wθ e ( we − wi )( we − w3−i ) ) + 4k e (( Ri − Pi ) − ( R3−i − P3−i ) + 3t ) / θ e + θ e (( P3−i − C 3−i ( wi )) − ( Pi − C i ( wi )) ) / t . The necessary
~ ) / ∂w first-order condition to the manufacturers’ warranty coverage problem is ∂π i (w i ~ ) /(36 k ) * ∂h ( w ~ ) / ∂w = 0 , which is equivalent to ∂h ( w ~ ) / ∂w = 0 , since the assumption = hi ( w e i i i i ~ ) ≠ 0 . This condition is equivalent of (strictly) positive firm profits in equilibrium implies hi ( w
to (A2). ■ Lemma A6: A necessary condition for a positive solution to (A2) to exist is θ e2 m e < 2k e tPe . Proof: Equation (A2) can be written as Pe / me − θ e2 /( 2k e t ) = k iθ e2θ w wi ( we − wi ) 2 /( Pe m e k e t ) , where the right-hand side of the equation is strictly positive for wi > 0 . ■ Lemma A7: Over the area of interest, each manufacturer’s profit π~i ( w ) is quasi-concave in wi . Proof: We prove quasi-concavity of π~1 (w) in w1 . (The same proof applies to the profit function of manufacturer 2.) The first derivative can be written as ∂π~1 (w) / ∂w1 = U (V + W ) / Z , where
29
(
)
U = Pe2 /(θ w ( we − w1 ) 2 ) − m e Pe /(θ w ( we − w1 ) 2 ) + 2k1 w1 θ e2 /( 2k e t ) , V = 2d (r2 ) / 3 , W = Pe ( 2 − r1 )( w2 − w1 ) /( 6t ( we − w2 )) , and Z = θ e2 /( 2k e t ) > 0 . The conditions d (r2 ) = 0 and
d (r2 ) = 1 provide implicit lower and upper bounds on w1 , respectively. At d (r2 ) = 0 we have V = 0 and W > 0 , since w1 > w2 would imply d (0) < 0 . Inspection of (A2) and the condition in
~ , where w ~ is interior by assumption. Hence, Lemma A6 guarantees that U > 0 for all w1 < w 1 1 ∂π i ( w ) / ∂wi > 0 at d (r2 ) = 0 . At d (r2 ) = 1 , we have V + W > 0
~ ⇔ 2 / 3 + Pe ( 2 − r1 )( w2 − w1 ) /( 6t ( we − w2 )) > 0 ⇔ ( S1 − d (0)) − ( d ( r2 ) − d (0)) + 1 > 0 ~ ~ ⇔ ( S 1 − d (0)) − (1 − d (0)) + 1 > 0 ⇔ S 1 > 0 . Inspection of (A2) and the condition in Lemma A6
~ , where w ~ is interior by assumption. Hence, guarantees that U < 0 for all w1 > w 1 1 ~ < w , equation (A2) is equivalent to ∂π i ( w ) / ∂wi < 0 at d (r2 ) = 1 . Since w 1 e ~ (w − w ~ ) 2 = ( 2k tP 2 − m P θ 2 ) /( 2 k θ 2θ ) . The right hand side of this equality is a constant, w i e i e e e e e i e w
whereas the left hand side is a cubic function, so there can be at most three solutions to this ~ , and it can easily be shown that the equality. The cubic function has a positive coefficient at w 1
~ = w , such that there can be at most two solutions to (A2), location of its minimum is at w 1 e
limiting the number of possible extreme points of π~1 (w) to two. Since manufacturer profits are continuous (in the region of interest), π~1 (w) is quasi-concave in w1 . ■
30
Appendix B – Proofs Proof of Proposition 1: In the absence of extended warranty sales, there is no difference between the scenarios with sequential and simultaneous choice. With me = 0 , the result can be easily obtained following the logic described in Section 5.1. ■ Proof of Proposition 2: The last term in (14) is the only term affected by the profitability of extended warranty sales ( me ). This term is positive if and only if wi > w3−i . ■ Proof of Proposition 3: Equation (A1) can be written as m e Pe /(θ w ( we − wi* ) 2 ) = 2k e tθ w / θ e2 − 2k i wi* . The left-hand side of this equation is strictly
positive and strictly increasing in wi . The right-hand side is strictly decreasing in wi , and it is zero at wi = wi = θ w k e t /(θ e2 k i ) . ■ Proof of Proposition 4: By inspection of (A1) and (A2). The left hand sides of both equations are identical and both are convex increasing. The right-hand side of (A1) is a constant, and it is ~ )) )2 < 1 ~ ) 2 ) < θ ⇔ (P /(θ ( w − w strictly smaller than that of (A2), since Pe2 /(θ w ( we − w i w e w e i ⇔ ri < 1 . ■
Proof of Proposition 5: Since the necessary conditions for the optimal warranty levels in (A1) and (A2) are independent of the manufacturers’ respective product parameters, and since there is at most one interior solution to either condition (cf. Lemmas A3 and A7), for k i = k any solution of interest must be symmetric. Substituting the corresponding equilibrium sales effort in (13) and (17) and sales commissions in (14) and (18), retailer profits π~ and π * can be derived from (9), R
R
~ )(k ( w* + w ~) and manufacturer profits π i* and π~i from (5). Part (a): π~R − π R* = ( w* − w
(
)
~ )θ , which is positive by Proposition 4. Part (b): Substituting the + me Pe / ( we − w* )( we − w w
~ − m* = k ( w* − w ~ )( w* + w ~ ) = C ( w* ) − C ( w ~ ) , which optimal decisions and simplification gives m i i is positive by Proposition 4. Part (c): Simplification of terms directly reveals that π i* = π~i . Part (d): For symmetric warranties, the indifference line d (r ) between the two products is vertical and it can be easily shown that sales effort (and consequently d (0) ) is identical under all scenarios. Hence, in each scenario customers derive the same average utility from the products alone, i.e. before considering the utility derived from warranties. We next consider the utility that 31
customers derive from the base warranties and the retailer’s extended warranty. Consider the two ~ )) and scenarios with sequential and simultaneous decision making. Let ~ r = P /(θ ( w − w e
w
e
~ w* by Proposition 4. We distinguish three r < r * , since w< r * = Pe /(θ w ( we − w * )) , and note that ~ intervals of customer warranty valuations. (1) Customers with r ≥ r * purchase the extended ~ warranty in both cases, so U * = U . (2) Customers with ~ r ≤ r < r * purchase the extended warranty only under the simultaneous choice scenario. Under the simultaneous choice case, a ~ customer with warranty valuation r derives a (net) utility U w = rθ w we − Pe from purchasing the extended warranty. Under the sequential choice case, this customer derives a utility U w* = rθ w w *
~ ~ from the manufacturer warranty. U w* > U w ⇔ r < r * , so U * > U . (3) Customers with r < ~ r do ~ ~.■ not purchase the extended warranty in either case, so U * > U , since w * > w
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Appendix C – Details on the Numeric Study The numeric study is based on a full factorial design. To study the impact of differences in product characteristics, we vary the differences in product cost, retail price, and reservation price, and the ratio of warranty costs. The specific parameter values used in the study are given in the following. Parameter C1 C2 − C1 P1 P2 − P1
Values 10 -10, 0, 10 50 -10, 0, 10 90 -10, 0, 10 0.1, 1, 3, 5 ¼, ½, ¾, 1 5, 10 2, 5, 8 2, 5, 8 1, 3, 5 15, 20 5, 10 2, 5
R1 R2 − R1 k1 k 2 / k1 t ke
θe θw we Pe me
Comments on the numeric observations: •
Among all possible combinations of parameter values, 32,132 scenarios satisfy the conditions for an interior equilibrium.
•
For (a), given the result of Proposition 5a, it is sufficient to provide an example where retail profits are higher under sequential choice. Such an example is given by C1 = 10 ,
C 2 − C1 = 0 , P1 = 50 , P2 − P1 = 10 , R1 = 90 , R2 − R1 = 0 , k1 = 5 , k 2 / k1 = 1 / 4 , t = 5 , k e = 5 , θ e = 8 , θ w = 5 , we = 15 , Pe = 10 , and me = 5 .
•
Insights (b) and (c) are true for all scenarios that satisfy our interior equilibrium assumption.
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