Overcoming Product Cannibalization in the Online Channel using Personalization Technology, Community Access, and Intertemporal Price Discrimination
Frederick J. Riggins Carlson School of Management University of Minnesota, Minneapolis, MN
[email protected] Phone: 612-624-5760 Fax: 612-626-1316 Sridhar Narasimhan DuPree College of Management Georgia Tech, Atlanta, GA
[email protected] Phone: 404-894-4378 Fax: 404-894-6030
November 2001
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Overcoming Product Cannibalization in the Online Channel using Personalization Technology, Community Access, and Intertemporal Price Discrimination Abstract We develop a model of separating equilibrium where a monopolist markets a physical product to two types of consumers in the online channel. We show how the seller may use personalization technology to limit or even eliminate the distortion caused by the cannibalization problem. This results in higher product quality levels and earlier product introductions for goods aimed at low type consumers. We find that personalization technology also lessens the adverse effects caused when the seller cannot credibly commit to future actions. We show that the seller should focus all of its personalization efforts on high type consumers, and must concern itself with the level of patience of high type consumers and not low types. We also examine three different seller strategies for bundling the sale of the physical good with customer access to a seller-sponsored online community. When personalization capabilities are relatively low, the seller should segment consumers into two communities by allowing consumers to have access to the community associated with the type of physical good that was actually purchased. When personalization capabilities are sufficiently high, the seller should switch from the segmented communities strategy and merge all consumers into one community to take advantage of externality effects.
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1. Introduction Conducting business over the Internet allows firms to employ new online technologies and marketing strategies to serve customers in new ways. In particular, the online channel enables new interactive communications capabilities that can add value to buyers and sellers. For example, online sellers can make use of both active and passive customer feedback mechanisms to better understand their customers’ preferences and thereby provide highly customized product offerings. In addition, customers may interact with one another within a seller-sponsored online community to learn about new products and share opinions on the value of the firm’s offerings. Effective utilization of these types of online technologies is an essential component of the overall value proposition that e-business offers relative to traditional forms of commerce. One of the problems that plague sellers in any marketplace is the cannibalization problem that occurs when a seller attempts to market to different types of consumers within a given channel, but is not able to identify a particular consumer’s type. For example, with two types of consumers the seller will attempt to sell two versions of a good where a high quality, high priced good is targeted at high type consumers and a low quality, low priced good is aimed at low type consumers. However, the cannibalization problem is based on the fact that if the seller sets the price of the low quality good at the low type consumer’s willingness to pay, high type consumers may view that version as a bargain and be attracted to it rather than the high quality good. This is because high type consumers typically place a greater value on a given level of quality than low types. This distortion caused by the cannibalization of sales of high-end goods will result in lower profits for the seller. To ensure that consumers purchase the appropriate product, sellers may practice second-degree price discrimination by setting their price and quality levels to create a separating equilibrium where consumers self-select into their appropriate consumer segments. This separating equilibrium may result in the seller lowering the quality of goods normally targeted at low type consumers to make them less attractive to high type consumers (Moorthy and Png 1992). If the potential for cannibalization is particularly high, sellers may focus entirely on high type consumers such that low types may not be served at all.
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In an effort to avoid the cannibalization problem, sellers often attempt to segment the market by employing intertemporal price discrimination by offering high-end goods early and low-end goods at a later time (Bensanko and Winston 1990). Rather than lowering the actual quality of the low good, the seller degrades the product by using delay to force low type consumers to wait for the introduction of products suitable to their needs. However, certain unique features of the online channel may provide the seller with additional ways to combat the cannibalization problem. For example, because personalization technology allows the seller to better identify a prospective customer’s preferences, the seller may be able to use personalization to mitigate the cannibalization problem and move toward first-degree price discrimination in the online channel. In addition, the seller may be able to provide an additional incentive to entice customers to reveal their preferences by bundling the purchase of the physical good with access to a value-added online community. If the seller is able to restrict community access based on specific consumer purchasing behavior, the seller may be able to entice consumers to reveal their true purchase preferences. In this paper, we develop a model of separating equilibrium where a monopolist seller markets a physical product to two types of consumers in the online channel. We show how the seller may be able to use personalization technology to move from seconddegree price discrimination toward first-degree price discrimination and thereby limit or even eliminate the market distortion caused by the cannibalization problem. In particular, we show that when the seller employs personalization technology, low type consumers may experience higher product quality levels and earlier product introductions.
In
addition, we will show that increased personalization capabilities can result in less restrictive access to online community interaction for all customers. The results of this analysis are pertinent for information technology budget managers and Internet marketing strategists. The organization of the paper is as follows. We begin in the next section by reviewing the relevant literature upon which we construct our model. The single period model is developed in §3 where we show the impact of personalization technology on the seller’s strategy in terms of the price and quality selection, and the resulting profits to the seller. In §4, we analyze the seller’s strategy when the seller can bundle the purchase of
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the physical good with access to an online community.
We show that the optimal
strategy for community segmentation and customer access is dependent upon the extent to which the seller engages in personalization. We investigate the timing of product introductions in §5 where we develop a two period model when the seller is able to commit to future product introductions and when the seller is not able to credibly commit to future actions. We show how the seller is able to substitute personalization technology for intertemportal price discrimination. In other words, when the seller is able to practice personalization in the online channel, low type consumers need not be forced to wait for the introduction of products appropriate for their level of spending. We conclude with a discussion of our results in §6 and directions for future research.
2. Previous Modeling of the Cannibalization Problem Several researchers have examined pricing strategies of sellers that practice intertemporal price discrimination.
Conner (1988) illustrates how a firm may spend
aggressively on research and development to create a new version of an old product, only to set the new product aside until the old one is challenged by a competitor. Besanko and Winston (1990) model the monopolist’s optimal timing and pricing strategy in the introduction of a new product when consumers are intertemporal utility maximizers versus being myopic.
They show that prices are always lower when consumers act
rationally as opposed to myopic, allowing the seller to practice intertemporal price discrimination. Similarly, Levinthal and Purohit (1989) show how expectation of a future product improvement cannibalizes sales of the current version of the product. They show conditions under which the seller should phase out the old product versus instituting a buy-back policy when the new product is introduced. Purohit (1997) develops a two-period model of a manufacturer that markets its goods in two channels – a rental agency and a dealership. He determines the profitability of the manufacturer under three different channel structures that are used to explain how automotive manufacturers coordinate their rental and dealership relationships. Zettelmeyer (2000) examines how the size of the Internet affects the firm’s pricing and communications strategies. He shows that when the Internet is relatively small in size, firms will provide more information online and prices will be lower than in conventional
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channels. As the number of users on the Internet increases, the amount of information the firm provides through the Internet channel and the firm’s online pricing policy will be similar to that in the conventional channel. Balasubramanian (1998) adapts Salop’s (1977) circular city model to compare the direct mail efforts of a physically unconstrained catalog retailer versus the efforts of traditional retailers who cater to neighboring customers. While he indicates the model can be used to illustrate the efforts of an online Internet retailer he doesn’t examine the use of online features such as personalization or community. In another model, Roy (2000) examines how targeted direct marketing can result in complete market segmentation between two competing firms. Mason and Milne (1994) conduct an empirical study of the cigarette industry to show how the proliferation of brands results in cannibalization of other product lines, leading firms to reduce the number of brands they sell. They develop a method of identifying the degree of cannibalization in mature retail markets. The current analysis is most closely related to Moorthy and Png (1992) who develop a model of separating equilibrium where a monopolist produces a durable good that can be differentiated along some dimension of quality. The monopolist sells to a market that is made up of high and low type consumers, where high types have a greater value for a given level of quality than low types. Given this scenario, the seller will produce two versions of the product – a high quality product targeted at high type consumers, and a low quality, low priced product targeted at low types. The authors show that the optimal solution to the cannibalization problem is to give high type consumers a price discount and lower the quality (and corresponding price) of the low quality good to the point that the high type consumer is not interested in that version of the product. Indeed, the cannibalization distortion may be so strong that the seller may lower the quality of the low good to the point that it essentially doesn’t exist, i.e. the low type consumer is not served in the marketplace. This distortion has two important effects on the market. First, low type consumer choice is reduced since they receive a lower quality product. Second, this distortion lowers the profits of the seller who must contend with the moral hazard associated with second-degree price discrimination. They extend their model to consider the impact of sequential product introductions. By offering the
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high quality product in the first period and the low quality product in the second period, the seller is able to mitigate the cannibalization problem when buyers are relatively more impatient than the seller.
In the remainder of this paper, we extend their model to
incorporate the impact of the seller’s employment of personalization technology and community features in the online channel.
3. Single Period Separating Equilibrium with Personalization We begin with the basic single-period model with personalization where a monopolist produces a durable good and markets it in the online channel.
The
cannibalization problem arises because the seller is not able to distinguish a prospective customer’s type and therefore must practice second-degree price discrimination. As the seller is able to collect user information and thereby personalize the online offering, the seller is able to move away from second-degree price discrimination and move closer to first-degree price discrimination. Indeed, in an environment where the seller is able to gather perfect information about the user, he would be in a position to extract all consumer surplus by setting the price at each consumer’s willingness-to-pay.
For
example, once enough information is collected, an online high type user would only have access to pages promoting high quality goods and may never see low quality goods in the online channel.
It is easy to see how in the extreme this would eliminate the
cannibalization distortion. We consider a market for a durable good that can be differentiated according to some dimension of quality, q. There are two types of consumer segments in the market, h and l, where nh is the number of high types and nl is the number of low types. Further, high type consumers value a given level of quality q at vhq, while low types value the same item at vlq. Let vh > vl > 0 such that high types value a given level of quality more than low type consumers. Let vlh =vh/vl, nlh =nh/nl and R= nlh ( vlh –1) where R is a measure of the degree of cannibalization as shown in Moorthy and Png (1992). The seller’s marginal cost of supplying one unit with quality q is cq2, where c > 0. Finally, assume that a consumer buys at most one unit of the durable good and then exits the marketplace. To model the seller’s use of personalization technology we introduce a personalization parameter, ω ∈ (0, 1), which measures the extent to which the online 7
seller is able to know the user’s likes and dislikes, and correspondingly personalize the online channel offerings. When ω is close to 0, the seller is not able to personalize at all. When ω is close to 1 the seller knows everything about the user and is able to practice first-degree price discrimination. When this occurs the seller would be able extract all consumer surplus. With two consumer segments in a single channel, there can be at most two “products” or levels of qualities – a high quality good targeted to the high type consumers and a low quality good offered to the low type consumers. We can calculate the efficient qualities of the two products as the qualities that maximize the difference between the targeted customer’s valuation and the firm’s marginal cost of quality. Specifically, the efficient qualities for the two products are qh * =
vh 2c
(1)
and vl . 2c Given that vh > vl > 0, we know that q h * > q l * . ql * =
(2)
With this scenario, our goal is to understand when and how the seller will offer products to the two market segments. With two segments, there are at most two products and at most two possible product introduction dates. The seller can execute one of the following strategies: 1) offer both products simultaneously in the first period; 2) offer the high quality product in period one and the low quality product in period two; 3) offer the high quality product in period one and not serve the low type consumers; or 4) offer neither product at any time. The fourth scenario is trivial and occurs when the cost, c, is too high to encourage entry into this market, i.e. qh = ql = 0. Also, it should be noted that if the seller enters the market it will never delay offering the high quality product and the low quality product will never be offered before the high quality good. While the seller may degrade the low quality product to avoid the cannibalization problem, he will never delay offering the 8
high quality good, since delay is a form of product degradation. This is so because, while the high type consumers may be tempted to buy the low quality good, the low type consumers will never consider purchasing the high quality good. We now turn our attention to the first situation noted above where the seller introduces all products in the same period and commits to no further product introductions.
Clearly, there is no reason to delay both introductions, so this case
considers simultaneous first period introductions. When the seller targets the appropriate good to the appropriate consumer segment, the seller’s problem is to select the quality levels, qh and ql, and prices, ph and pl, according to the following problem
(
) (
)
(3)
vl ql − pl ≥ (1 − ω )[ vl q h − p h ]
(4)
v h q h − p h ≥ (1 − ω )[ v h ql − pl ]
(5)
max nh p h − cq h 2 + nl pl − cql 2
qh , ql , p h , pl
subject to:
vl ql ≥ pl
(6)
vh qh ≥ ph .
(7)
The constraints (4) and (5) are the self-selection constraints for the two consumer segments. Since the seller must practice second-degree price discrimination, he must set the quality and price levels so that each segment chooses the appropriate quality and price offering. Constraints (6) and (7) are the participation constraints that ensure that each consumer type will participate in the market. As pointed out by Moorthy and Png (1992), because high type consumers value a particular level of quality more than low type consumers, the seller cannot extract all of the consumer surplus from both types by binding constraints (6) and (7) simultaneously. If the seller attempted this, the high type consumers would forgo purchasing the high quality good and instead purchase the low quality good, thereby gaining some positive surplus. In fact, if the seller sets the price of the low quality good within the low type consumer’s price range, the high type consumers are sure to participate in the market. The seller’s problem is to make sure low type consumers participate and that high type consumers buy the appropriate good. Therefore, the seller will bind constraint (6) such that
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pl = vl ql .
(8)
Also, the seller should set the price for the high quality good such that high type consumers are indifferent between the high quality good and the low quality good. This is accomplished by making constraint (5) bind, such that ph = ω vh qh + (1 − ω )[ vh qh − (vh − vl )ql ].
(9)
Substituting these prices into the objective function and maximizing with respect to the two levels of quality, we see that ql =
vl [1 − R(1 − ω )] 2c
(10)
and qh =
vh 2c
(11)
The seller’s profits are
nl v l 2 nh vh 2 2 Π= [ 1 − R(1 − ω )] + . 4c 4c
(12)
The two terms in equation (12) represent the profit from selling to low type consumers and high type consumers, respectively. This two-product solution is feasible, if and only if ql > 0 , i.e., when R(1 − ω )< 1 . When R(1 − ω )≥ 1 , the seller is able to increase profits by lowering the quality of the low quality product, and does so until the point that it essentially doesn’t exist – the low type consumer is not served in the online market. As Moorthy and Png (1992) show, the seller should supply the high type consumers their efficient qualities from (1) and price them according to (9). Low type consumers receive a product that has a quality level lower than the efficient amount provided that
R(1 − ω )> 0 . As R(1 − ω )→ 1 , profits are increased as ql goes down. In the limit, no two-product solution can have profits greater than nhvh2/4c. Therefore, the profits with two distinct products for the single period introduction case where the seller can commit to no further product introductions are = Π12c p
nl vl 2 nh vh 2 [1 − R(1 − ω )]+ 4c 4c 2 nh vh 4c
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if if
R(1 − ω )< 1 R(1 − ω )≥ 1.
(13)
As expected, this result is the same as Moorthy and Png (1992) when ω → 0 . Moorthy and Png (1992) also show that if the seller attempts to sell only one product, q, at price, p, it will serve only the high type segment with a price p = vhq at the efficient quality level, such that Π11c =
nh vh 2 . This is better than (12) when R(1 − ω )≥ 1 . For the case where 4c
the seller employs personalization technology, we can now state Proposition 1 as
PROPOSITION 1. If the seller is able to personalize according to the personalization parameter, ω ∈ (0, 1), and chooses to introduce products in one period only, then he will do so in the first period, and offer two qualities if R
0 be the relative value to consumer of type i of having a consumer of type j in the online community. We consider three ways that the seller can segment the online community and provide community access to consumers1: 1) offer one community that is open to all consumers who purchase either physical good; 2) segment the community into two separate communities where one is promoted as being for low type consumers and the other is promoted as meeting the needs of high type consumers. When a consumer makes a purchase of a physical good, the consumer may choose to have access to one community or the other; and 3) segment the community into two separate communities based on the purchase of a physical good. When a consumer makes a purchase of a physical good, the consumer is given access to the community associated with the particular good that was purchased. 4.1 Strategy 1: Single Online Community for All Customers The first strategy is where a consumer receives access to the single community made up of all of the seller’s customers. The seller’s problem is
(
) (
max nh p h − cq h 2 + nl pl − cql 2
qh , ql , p h , pl
)
(14)
subject to: v l q l + κll nl + κlh n h − p l ≥ (1 − ω )[ v l q h + κll nl + κlh n h − p h ]
(15)
v h q h + κhl n l + κhh n h − p h ≥ (1 − ω )[ v h q l + κhl nl + κhh n h − p l ] (16) v l q l + κll nl + κlh n h ≥ p l
(17)
v h q h + κhl n l + κhh n h ≥ p h .
(18)
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There are many other ways to offer access to communities not considered here. Future research should examine the role of communities provided for free to build brand or communities that require a periodic subscription fee.
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Proceeding in the same manner as before, the seller would bind (16) and (17), such that the two prices would be p l = v l q l + κll nl + κlh n h
(19)
and p h = ω (v h q h + κhl nl + κhh n h )+ (1 − ω )[ v h q h − (v h − v l )q l + κll n l + κlh n h ].
(20)
As in the previous case the seller is able to extract all consumer surplus from the low type consumers such that if they value community interaction, the seller is able to charge them their willingness to pay for that service. This is not the case for high type consumers, except when ω is near 1. When ω is near 0, the seller charges high type consumers what the low type consumers are willing to pay. This is because this is the markup for the low quality good in (19), so the seller is able to charge that to the high types regardless of which product they choose. As ω increases towards 1, the seller is able to increase this mark-up to reflect the extent to which high type consumers value community access. Again, using (19) and (20) to solve the objective function, we see that ql =
vl [1 − R(1 − ω )] 2c
(21)
and qh =
vh 2c
(22)
just as in the previous section. We can calculate the seller’s profits for Strategy 1 as
Π (1) = Π (0) + κlh [n l n h + (1 − ω )n h 2 ] + κhl [ω nl n h ] + κhh [ω n h 2 ]
[
2 nl v l 2 2 nh v h where Π (0) = [ 1 − R(1 − ω )] + + κll nl 2 + (1 − ω )nl n h 4c 4c
] and
(23)
represents a
portion of the seller’s profits that is common to all three strategies under consideration.
4.2 Strategy 2: Segmented Communities by Consumer Type The second strategy is where a consumer must choose to receive access to either the high type consumer community or the low type consumer community. In this portion of the analysis, we will assume that when given the choice of choosing between one community segment or the other, the consumer will choose to receive access to the community with consumers of the same type as themselves. We could investigate other 14
scenarios, but the basic results given below would not be altered.2 In this case, the seller’s problem is
(
) (
max nh p h − cq h 2 + nl pl − cql 2
qh , ql , p h , pl
)
(24)
subject to: vl ql + κll nl − p l ≥ (1 − ω )[ v l q h + κll nl − p h ]
(25)
v h q h + κhh n h − p h ≥ (1 − ω )[ v h ql + κhh n h − p l ]
(26)
vl ql + κll nl ≥ p l
(27)
v h q h + κhh n h ≥ p h
(28)
p l = v l q l + κll nl
(29)
p h = ω (v h q h + κhh n h )+ (1 − ω )[ v h q h − (v h − v l )ql + κll nl ]
(30)
whereby
and
leading again to ql =
vl [1 − R(1 − ω )] 2c
(31)
and qh =
vh . 2c
(32)
Here, the seller’s profits for Strategy 2 are
Π (2) = Π (0) + κhh [ω n h 2 ] .
(33)
We can now state Proposition 3 as
PROPOSITION 3. In terms of the seller’s profits, Strategy 1 weakly dominates Strategy 2. The two strategies are equal when consumers do not value interaction with types other than their own.
2
If we allow consumers to select a community other than the one targeted for their type, the quality levels would be unaltered and the seller’s profits would be between that found in (23) and (33) with no change to the propositions given below.
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This should not be surprising since a consumer will believe that “more is better”. If the consumers do not value interaction with other types of consumers, then the profits from the two strategies are identical. However, if consumers value interaction with other types at all, then consumers receive more value in Strategy 1 and can be charged accordingly, thereby raising the seller’s profits.
In particular, note that the seller’s selection of
Strategy 1 versus Strategy 2 does not affect the consumer’s physical product selection – Strategy 1 simply results in more value to the consumers. This is not the case with the third strategy.
4.3 Strategy 3: Segmented Communities Based on Physical Product Purchased In the third strategy, the seller segments the consumers into two community segments and provides the consumer with online access to the segment associated with the particular physical product that was purchased. Unlike the first two strategies, the seller is essentially providing added incentive to entice the consumer to select the “appropriate” physical good, provided that consumers value interaction with their own type. The seller’s problem is
(
) (
max nh p h − cq h 2 + nl pl − cql 2
qh , ql , p h , pl
)
(34)
subject to: vl ql + κll nl − pl ≥ (1 − ω )[ vl q h + κlh nl − p h ]
(35)
v h q h + κhh n h − p h ≥ (1 − ω )[ v h ql + κhl n h − pl ]
(36)
vl ql + κll nl ≥ p l
(37)
v h q h + κhh nh ≥ p h
(38)
pl = vl ql + κll nl
(39)
whereby
and p h = ω (v h q h + κhh n h )+ (1 − ω )[ v h q h − (v h − vl )ql + κll nl − κhl nl + κhh nh ]
(40)
leading again to ql =
vl [1 − R(1 − ω )] 2c
and 16
(41)
vh . 2c
(42)
Π (3) = Π (0) − κhl [(1 − ω )nl n h ] + κhh [n h 2 ] .
(43)
qh =
Here, the seller’s profits for Strategy 3 are
Since Strategy 1 weakly dominates Strategy 2, we want to compare the seller’s profits for Strategy 3 with Strategy 1. First, we can state Proposition 4 as
PROPOSITION 4. In terms of the seller’s profits, if consumers do not value interaction with types other than their own, then Strategy 3 weakly dominates Strategy 1, and therefore Strategy 2, where the three strategies are equal when ω is near 1.
What about when consumers do value interaction with other types? Comparing (23) and (43) we see that Π(3) > Π(1) when n (κ + κlh ) ω < 1 − l hl . nh (κhh − κlh )
(44)
When κlh = κhl = 0, then Π(3) > Π(1) when ω < 1 as we stated in Proposition 4. However, when κlh > 0 or κhl > 0, then Π(1) > Π(3) for high levels of ω, provided that κhh > κlh. In other words, if consumers value interaction with other types and the seller is not able to employ sophisticated personalization technology, then the seller can fight the cannibalization distortion by segmenting the community into two separate groups and allowing consumers to have access only to the community associated with the physical product purchased.
However, when the seller is able to employ high levels of
personalization technology, then personalization eases the cannibalization distortion, such that the seller is able to increase profits by merging the community segments into one large community and charging consumers accordingly for the added value.
When
consumers do not value interaction with other consumer types, then the seller should segment the community into two groups and allow access only to the community associated with the good purchased.
The exception occurs when κlh > κhh where
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nl (κhl + κlh ) 1 − > 1 so that (44) is always satisfied and therefore Π(3) > Π(1). We can nh (κhh − κlh )
state the key result in Proposition 5 as follows n (κ + κlh ) PROPOSITION 5. For low levels of personalization, i.e. when ω < 1 − l hl , n h (κhh − κlh )
the seller’s profits are greater with Strategy 3 than Strategy 1 or 2. For high levels of n (κ + κlh ) personalization, i.e. when ω > 1 − l hl , the seller’s profits are greater with n h (κhh − κlh )
Strategy 1 than Strategy 3 or 2.
Essentially, bundling the purchase of the physical good with access to the associated online community segment provides an additional incentive to entice the consumers to select the appropriate physical good.
This bundling provides an additional weapon
against the cannibalization problem that should be used when personalization capabilities are relatively low. On the other hand, relatively high personalization capabilities allow the seller to move toward first-degree price discrimination such that the seller should provide full access to online community members and charge consumers accordingly in order to take advantage of potential network externality effects.
5. Sequential Product Introductions with Personalization We now extend our model to two periods to consider the second case outlined earlier where the seller can employ sequential product introductions. In an effort to circumvent the cannibalization problem, sellers often use delay, or intertemporal price discrimination, as a way of segmenting the marketplace by offering high-end goods early and low-end goods at a later time. Examples of this tactic are visible in many markets. For example, hard copy books are released several months before paperback versions, movie goers enjoy the superior visual and audio experience of the movie theater nearly a year before the same movie is released on home video cassette, and season tickets with priority seating go on sale long before single-game tickets are sold. While the model
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becomes intractable if we include community features in the two period setting, we will continue to include the personalization parameter in our model.
5.1 Sequential Product Introductions with Commitment We continue to look at the case where the seller can credibly commit to future price and quality levels. When considering the option of delay, the seller would consider delaying the introduction of the low quality good and not the high quality good, since delay is a form of product degradation. Therefore, for the two-period scenario, we introduce the high type consumer’s discount factor, δh ∈ (0, 1), which is the cost of waiting until the second period to purchase the low quality good, the low type consumer’s discount factor, δl ∈ (0, 1), and the seller’s discount factor, δs ∈ (0, 1), which is the cost of waiting until the second period for profits from those sales.
The
interpretation is that the discount factor is a measure of the particular party’s patience. For example, when δh is close to 0, the high type consumer has no patience and would gain no value from a second period purchase. When δh is close to 1, the consumer is perfectly patient and derives the same value from a first or second period purchase. The seller’s problem is now
(
)
(
max nh ph − cqh 2 + δs nl pl − cql 2
qh , ql , p h , pl
)
(45)
subject to: δl (vl ql − pl )≥ (1 − ω )[ vl qh − ph ]
(v h q h −
p h )≥ δh (1 − ω )[ v h q l − pl ]
(46) (47)
vl ql ≥ p l
(48)
vh qh ≥ ph .
(49)
pl = vl ql
(50)
ph = [ 1 − δh (1 − ω )]vh qh + (1 − ω )δh [ vh qh − (vh − vl )ql ]
(51)
Proceeding as before, we have
and
where the quality levels are
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qh =
vh 2c
(52)
and ql =
[
]
vl 1 − δsh R(1 − ω ) 2c
(53)
where qh is offered in the first period, ql is offered in the second period when
δsh R(1 − ω )< 1 , and δsh = δh/δs.3 The seller’s profit for two products offered over two periods with commitment is
[
]
δs nl v l 2 2 n v 2 = 1 − δsh R(1 − ω ) + h h 4c 4c Π 22c 2 n v p h h 4c
if
δsh R(1 − ω )< 1
if
δsh R 1 −
(54)
(
ω )≥ 1.
We can follow the methodology of Moorthy and Png (1992) to derive the seller’s optimal product introduction strategy for four different cases: 1 1 δs Case 1: R ≥ max , . By Proposition 1, the seller should offer one product 1 − ω 1 − ω δ h
and commit not to offer any future products. By (54), offering two products does not increase profits, so the seller’s appropriate strategy is to introduce one product only (the high quality good) in the first period and commit not to introduce any more products in future periods. In this case, the cannibalization distortion is go great that the seller will not offer a product to low type consumers.
Notice that in the limit, as ω → 1 ,
personalization technology will make Case 1 infeasible. Therefore, just as we saw after Proposition 1, if ω → 1 the seller will never offer only one product, but will serve both high and low type consumers, or neither if c is too high.
Case 2:
1 1 δs ≤R < . Again, the optimal one period solution is to offer one 1− ω 1 − ω δh
product only and commit to no future offerings. However, we see from (54) that the two-
3
Similarly, let δhs = δs/δh. 20
period solution has a higher profit, so the seller’s optimal strategy is to introduce two products sequentially over two periods.
Case 3:
1 δs 1 ≤R < . In this case, we see from (14) that introducing two 1 − ω δh 1− ω
products in the first period maximizes the seller’s profits, and this profit is greater than the two-period solution in (54).
Therefore, simultaneous first period product
introductions are best. 1 1 δs Case 4: R < min , . In this case, from (14) and (54), we see that the two 1 − ω 1 − ω δh
product solution is optimal in both one and two-period solutions. Using (14) and (54), we can show that Π 22c > Π12c if and only if R
