Product Differentiation and Market Segmentation of Information Goods

Transcription

1 Product Differentiation and Market Segmentation of Information Goods Xueqi (David) Wei and Barrie R. Nault Haskayne School of Business University of Calgary December 2, 2005 We thank the Natural Science and Engineering Research Council of Canada, the Social Science and Humanities Research Council of Canada, and the David B. Robson Endowment and the irc at the Haskayne School of Business at the University of Calgary for support. Copyright c 2005 by David Wei and Barrie R. Nault. All rights reserved. Preliminary Draft: Please do not cite or quote without the authors permission. Comments are welcome.

2 Abstract Large sunk costs of development, negligible costs of reproduction and distribution and substantial economies of scale make information goods distinct from physical goods. Consequently, how to take advantage of the specific characteristics of information goods is an important managerial problem. Price discrimination and product differentiation are common ways this issue has been addressed. In previous literature, vertical differentiation and related pricing strategies have been researched in contexts such as nonlinear utility functions, network externalities, competition and anti-piracy. Little attention has been paid to the relationship between market segmentation and product differentiation. In this paper, we emphasize the interaction of market segmentation and product differentiation as we believe that any product differentiation must be based on existing market segmentation. In our model, we treat vertical differentiation as a special case of horizontal differentiation, and we model the interaction between different market segments showing the differences in product differentiation strategies when moving from horizontal to vertical differentiation. We find that it is always sub-optimal to differentiate information goods if the market is not fully differentiated or if characteristics of the information goods are not specifically designed for certain market segments. We divide characteristics of information goods into four categories according to the ease of differentiation and design guidelines for firms to differentiate their goods based on these characteristics. We further provide guidance on whether to merge one or several versions when costs for versioning information goods are significant. Keywords: Information Goods, Market Segmentation, Product Differentiation, Versioning Strategies, Pricing Strategies.

3 1 Introduction Large sunk costs of development, negligible costs of reproduction and distribution, and the resulting substantial economies of scale make information goods distinct from physical goods. Consequently, how to take advantage of the specific characteristics of information goods is an important managerial problem. Previous Literature. There is broad literature in the research of product differentiation and market segmentation. Frank, Massy and Wind (1972) propose a model of third degree price discrimination which assumes market segments are isolated and consumers from one segment cannot purchase goods from another segment. Moorthy (1984) investigates on consumer self-selection and proposes product line design strategies based on second degree price discrimination. By using consumer self-selection, consumers choose between products in different market segments based on their valuation. Product differentiation becomes the focus for firms to implement price discrimination. Pricing of products designed for different market segments are related with each other and cannibalization occurs between different market segments. Moorthy and Png (1992) further address the market cannibalization problem using timing as an effective way to reduce cannibalization when consumers are relatively more impatient than the seller. For most information goods distributed through Internet, consumer self-selection is the only choice for firms deciding their pricing strategies. So research on effective methods in dealing with market cannibalization and optimal product line design are topics in the most recent literature. Price discrimination and product differentiation are common ways this problem has been addressed. In previous literature, vertical differentiation and pricing strategies are modeled in different contexts such as network externalities (Jing, 2002), competition (Jones and Mendelson, 2005) and anti-piracy (Wu, Chen and Anandalingam, 2003). They all reach the conclusion that vertical differentiation is not optimal without certain constraints, consistent 1

4 with Bhargava and Choudhary (2001). Bhargava and Choudhary (2005) examine nonlinear utility functions for vertical differentiation of information goods and propose that vertical differentiation is optimal when lower type consumers have greater ratios of valuations than higher type consumers. Lilien, Kotler and Moorthy (1992) recognized that vertical differentiation would be attractive when consumers were sufficiently heterogeneous because versions could differentiate users. Nault (1997) researched quality differentiation using interorganizational information systems (IOS) and found that IOS could effectively differentiate consumers and reduce competition in a duopoly situation. Bakos and Brynjolfsson (1999) studied the strategy of bundling information goods and found that bundling large numbers of unrelated information goods can be profitable, but when different market segments of consumers differ systematically in their valuations for goods, simple bundling is no longer optimal. Sundararajan (2004) showed that fixed-fee and usage-based pricing can be used together to maximize firm s profit for information goods. Background Examples. Although the modeling results from the previous literature are consistent with many empirical observations, there are other observations that are not effectively explained. The most well-known is Microsoft s Operating Systems. The latest Windows XP has five editions: Home Edition, Professional, Media Center Edition, Tablet PC Edition and Professional x64 Edition. The Home Edition and Professional Edition are vertically differentiated, but the others are horizontally differentiated. The Windows Server 2003 family has six editions and they are not purely vertically differentiated as each edition has its own focus. Another typical example is the product line of Kurzweil, a software firm of voice recognition products (Shapiro and Varian, 1999). Kurzweil offers seven versions of its voice recognition products. Among them Office Talk is designed for office staff, Law Talk for lawyers and Voice Med for medical staff. Each version is priced differently while all of the versions share a certain amount of common vocabulary (about 20,000 words). The high-end version for surgeons is priced a hundred times higher than the entry-level software. In both of these examples, product differentiation strategies are a mix of both vertical and horizontal 2

5 differentiation. There are numerous similar examples of information goods differentiation. Although it is technically possible for the firms to generate a super-version which contains all the characteristics in their product line and then degrade it to generate vertically differentiated versions, most firms still choose to differentiate their products horizontally whenever possible. We do not have a model framework that effectively explains what we observe in practice and guides the combined strategies of both vertical and horizontal differentiation. Our Contributions. Little attention has been paid to the relationship between market segmentation and product differentiation in the context of information goods. In this paper, we follow the self-selection model of consumer choice, emphasizing the interaction of market segmentation and product differentiation of information goods as we believe that any product differentiation must be based on existing market segmentation. We treat vertical differentiation as a special case of horizontal differentiation, and model the interaction between different market segments showing how product differentiation strategies differ when moving from horizontal to vertical differentiation. If the market is not fully differentiated or if characteristics of the information goods are not specifically designed for certain market segments, then we find that it is always sub-optimal to differentiate information goods. We divide characteristics of information goods into four categories according to the ease of differentiation, and design guidelines for firms to differentiate their goods based on these characteristics. We further provide guidance on whether to merge multiple versions when costs for versioning information goods are significant. 2 Modeling Following the hedonic hypothesis that goods are valued for their utility-bearing attributes or characteristics (Rosen, 1974), we define information goods as a set of characteristics. 3

6 We allow for M characteristics, χ = {x 1, x 2,..., x M }, and the situation independent value of characteristic m is x m R +. Each good contains a subset of these characteristics, for example χ X 1, X 2,..., X I where there are I possible information goods. We treat the quality of a given information good as the sum of the situation independent values of its characteristics, q i = x m X i x m. Based on our definition of information goods, although characteristics are not comparable between different goods, quality is comparable between them because in our model, quality is a sum of values that are R +. As assumed in most prior research, consumers are heterogeneous and continuously distributed in their individual taste for quality. However, in our model, we define a second feature that determines an individual s taste for quality: a group taste. We denote the individual consumer taste as θ which belongs to [θ 0, θ N ]. We assume that θ has density and cumulative density functions f(θ) and F (θ), so that the target consumers are normalized with a unit population. The density is strictly positive over its support and continuously differentiable. Consumers are also divided into groups and these groups are correlated with individual tastes. Consumers with individual taste in [θ n 1, θ n ] belong to group n, n {1, 2,, N}. Consumers in the same group n share the same group taste k n and higher groups have greater tastes for quality, which means k n+1 > k n. We represent the taste for quality as a product of the individual and group taste so that it can be represented by k n θ. Without loss of generality (as we can rescale q), we assume a linear relationship in the consumers willingness to pay U(q, θ, k n ) between taste θ and quality q. So the utility function of consumers in group n who purchase information good with quality q can be expressed as U(q, θ, k n ) = k n θ q, n {1,..., N}, θ [θ n 1, θ n ). The Diagram 1 illustrates the utility that consumers from different groups receive based on the above utility functions. The combination of individual and group tastes allows us to represent discontinuous consumer heterogeneity. 4

7 *** insert Diagram 1 about here *** For a better control of the model, we have the following assumption about the distribution of individual consumer taste θ Assumption 1 The hazard function f(θ) 1 F (θ) is non-decreasing. From Assumption 1, the hazard function f(θ), 0 δ 1 is also non-decreasing, δ F (θ) F (θ) (δ ) 0, for 0 δ 1. θ f(θ) This extension will be used frequently to guarantee unique solutions to our profit maximization problems. Based on consumer self-selection, in market segment n where the consumer only chooses between buying the good designed for her segment and not buying, we define θ n as the indifferent consumer and the price assignment is p n = U(q n, θ n, k n ). (1) In the market segment n where the consumer chooses between buying the good designed for her segment n and a good designed for another segment i, we define θ n as the indifferent consumer type and the price assignment is p n = p i + U(q n, θ n, k n ) U(q i, θ n, k n ). (2) In this formulation, the profit maximization problem for a monopolist that serves all the N market segments is max {Π( θ n ) = θ n,n {1,2,,N} N p n (F (θ n ) F ( θ n ))}, θn [θ n 1, θ n ). n=1 5

8 3 Market with Only One Consumer Group If all consumers share the same group taste, then there is only one consumer group in the market, k n = k n N. The utility function can be expressed as U(q, θ, k) = k θ q, θ [θ 0, θ N ]. Since there is one group, all the characteristics designed for this group are valued by all consumers. We start with the situation where firm provides at most two quality levels of the information good, we denote them as q h and q l respectively for high quality and low quality. Here we denote θ h as the consumer type indifferent between buying q h and q l ; θ l is the consumer type indifferent between buying q l and not buying. Obviously, we have θ l θ h. Generally, for vertically differentiated information goods, we have the following relationships for profit-maximizing prices p l = U(q l, θ l, k), (3) U(q h, θ h, k) p h = U(q l, θ h, k) p l, q l [0, q h ]. (4) (3) means the consumer type θ l is indifferent between buying q l and not buying. (4) means the consumer type θ h is indifferent between buying q h and q l. Solving for (3) and (4) we can derive the relationship between p h, p l and θ h, θ l. Normally firms choose prices, p h and p l, to maximize profits. But in our model, it is complicated to deal with the profit maximization problem in prices. In Appendix 1 we show that it is equivalent to express and maximize the firms profit as function of price, Π(p h, p l ), and as function of indifferent consumer types, Π(θ h, θ l ). In what follows we choose to maximize firm profits by choice of indifferent consumer types θ h and θ l. We assume that the high quality good, q h, has already been developed (the development cost is sunk) and the lower quality good, q l, can be produced with no extra costs. The firm 6

9 chooses θ h and θ l to maximize its profit. Our profit maximization problem is subject to max{π(θ h, θ l ) = (1 F (θ h ))[U(q h, θ h, k) U(q l, θ h, k)] + (1 F (θ l ))U(q l, θ l, k)}, θ h,θ l θ 0 θ l θ h θ N. Using numbered subscripts to denote partial derivatives of the utility function with respect to its corresponding arguments, the first order conditions imply that the optimal θ h and θ l satisfy and f(θ l ) 1 F (θ l ) = U 2(q l, θ l, k) U(q l, θ l, k), f(θh) 1 F (θh ) = U 2(q h, θh, k) U 2 (q l, θh, k) U(q h, θh, k) U(q l, θh, k). Because the utility function takes the form of U(q, θ, k) = kθq we can simplify the first order conditions as θ l = 1 F (θ l ) f(θ l ) and θ h = 1 F (θ h) f(θ h ). Because the inverse hazard function 1 F (θ) f(θ) is non-increasing by Assumption 1, θ = 1 F (θ) f(θ) unique solution (considering the constraints θ 0 θ l θ h θ N, θ can be corner solutions, has in this case θ = θ 0 ). Therefore θ l = θ h, which means no consumer chooses q l and a single version is optimal. This yields the following theorem: Theorem 1 If there is one group in the market, it is not optimal to version information goods. This is the classic one version case, which using our formulation replicates the findings of Jones and Mendelson (1998), Bhargava and Choudhary (2001) and basic argument of Jing (2001), and Wu, Chen and Anandalingam (2003). 7

10 4 Horizontal Differentiation of Information Goods 4.1 Market with Multiple Groups and Perfectly Differentiated Goods Consider when there are multiple groups in the market that are completely different in their taste and quality requirements. Here we define q h the highest quality version and q n the quality tailored for group n. We define X h as the set of characteristics for the highest quality version, which includes all the characteristics for each market segment. Perfectly differentiated goods means there is no overlap in between the characteristics of the versions offered to any two different groups. So we have N = X i X j for i j, X h = X 1 X 2 X N, and q h = q i. i=1 Different groups also have different group taste coefficients k n. Thus the utility function for each segmented group is U(q i, θ, k n ) = { kn θq i if n = i; 0 if n i. If a consumer from group n chooses the right good (the good designed for her group), then she gets utility level k n θq i ; if she chooses the wrong good (good designed for another group), then she gets zero utility. For perfectly differentiated goods, firms never worry that consumers from one market segment buy goods from other markets. We call this market a market without cross purchasing problems. Consequently we can deal with each market segment separately. Based on Theorem 1, we know one version is optimal for each market segment. We denote Π n the profit obtained from market segment n. The profit maximizing problem of market segment n is 8

11 max{π n (θ) = (F (θ n ) F (θ))u(q n, θ, k n )}, θ [θ n 1, θ n ). θ From the first order conditions, we get θ = F (θ n) F (θ). f(θ) We denote θ n as the indifferent consumer type which maximizes profit in market segment n without considering interaction with other market segments. Since the inverse hazard function F (θn) F (θ) f(θ) is non-increasing by Assumption 1, θ = F (θn) F (θ) f(θ) has unique solution θ n (considering the constraints θ [θ n 1, θ n ), θ can be corner solutions, in this case θ n = θ n 1 ). We can see that in this case, each segment market is treated independently and the indifferent consumer type θ n for each market segment is also solved separately. Each segment market may or may not be covered based on θ n (covered if θ n = θ n 1 and not covered if θ n > θ n 1 ). Summarizing, we have the following theorem. Theorem 2 For a market with multiple groups and completely different tastes, each market segment needs one version of differentiated good which is tailored for it. In this case the firm provides perfectly differentiated goods for different market segments. With information goods, the firm may benefit from economies of scale in production. 4.2 Market with Multiple Groups and Differentiated Goods with Shared Characteristics Market without Threat of Cross Purchasing Perfectly differentiated goods for different groups is an idealized model. However, in most real cases, different groups get value from a shared set of basic characteristics of the information 9

12 good, while other characteristics can be tailored for different groups. We use X a to denote the basic characteristics of the information good and q a = x m X a x m the quality index for X a. Since X n is the set of characteristics of the information goods for group n, we get X n X a as the set of special characteristics tailored for group n. Only this specific group values those special characteristics. So we have N X a = X i X j i j, and q h = q a + (q n q a ). n=1 The relevant utility function can be expressed as { kn θq U(q i, θ, k n ) = i if n = i; k n θq a if n i, which means if a consumer from group n purchases the information good tailored for her, then she gets utility k n θq n. Otherwise, if she buys the wrong information good (those tailored for other groups), she only gets utility from the shared characteristics, k n θq a. To avoid cross purchasing, which in this case means avoiding consumers buying the wrong information good, we add the following constraints U(q i, θ, k n ) p i 0 n, n i and θ [θ n 1, θ n ). To prevent cross purchasing problem mentioned above, we have Lemma 1 Lemma 1 The necessary and sufficient conditions to prevent cross purchasing between different groups in a market with multiple groups is q a k nθn, n {1, 2,, N 1}. q n k N θn Lemma 1 is the special case of the more general condition U(q a, θ N, k N ) U(q n, θ n, k n ), n {1, 2,, N 1}. 10

13 As shown in the previous section, θn is the indifferent consumer type which maximizes profit in market segment n without considering interaction with other market segments. Because consumers with high individual tastes also have high group tastes, market segment N will be the first to cross purchase goods designed for other segments. Lemma 1 indicates that the basic characteristics do not provide enough value for consumers in market segment N to purchase the goods designed for other segments, and thus guarantees the separation of all the market segments. If we can prevent cross purchasing, then we can treat each market segment separately. And in this situation, we get the following theorem. Theorem 3 For markets with multiple groups and differentiated goods with shared characteristics, if there is no threat of cross purchasing, then it is profit maximizing for the firm to provide each market segment only one version of the differentiated good which is tailored for it. The rationale behind Theorem 3 is simple. If the value of the common characteristics is relatively low as compared to the value of the special characteristics, then each consumer chooses exactly the right version for her. Otherwise, consumers with high willingness to pay may find themselves better off purchasing the versions tailored for low willingness to pay groups Market Under Threat of Cross Purchasing Now we analyze the conditions where the constraints in Lemma 1 cannot be satisfied. Generally, for consumer group i, if we have qa q i > k iθi k j, 1 i < j N, which means θ θj j gets more value from q a than θi gets from q i, then there is potential threat that part of market segment j will purchase good X i instead of X j. So how does the firm deal with this problem? To better address this problem, we further assume that cross purchasing only occurs between market segment i and market segment 11

14 j. Since only high market segment is threatened by information good designed for low market segment (refer to the Appendix for proof), we have i < j. Under the threat of cross purchasing between market segment i and market segment j, the information good firm changes the price constraints in both market segments i and j. We denote θ j the indifferent type for market segment j who is indifferent between buying good X j and X i, and θ i the indifferent type for market segment i who is indifferent between buying good X i and not buying. Then the price constraints are p i = k i θi q i, θi [θ i 1, θ i ), (5) k j θj q j p j = k j θj q a p i, for θ j [θ j 1, θ j ). (6) In the market segment j, there is another indifferent type which we denote as consumer type ˆθ j, who is indifferent between buying X i and not buying. Thus, we have the additional constraint k j ˆθj q a = k i θi q i, for ˆθ j [θ j 1, θ j ]. (7) Based on the constraints of equations (7), we have ˆθ j = max{ k iq i θi k j q a, θ j 1 } since ˆθ j θ j can always be satisfied. Here we have three possible consumer groups. Consumers in [ θ i, θ i ] who buy X i, consumers in [ˆθ j, θ j ) who buy X i and consumers in [ θ j, θ j ] who buy X j. Consumers in [ˆθ j, θ j ) are market encroachment of good X i in market for X j. Substituting equations (5) and (6) into the profit maximization model as described in section 2, we get max θ i, θ j {Π( θ i, θ j ) = k i θi q i (F (θ i ) F ( θ i ) + 1 F (ˆθ j )) + k j θj (q j q a )(1 F ( θ j ))}, 12

15 Subject to θ i [θ i 1, θ i ), θ j [θ j 1, θ j ), ˆθ j = max{ k iq i θi k j q a, θ j 1 }. From the first order condition with respect to θ j, we have θ j = 1 F ( θ j ). f( θ j ) Solving the above equation, we get θ j = θj, which means the market share for good X j is the same as without the threat of good X i. However, from (6) we know the price p j is lower than when there is no cross purchasing problem. So we get that under threat of cross purchasing from market segment i, the profit from good X j decreases. For the market share of good X 1 in market segment 1 and there are two situations. 1. If market segment j is already covered by X j, or if we have k iq i θi k j q a θ j 1, which means market segment j is jointly covered by X i and X j, then we have ˆθ j = θ j 1. The first order condition with respect to θ i is Since F (θ i) F (θ)+1 F (θ j 1 ) f(θ) θ i = F (θ i) F ( θ i ) + 1 F (θ j 1 ). f( θ i ) > F (θ i) F (θ) f(θ), we get θ i > θ i. Note that in this case, market segment j is covered. It can be covered by good X j alone or by both X i and X j. 2. If market segment j is not covered, then we have θ j 1 < k iq i θi k j q a ˆθ j = k iq i θi k j q a.the first order condition with respect to θ i is < θ j. Thus we get θ i = F (θ i) F ( θ i ) + 1 F (ˆθ j ) f( θ i ) + k iq i. k j q a f(ˆθ j ) 13

16 Since 1 F (θ) f(θ) is non-increasing and qa q i > k iθi k j, we have θj 1 F (ˆθ j ) k i q i k j q a f(ˆθ j ) k jq a 1 F (θj ) k i q i f(θj ) = k jq a k i q i θ j > k iθ i q i k i q i = θ i. And we know θi = F (θ i) F (θi ). So we have f(θi ) θ i = F (θ i) F ( θ i ) + 1 F (ˆθ j ) f( θ i ) + k iq i k j q a f(ˆθ j ) > θ i. So under both conditions we have θ i > θi, which means the firm shrinks its market share for good X i in segment i to maximize its overall profit. And the higher θ i can also make the price of good X i and X j relatively higher. We use the Diagram 2 to illustrate this situation. *** insert Diagram 2 about here *** We generalize the analysis above and have the following theorem Theorem 4 For a market with multiple groups and differentiated goods with shared characteristics, if there is threat of cross purchasing between the high-end market and the low-end market, the firm retains the market share of version designed for the high-end market in the high-end market segment while shrinking the market share of version designed for the low-end market in the low-end market segment. What are the consequences if qa q i is increasing? Two situations can result: 1. More market segments are under threat of cross purchasing by information good X i. The sufficient condition for cross purchasing between market segment i and j is qa q i > 14

17 k i θi k j. And we know for i < j, k iθ θj i k j < 1. If qa θj q i is increasing, this condition is easier to be satisfied. Consequently, more high-end market segments are involved in the cross purchasing problem. When qa q i is close to 1, all the high-end market segments (for those which are higher than segment i) are under threat of cross purchasing by X i. 2. The high-end market segment j is more likely to be covered. The sufficient condition for market segment j to be covered is k iq i θi k j q a θ j 1. With the increase of qa q i, the above condition is easier to be satisfied. As a direct consequence, θ i is more likely to reach its upper bound θ i, which means market segment i is not served any more. There are two extreme situations for goods with shared characteristics. One is that the common quality q a is zero, which is the perfect quality differentiation situation we discussed in the previous section. The other extreme is that the special quality is zero, which means q h = q a, consumers in different groups value all the characteristics of the information good, although at different utility level, which returns to the vertical differentiation model. This is the focus of the next section. 5 Vertical Differentiation of Information Goods 5.1 Vertically Differentiated Goods with Undifferentiated Characteristics In this section we analyze the situation where consumers from any group value all the characteristics of the information goods of quality q h. However, different groups put different values on those characteristics. The difference of the valuation depends on the group coefficient k n and the consumer type θ. So for given quality q, the utility a consumer receives is U(q, θ, k n ) = k n θq, for n {1, 2,..., N} and θ [θ n 1, θ n ). 15

18 Usually for information goods, after the highest quality q h is developed, firms can degrade it to generate different lower quality versions at very low cost. In our case we suppose the versioning costs are zero. As a result, firm may offer different versions of the information good for different groups to choose from, or they can only offer the highest quality good to the whole market, depending on which is profit maximizing. From the analysis in the previous section, we know there is unique solution for θ = 1 F (θ) f(θ), θ [θ 0, θ N ]. Here we denote it as θ and the market segment it belongs to as market segment e, so θ [θ e 1, θ e ). We have the following well-known theorem Theorem 5 For a market with multiple groups and vertically differentiated goods, only the highest quality is provided and versioning is not profit maximizing. Consumers with θ θ m are served, where θ m is defined as θ m = max {k e θ (1 F (θ )), k n θ n 1 (1 F (θ n 1 ))}, for n > e. θ We use the following example to better illustrate the ideas of a market with vertically differentiated goods. We suppose there are only two market segments, k 1 < k 2, and for consumers in group 1 θ [θ 0, θ 1 ) and for consumers in group 2 θ [θ 1, θ 2 ]. We also denote θ m as the indifferent consumer type when optimal profit is generated. Diagram 3 illustrates the relationship between profit and consumer group division. *** insert Diagram 3 about here *** Here, we define, θ k = max{k 2 qθ(1 F (θ)) = k 1 qθ (1 F (θ ))}, θ [θ 0, θ 2 ]. θ When the firm does not consider versioning, we have, 16

19 1. If θ 1 [θ 0, θ ], the optimal profit is R 1 = k 2 q h θ (1 F (θ )). 2. If θ 1 (θ, θ k ), the optimal profit is R 2 = k 2 q h θ 1 (1 F (θ 1 )). 3. If θ 1 [θ k, θ 2 ], the optimal profit is R 3 = k 1 q h θ (1 F (θ )). Suppose the firm considers versioning, which means a lower quality version q l is developed for group 1, and q h is only for group 2. Then 1. If θ 1 [θ 0, θ ], then R (θ h, θ l ) = q h k 2 θ (1 F (θ )) q l [k 2 θ (1 F (θ )) k 1 θ l (1 F (θ l ))] q h k 2 θ (1 F (θ )). And when q l = 0, R = R If θ 1 (θ, θ k ), then R (θ h, θ l ) = q h k 2 θ 1 (1 F (θ 1 )) q l [k 2 θ 1 (1 F (θ 1 )) k 1 θ (1 F (θ ))] q h k 2 θ 1 (1 F (θ 1 )). And when q l = 0, R = R If θ 1 [θ k, θ 2 ], then R (θ h, θ l ) = q h k 2 θ 1 (1 F (θ 1 ))+q l [k 1 θ (1 F (θ )) k 2 θ 1 (1 F (θ 1 ))] k 1 q h θ (1 F (θ )). And when q l = q h, R = R 3. None of the above cases support versioning. 17

20 5.2 Vertically Differentiated Goods with Group Related Characteristics From the analysis in the previous section, we found that if all the characteristics are treated equally by all the groups, then versioning is sub-optimal although there are multiple groups in the market. However vertical differentiation can be optimal in different cases. Suppose there are some special characteristics of information goods that are valued equally by all the consumers, no matter what their types are and no matter what groups they are in. Mathematically, for those characteristics X n whose quality index is q n, the utility function for those characteristics is U(q n, θ, k n ) = Kq n, where K is constant for all θ [θ 0, θ N ]. Obviously, it is always optimal to sell those characteristics at price Kq n separately as a new version and it satisfies the uncovered market without affecting the sales of any other existing versions. But it is an idealized situation. Few real life examples support all the consumers valuing the information goods equally (above zero, of course). In this section we propose a situation that is more realistic. We suppose characteristics are group related. It means, if characteristics set X 1 is related to group 1, then not only consumers in group 1 have group coefficient k 1, all the higher taste groups also have group coefficient k 1 for the characteristics set X 1. However, consumers still differ in their individual tastes. Generally, if X i is related to group i, then for consumers who belong to a higher group have the group coefficient k i for the characteristics set X i, and consumers who belong to a lower group place a zero value on X i. The typical example is the Windows Operating Systems. Characteristics designed for the Home Edition are valued by both home users and power users while special features designed for Professional Edition are only valued by power users. Let us suppose the highest quality information good X h with quality index q h is made up of all group related characteristics {X 1, X 2,, X N } with relevant quality indices {q 1, q 2,, q N }. 18

21 We assume there is no overlap between any two sets of characteristics, which is X i X j = for i j. Then the utility function of a consumer in group i for information good X h is i U(q h, θ, k i ) = θ k t q t, for θ [θ i 1, θ i ). t=1 In this case, if versioning is considered, then versioning strategies must be bottom-up. It means the higher quality version includes all the characteristics related with the lower groups. The price relationship between any two indifferent consumer types from market segments i and j (j > i) who choose two neighboring versions is We have the following theorem j p j = p i + θ k t q t, for θ [θ j 1, θ j ). t=i+1 Theorem 6 For market with multiple groups and vertically differentiated goods, if all the characteristics are group related, then 1. Versioning is optimal only if the highest market segment N is covered by the highest version. 2. The optimal versioning strategies are Any market segment i that is lower than e (i < e) is not served, where market segment e is defined as before. Market segment e is provided the version with quality e t=1 q t, the optimal price is p e = θ e t=1 k t q t, where θ is defined as before. Any market segment j that is higher than e (j > e) is provided a version with quality j t=1 q t, and the optimal price is p j = e t=1 k t q t θ + j t=e+1 k t q t θ t 1. 19

22 Based on the optimal strategies in Theorem 6, we can calculate the total profit for the firm, which is Π = e t=1 k t q t θ (1 F (θ )) + N t=e+1 k t q t θ t 1 (1 F (θ t 1 )). We extend the example from the previous section to illustrate the versioning strategies with group related characteristics. Here we have q 1 as quality of group 1 related characteristics X 1, q 2 as quality of group 2 related characteristics X 2. Diagram 4 illustrates the optimal profit comparison between versioning and non-versioning (Since providing X 1 to both groups is never optimal, we do not show this situation). *** insert Diagram 4 about here *** When the firm does not consider versioning 1. If θ 1 [θ 0, θ ], then optimal profit is Π 1 = (k 1 q 1 + k 2 q 2 )θ (1 F (θ )). 2. If θ 1 (θ, θ 2 ], then optimal profit is Π 2 = (k 1 q 1 + k 2 q 2 )θ 1 (1 F (θ 1 )). Suppose the firm considers versioning 1. If θ 1 [θ 0, θ ], then optimal profit is Π v 1 = k 2 q 2 θ (1 F (θ )) + k 1 q 1 θ 1 (1 F (θ 1 )) < Π 1, which means versioning is not optimal; 2. If θ 1 (θ, θ 2 ), then optimal profit is Π v 2 = k 1 q 1 θ (1 F (θ )) + k 2 q 2 θ 1 (1 F (θ 1 )) > Π 2, which means versioning is optimal. 5.3 Transaction Costs and Market Aggregations We know from the previous section that without considering versioning costs, consumers with taste coefficient θ [θ 0, θ ] are not served. That is, low taste consumers are not served. 20

23 Consumers with taste coefficient θ [θ, θ N ] are served with versions according to which market segments they belong to. So the served market segments are e, e + 1,, N. Each market segment i (i e) is provided with one different version, the total number of versions provided is N e + 1. Here we consider the situation where versioning costs are significant. In real versioning cases of information goods, versioning costs include not only technical costs that are incurred to generate different versions, but also extra marketing costs for selling different versions. If versioning costs are large enough to counterbalance the benefits obtained from versioning, then versioning is no longer optimal. Firms have an incentive to aggregate one or several existing market segments to reduce the number of versions. To model this problem, we define v m as the maximum number of versions provided by an information good firm. From the above analysis, we know when versioning costs are not considered, firms provide this number of versions. Thus we get v m = N e + 1. To make this problem less trivial, we suppose v m 2. We assume C(τ) is the versioning costs function when τ versions are actually provided. Here we have τ {1, 2,, v m }. And we can further assume that C(τ) is non-decreasing with τ because it is quite reasonable that the more versions are provided, the more versioning costs are incurred. Also we have C(1) = 0 since when only one version is provided, no versioning costs are incurred. C(τ) is determined by the technical parameters and marketing parameters which are available to the firms. So C(τ) is known to the firms. We define L(s) as the least profit loss function when s market segments are aggregated. It means when a firm chooses to aggregate s market segments, L(s) is the least possible loss in total profit among all the possible aggregation arrangement. Here we have s {0, 1, 2,, v m 1 }. L(s) is strictly increasing with s because the more market segments are aggregated, the more the profit loss is. Also we have L(0) = 0 since when there is no market aggregation, there is no profit loss. 21

24 For simplicity of notation, we define V = θ (1 F (θ )), V i = θ i (1 F (θ i )) and U i = k i q i. Diagram 5 illustrate the profit loss when market aggregation occurs. *** insert Diagram 5 about here *** Now we start to work out the algorithm for determining the optimal market aggregation strategy. Firstly, let us consider the profit loss when a firm considers aggregating one market segment. 1. If market segments e and e + 1 are aggregated, the firm can have the following two options. Merge market segment e into segment e + 1. The best strategy is to close market segment e and serve market segment e + 1 with quality e+1 t=1 q t. Thus the price for segment e + 1 is increased to p e+1 = θ e e+1 t=1 U t, the profit loss is Π e = (V V e ) e t=1 U t. Merge market segment e + 1 into segment e. The best strategy is to serve both market segments e and e+1 with quality e t=1 q t. Thus the price for both segments is p e = θ e t=1 U t, the profit loss is Π e+1 = (V e V e+1 )U e If market segments j and j + 1 (j {e + 1, e + 2,, N 1}) are aggregated, the firm can have the following two options. Merge market segment j into segment j + 1. The best strategy is to serve market segment j + 1 with quality j+1 t=1 q t with price p j+1 = p j 1 + θ j (U j + U j+1 ). Thus consumers in segment j will buy version for segment j 1 at price p j 1. The profit loss is Π j = (V j 1 V j )U j. 22

25 Merge market segment j + 1 into segment j. The best strategy is to serve both market segments j and j+1 with quality j t=1 q t. Thus the price for both segments is p j = p j 1 + θ j 1 U j, the profit loss is Π j+1 = (V j V j+1 )U j+1. We define Π m = min{ Π e, Π e+1,, Π N }. Thus we get L(1) = Π m, and market segment m is merged into its neighboring segments. According to the versioning costs function C(τ), the costs saving due to the aggregation of one market segment is C(v m ) C(v m 1 ). So if C(v m ) C(v m 1 ) > L(1), which means costs saving due to market aggregation is larger than profit loss, then market aggregation is optimal, otherwise aggregation is not optimal. Based on the same logic, we state our algorithm for the information goods monopolist to determine the optimal solutions to aggregate its market segments when versioning costs are taken into consideration. Theorem 7 The following algorithm determines an optimal solution for the information goods monopolist to aggregate its market segments. 1. The following steps are designed for determining L(s). Denote j, j {e, e+1,, N} as the market segment to be merged, Π j as the relevant profit loss. Initiate s = 0, g(s) = 0. Step 1. If j = e, then Π j = (V V e ) e t=1 U t. If e < j N, then Π j = (V j 1 V j )U j. Step 2. If Π e = Π e+1 = = Π N = 0, then stop. Otherwise, s = s + 1, g(s) = {j : min( Π j, for j {e, e + 1,, N}and Π j > 0)}, L(s) = Π g(s). 23

26 Step 3. If j = e, then set U j+1 = U j+1 + U j, U j = U j+1, V = V e ; If e < j < N, then set U j+1 = U j+1 + U j, U j = U j+1, V j 1 = V j ; If j = N, then set V j 1 = V j ; Return to step Determine the optimal market aggregation arrangement. If for all s {1, 2,, N 1}, C(v m ) C(v m s) L(s), then market aggregation is strictly sub-optimal. Otherwise, we set l = max{s : C(v m ) C(v m s) L(s), for s {1, 2,, N 1}}. The optimal market aggregation arrangement is a. l market segments will be merged. b. The merged market segments are : g(1), g(2),, g(l). 5.4 Social Welfare Analysis For information goods, if we assumed that marginal cost of reproduction is zero, then the Pareto optimum can only be reached when the price to sell the information goods is also zero, which is obviously not acceptable by the firms, especially when they are monopolists in their fields. With monopoly, firms set the price of information goods to maximize their profit under certain constraints. In the meanwhile, the consumers surplus is minimized. So how do transaction costs influence social welfare? From the analysis in the previous section, we know versioning costs have impact on optimal versioning strategies of information goods. If versioning costs are not large enough to affect the optimal versioning strategies, then the optimal price for different versions are not changed. Consequently, consumers surplus is not changed. But the profits of the firms are reduced, thus the total social welfare is reduced. If versioning costs cause market aggregation, then consumers from the merged market segments are either provided with lower quality or are not served any more. In this 24

27 case, consumers surplus is reduced. Also the firms surplus is reduced because their net profits are reduced and costs are increased. So the total social welfare is reduced. Considering this problem the other way, we conclude that if versioning costs are reduced significantly, then both firms profits and the total social welfare are greatly increased. So the information goods firms have great incentive to reduce versioning costs as much as possible. 6 Product Line Design For successful development of information goods, market research usually goes first. In addition, product line design is sometimes planned before the development of the final goods. Market segmentation can be based on demographic factors such as age, stage in life cycle or place of living, social-economic characteristics such income, education or occupation and many other factors such as consumption patterns and personality (Frank, Massy and Wind, 1972). With careful market investigation, firms decide which market segments they focus on and what kind of characteristics are developed for those segments. Based on our model, we divide information goods characteristics into four types 1. Type I characteristics. We also call them situation independent characteristics. All the consumers from all market segments value these characteristics equally, no matter what market segment there are in or what consumer types they are. It is an idealized category since it is hard to get exact match for those characteristics in real information goods development. But usually we can include the basic functions of the software (like copy, paste, open a file, browse) or basic contents of electronic journals in this type. 2. Type II characteristics. We call them group related characteristics in the previous section because they are 25

28 usually related to certain group. All the higher market segments share the same group taste as the group for which these characteristics are developed. All the lower market segments place zero value on these characteristics. The typical example is the Windows Operating Systems we mentioned before. Other examples can be resolutions of digital pictures, or superior quality of digital music, where high resolution is greatly valued only by those professional groups. Adobe reader characteristics can also be included in this category since common users value reader characteristics essentially the same way while the editing characteristics are specially valued by certain groups such as professors and journal editors. 3. Type III characteristics. We call this type undifferentiated characteristics since those characteristics are developed for all the market segments. Different consumers in different groups value these characteristics differently based on their group tastes and their individual tastes. Online movies, electronic dictionaries, electronic encyclopedia and anti-virus software fall into this category. 4. Type IV characteristics. We call these characteristics group specific characteristics because only specific groups value these characteristics while consumers from other groups place zero value on them. A good example in this category is the voice recognition software where special vocabularies for lawyers, medical staff and office staff will be valued only by those specific groups. The first three types are vertically differentiated characteristics and the last type belongs to the horizontally differentiated characteristics. Once these characteristics can be recognized and categorized, product differentiation can be performed in routine procedures. 1. Type I characteristics come together to form a separate version. And these character- 26

29 istics are added to all the other versions. 2. Type II characteristics are suitable for vertical differentiation. Based on our previous modeling analysis, versioning usually happens for the higher market segments. 3. Type III characteristics are not suitable for vertical differentiation. Information goods with only Type III characteristics should not be versioned. If there are other characteristics that facilitate versioning, then they are only included in versions for higher market segments. 4. Type IV characteristics are always effective for versioning. Specific characteristics are included in versions for specific groups. Based on our characteristics categorizaton and versioning guidelines, versioning information goods can be easily managed and routinely performed. Also our characteristics based modeling better explains why some information goods only have one version while others may have multiple versions. In the previous literature, network externalities can explain the existence of a maximum of two versions (Jing, 2001) and Goldilock Effects can only explain the cases where three versions are possible for information goods (Varian, 1997). 7 Conclusions Since demand function cannot be used to direct the pricing strategies of information goods, utility function is broadly discussed. In the current literature, there are many different ways to deal with the utility function. Many of the initial work (Bhargava and Choudary, 2001, Jones and Mendelson, 2005) prefer linear form of the utility function because it is easy to understand and it is also convenient for further estimation in the empirical research. But almost all of them reach the same conclusion that versioning is not optimal with linear utility functions. Some resort to network externality and based on this, the utility function is in a 27

30 non-linear form and versioning is proved to be optimal in this case. Jing (2001) proposed that two versions are enough with network externality. Some resort to other constraints to restrict the utility function. Wu and Chen (2004) put the anti-piracy constraints and also generate the idea that versioning can be used when piracy is considered. Bhargava and Choudary (2005) directly research the general function form of the utility function and generate the idea vertical differentiation is optimal when lower type consumers have greater ratio of valuations than higher type consumers. Our modeling results are in accordance with Bhargava and Choudary (2005). However, our research based on market segmentation offers a new perspective. In our model, we keep the linear function form and introduce the group taste coefficient to make versioning constraints closer to the real market conditions. We first combine the research of horizontal differentiation and vertical differentiation and make comparison. We treat vertical differentiation as a specific form of horizontal differentiation and treat information goods as a set of combinations of characteristics. Based on this, we provide performable guidance for information goods firms. Based on our product line design principles, Varian s suggestion (1997) the right way to design the product will generally be to design for the high end of the market first, and then downgrade the product to get the versions for the other segments of the market may not be the best strategy for successful versioning. Our model takes full consideration of consumer heterogeneity before the development process, thus makes versioning more applicable and reduces the risks of the versioning strategy. And the optimal versioning strategies may well follow Varian (1999) Versions should be designed to accentuate the differences between groups in their tastes. We do not integrate network externalities in our model because network effects influence versioning in the same direction of our results. If we integrate network effects into our model, it is hard to differentiate which effects dominate. Intuitively, if we take network effects into consideration, they provide more incentive for the firms to generate the low quality version. 28

31 Even if Type I and Type II characteristics do not exist, it may still be optimal to vertically generate the low quality version. Meanwhile, network effects provide more incentive for the firm to lower price of low quality version to increase the installed base. The recent trend in versioning is to research versioning under competition. We know that because of zero marginal cost of information goods production and no limit in scale, information goods are natural monopoly. It means if competitive firms provide homogeneous information goods, Bertrand competition drives the price of the information goods to zero. Jones and Mendelson (2005) propose a competition model for information goods. Their results demonstrate that if there are two firms who choose quality simultaneously in the first stage and price in the second stage, the Nash Equilibrium is that both firms can have positive profit but the firm with high quality dominates the market. Their argument is based on regular linear utility function where versioning is not optimal. In our model, when versioning strategies are taken into consideration, firm with higher quality information good may effectively deter entry of the low quality good firm and maintain its monopoly position. How to design the appropriate product line to effectively deter entry is our next research topic. 29