Buyer Search Costs and Endogenous Product Design


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1 Buyer Search Costs and Endogenous Product Design Dmitri Kuksov University of California, Berkeley August, 2002 Abstract In many cases, buyers must incur search costs to find the price of a product. This search cost affects the behavior of consumers, and through that, it affects the profit maximizing behavior of the firms. As search costs change, so do the competitive marketing mix strategies of the firms. In predicting the effect of changing search costs on the equilibrium prices and allocations, it is important to take all effects into consideration. Through a model of buyer and seller behavior in the presence of buyer price search costs and seller uncertainty about the demand, I consider the effects of changing search costs on prices when product differentiation is fixed and when it is endogenously determined in equilibrium. While keeping product differentiation constant, lower buyer search cost for prices leads to lower equilibrium prices. At the same time, lower search costs also lead to higher incentives for the firms to invest in differentiating product design. The resulting higher level of product differentiation decreases the effects of lower search costs on prices, so that lower buyer search costs for prices may even lead to higher prices. Moreover, the overall effect of lower search costs on social welfare may be negative, and the effect on the industry profits may be positive. The result is especially interesting because recent technological changes, such as the Internet shopping, may be affecting the market structure mostly through lowering buyer (consumer) search costs. 1 Introduction Many technological changes affect the economy and the market equilibrium not only through affecting the production and distribution costs and availability of new products and services, but also through affecting the informational structure of the market and the type A rough draft, comments welcome 1
2 of interaction between market agents. Namely, technological advances change the amount and costs of information available to consumers, producers, and other market agents. Such changes in the informational structure of the market may affect equilibrium outcomes both directly, through their effects on buyer utility functions and seller prices, and indirectly through affecting other market structure parameters, such as the number of the firms in the market, vertical and horizontal contracts, and product design. In other words, the indirect effect is through the effect on the parameters that are constant in the short term, but, in the long run, are determined by market agents as well. Not accounting for these indirect effects may produce misleading results. As noted by Stiglitz (1979), It is important to recognize that market structure is itself an endogenous variable, a result (at least in many cases) of natural barriers to entry and incentives to agglomerate, some of which are related in an essential way to the cost of information. Search costs for price exist in many markets and in an essential way contribute to profitability of the market environment. However, the effects of search costs on all decisions by the firms have not been fully understood. In this paper, I consider the implications of buyer search costs for price on the product and price decisions by the firms in the presence of incomplete information. To give an example, let us consider the Internet. When ecommerce was in the early stages, most people advocated that the Internet will reduce prices, erode profits, and increase consumer surplus by making markets more efficient and competitive and bringing market outcomes closer to the theoretically predicted (Bertrand equilibrium) outcomes. 1...industry titans, such as Bill Gates,..., regale the world s leaders with the promise of friction free capitalism. The Economist, May 1997 The result [of the Internet] is fierce price competition, dwindling product differentiation, and vanishing brand loyalty. Business Week, May The following two quotes are reprinted from Brynjolfsson and Smith (1999). 2
3 The same predictions were supported in the academic literature (e.g., Wernefelt (1994), Alba et al. (1997), Bakos (1997), Brynjolfsson and Smith (1999)). The way this argument works is the following. When people think about what the Internet brings to the marketplace, one thing that immediately comes to mind is that the Internet reduces buyer search costs. Online search engines and shopbots are especially useful if one searches for digital attributes such as the price. Therefore, buyers are better informed about prices. Now a firm would lose a larger fraction of the demand if it raised the price, and on the other hand, it is sufficient for a firm to undercut the competitors just by a little bit, to gain a large market share. This leads to higher competition and lower prices. As a result, buyers are better off. Further, price dispersion is predicted to become lower as in the absence of frictions, the market prices should become closer to the perfectly competitive price. Social welfare increases both due to lower deadweight monopoly loss and due to probably lower total waste on search. The expectation that the total expenditure on search may be lower is based on the optimal search behavior when the cost per search and the price dispersion decrease (Stigler (1969)). Finally, if the decrease in prices is not offset by large decrease in the fixed costs of retailing, profits decrease. The empirical evidence is contrasting the above predictions. Price dispersion on line is considerable (Iyer and Pazgal 2002). In fact, Smith and Brynjolfsson (1999) and Clemons, Hitt, and Hann (2000) show that price dispersion online is larger than off line. Further, in some categories, prices are not close to marginal costs. Some consumers comment that they actually spend more on search on the Internet than they used to spend offline, which again, indirectly, supports the notion that online price dispersion is higher. The valuations of internet stocks, though much lower now than at their peak, still do not support the idea of complete erosion of profits in online competition. Missing in the above arguments is the consideration of the endogenous effects of lower search costs on the market structure, e.g., changes in the products offered by the firms. Prices and price competition have been studied, but this is not a complete picture. The complete picture includes effects of search costs on all decisions by the firms. One needs to examine the situation in more detail. It is important to have a good understanding of the process through which search costs affect the market in its entirety: products and prices alike. The model in this paper shows, in particular, how the consideration of the effects of 3
4 lower search costs on prices and products reconciles the fact that consumer search costs for price may decrease with the observation that the price dispersion increases and investors expect high profits in the electronic marketplace. Through explicit modelling, I consider how the interaction between incomplete seller information about the demand and buyer search costs for price results in an equilibrium intermediate between Bertrand and monopolistic pricing equilibrium, where the equilibrium price smoothly increases with search cost. I further use this framework to analyze the effect of changing search costs on the equilibrium pricing, profits, and the welfare related variables with and without endogenous changes in the products being offered. I find that not accounting for endogeneity of product development may lead not only to quantitative, but also qualitative (directional) mistakes in the analysis of the effect of the level of search costs on price, profits, consumer surplus, and social welfare. I find that, in general, product differentiation increases as search costs decrease. This result is consistent with the common belief that search costs and product differentiation are substitutes, or, in other words, with the statement that search costs to some extent play a role of product differentiation. Moreover, if product differentiation is endogenously determined by sellers through either cooperative or individual investment, then depending on the cost of the product development, the endogenous investment in product differentiation may more than counteract the increase in competition due to lower search cost for price. Further, especially if the product differentiation efforts do not increase the valuation of the products by the consumers, the resulting change of social welfare due to lower search costs may actually be negative. It is even possible that when search costs decrease, all agents become worse off. Search costs and product differentiation decreases competition between firms. In that, the two concepts appear similar. However, they are fundamentally different in their nature and the mechanism by which they affect the market. First, search costs are related to the lack of information, whereas differentiation is related to the preferences of agents involved. That is, search costs are about the availability of information, and differentiation is about the preferences based on the information present. Second, if the search costs are 4
5 the same for each agent, the population may be homogeneous in the presence of search costs. Contrary to this, if agents preferences are the same, there is no differentiation; i.e., differentiation requires differences in preferences, whereas search costs do not require any differences between agents. In particular, I consider the situation where search costs do not vary with the individual. Theoretical literature considered different dimensions of differentiation as substitutes (Iyer(2002)) as well as interaction of asymmetric information and differentiation (VillasBoas and SchmidtMohr (1999)). This paper examines the connection between search costs and endogenous product differentiation. Stiglitz (1987) provides an example of the different effects that search costs and differentiation produce on the market equilibrium: with differentiated market, higher number of firms result in higher competition, whereas in the presence of search costs, higher number of firms may result in lower competition. Therefore, in order to understand the impact of search costs on the market outcome, it is important to carefully model the effect of the search costs. The results of this paper have important managerial implications, since they help to predict the competitive environment online or anywhere where a change in buyer search costs is expected, and therefore help the firm to better develop its business strategy. For example, firms that consider entering a particular industry that is in the process of technological change need to estimate the changes to the industry structure. Also, a social planner needs to take all the implications into account when deciding which technological changes to support or hinder. The rest of the paper is structured as follows. The next section presents the intuition for the model of how search costs affect the equilibrium prices and product differentiation that I will use in this paper. Next, in Section 3, I present the formal model, followed by examples of a business environment (Section 4) where the assumptions of the model are likely to be well matched by reality. Then, I solve the model with and without product differentiation (Sections 5 and 6). In Section 7, I endogenize product differentiation by introducing the cost of product development, which allows us to consider the changes in model predictions that considering product differentiation as endogenous could bring (Section 7.3). This is followed by a discussion of the model extensions in Section 8, and 5
6 some preliminary empirical evidence in Section 9 that confirms that when search costs decrease, product differentiation tends to increase. Section 9 also contains an empirical test of increasing dependence of differentiation on search costs. The product differentiation time series data across different categories is obtained utilizing the Consumer Reports. Section 10 concludes. 2 Effect of Search Costs and Differentiation on Competitive Equilibrium Prices In order to consider the effects of changing search costs on firm s decisions, one first needs to understand how search costs affect the market equilibrium. The general idea is that consumer search and awareness of competitor prices does not allow a firm to raise its price much above the market price. In a monopoly setting, a firm sells the product to a given consumer as far as the consumer s expected utility from the product is above the price charged. In a competitive setting, a consumer buys from the firm if two conditions are satisfied: first, as in the monopoly case, consumer expected utility has to be higher than the price, and second, consumer should not view further search for a better price justified by the chances of getting a better deal put together with the cost associated with the search. From the firm s perspective, in a monopoly setting, the price is restricted by consumer valuations, and in a competitive setting, the price is additionally restricted by the expected distribution of competitor prices in relation to the buyer search costs, which I will further call the search constraint. If a firm has complete information about the costs and valuations of consumers and firms, then it can predict competitor prices. In reality however, a firm may not know what the competitor prices are because it does not know, for example, the assumptions the other firms make about the demand. Therefore, if there is a possibility that another firm thinks that the optimal price is lower, every firm may worry that its consumers may leave to the other firm. Product differentiation decreases competition because if products are differentiated, 6
7 offering a lower price is not enough to switch consumers from one firm to another, since consumers must be reimbursed for the adjustment to fit as well. Now a consumer will search for a better price when the benefit of a possibly lower price is high enough in relation to both search costs and the lower fit (I assume that consumers know their fit to products better than the prices since prices are changed more often than physical attributes of the products). Therefore, with high differentiation, search becomes a smaller constraint. This leads to higher prices, and the effect may propagate recursively. The intuition is that not only each firm itself fears less of the competitor s possible lower price, but also each firm expects the competitor to charge a higher price for the same reason. Lynch and Ariely (2000) has shown in an experiment that, in a competitive setting, there is benefit of accenting product attribute information, which can be argued to be differentiating between products by providing information that is different across products. But just noting that product differentiation is beneficial in the competitive environment does not answer the question whether firms should invest more in product differentiation when the search costs are falling. One needs to know not only whether there is a benefit of differentiation, but also whether the benefit increases when search costs are lower. The above consideration allows to make predictions in this direction as well. I argued that product differentiation leads to ability of the firms to charge higher prices. Since lower search costs lead to lower competitive prices and the profit function is concave due to downward sloping demand, the benefit of the increase in prices is higher when the original price level is lower, i.e., when the search costs are lower. In the next sections, I introduce a formal model of competition in the presence of search costs and possible differentiation. The formal model allows one to see exactly how the above intuition applies, and allows one to speculate on the relative size of the effects involved, so that one can hypothesize on the balancing effects of lower search costs in the presence of endogenous product differentiation on profits and consumer and social welfare. 3 The model Consider a market consisting of two sellers selling a homogeneous or differentiated good to a number of buyers. Each buyer knows her valuation of the product. The valuation can 7
8 also be interpreted as the expected valuation in the case the valuation is uncertain and the consumer has no means of finding the exact valuation, or in the case when the cost of finding the exact valuation is prohibitive. The fact that consumers may know their valuation of the product, but not the price comes from the reality that prices can be (and are) changed frequently, whereas product design that affects the valuation can not be changed too fast. For a discussion of search for multiple attributes of the products in an online environment see Lal and Sarvary (1999). This model could also be applied to situations where search for product valuation information precedes search for price. If search for valuation (consumer fit) and search for price are bundled (as in Bakos (1997)), the results may be subject to distributional assumptions (see Fath and Sarvary (2001)). Buyers have a single unit demand, all buyers and sellers are risk neutral, and each buyer knows one price to start with. 2 The cost s of finding the second price is the same for each consumer. A buyer has search cost associated with finding the price at any of the sellers, and can not buy the product at a seller without incurring the search cost associated with that seller. The later assumption reflects the idea that buyers may not be able to buy without incurring the cost of finding the price since they have to agree to pay the price to complete the transaction, or, explained alternatively, the search for the price includes the search for location. Also, no transaction can be complete before the price is known, and hence the cost of obtaining the price can not be more than the cost of making the transaction. The sellers have equal and constant marginal cost of the product, which is normalized to 0. 3 Sellers are uncertain about buyer valuations. This uncertainty can be interpreted in different ways. One can think of one buyer market when one buyer comes to the seller and the seller has to name the price based on what it can see about the buyer. Alternatively, one can think of a market with many consumers and with the aggregate demand function is not perfectly known to the firm. The demand function is known to sellers up to a certain 2 The rationality of at least one search, resulting in one price being known, can be explained, for example, by a downward sloping buyer demand, so that the purchase of the optimal amount (further known as the unit of the good) at the linear monopoly price leaves the buyer with enough surplus to cover the search cost. It can also be that at least one price quote is discovered during the time the buyer is looking for the product related information. 3 The key results would not change if the marginal cost is allowed to be variable. 8
9 Segment 1 t Segment 2 Firm 1 or Firm 2 V = V or V Figure 1: Consumer preference space. seller specific error. A part of the information that the sellers use, can be commonly known to both sellers, but sellers can also differ in the type or amount of information about the demand they privately receive, or in the way they handle the information. Some imperfect information about the way different retailers use the knowledge they possess can be modelled as a form of incomplete information. For example, if a retailer does not use certain types of information for decision making, it behaves as if it doesn t receive that kind of information. I model this informational structure by assuming that the buyer valuation is based on one valuation parameter V representing the general valuation level. Individual consumers have valuations that depend on V and their individual fit to the particular product. Sellers have a common prior on V, which I assume for simplicity to be either high V or low V with equal probability. Further, each seller j has individual data or beliefs of demand, represented by the signal x j of buyer valuation parameter V. For simplicity, I assume that the signal x given the valuation parameter V can either provide the seller with the exact valuation, or be completely noninformative with equal probability. In the first case, I denote the signal by the valuation level, i.e. I write x = V, in the second case, I denote the signal by the empty set: x =. Signals are independent across firms. Summarizing, { V, Prob. 1/2, (x V ) =, Prob. 1/2. I model the distribution of consumer preferences through a distribution of consumer ideal points, where the individual valuation depends on the distance of the consumer ideal point from the position of the product (as in the perceptual map). To simplify matters, I assume that given the valuation parameter V, there are two equal consumer segments at a distance t from each other. Namely, one values the product at V, the other at V +t (product is located at one of the ideal points), the total consumer mass is normalized to one. The 9
10 Prior, Nature draws V and s design x j price buyer dec. profits time Figure 2: Timing. structure of consumer heterogeneity is generalized in the Appendix, where I consider the case of uniformly distributed preferences (as in Hotelling model). The full possible space of consumer ideal points is represented by Figure 1. Product design (or positioning) decision by a firm is the decision of the choice of the position of the product in the space of the consumer ideal points (product space) subject to production (cost) constraints. The simplest form of the product design problem is whether to position the product at one or the other ideal point depending on the positioning of the competitive product and the cost of design. 4 The degree of uncertainty a seller has is represented by the difference between the possible values of the demand parameter V that can exist given the firm s knowledge, i.e. by δ = V V. Finally, timing of the game is as follows (see Fig. 2). Initially, sellers have the common prior on buyer valuations. The number of buyers and sellers is also common knowledge. If endogenous product design is considered, then the next step is sellers (simultaneous) decision on the product design. Then both sellers and buyers learn the decisions of sellers on product differentiation (so that buyers know their valuation of each product, and sellers have the common prior on buyers valuations of each product). Next, sellers receive the individual signals x j of demand (private knowledge to seller j, but there is common knowledge on distribution of x j s), and simultaneously set prices for their products. Finally, buyers decide whether to search and which product to buy (if any). The buyers decision on purchase define the final buyer (consumer) surplus and seller (profit) payoffs of the game. 4 One can also consider the case when a firm s differentiation efforts result in increasing consumer heterogeneity, i.e. when firms are located at 0 or 1, but the value of the parameter of heterogeneity t increases. Advertising campaign explaining the differences between the products may act as such product differentiated effort. The implications of such a model are similar. 10
11 The assumption that the firms decision on the product design precedes the decision on prices and also precedes the signals x j is realistic due to long time necessary to design products and implement the design in practice. To simplify calculations, assume that the uncertainty and consumer heterogeneity is not too large, so that a monopoly would serve buyers of all possible valuations. Without this assumption, the monopoly price may not be an increasing function of the expected demand. 4 Examples of the marketplace 4.1 Business to Business markets Let us consider an example where the above model directly applies. Consider a B2B market with several producers and N industrial buyers, such as, for example, the market of airplane engines. In such a market, the price is subject to individual negotiations, i.e. sellers have the ability to discriminate between buyers. Assume that the marginal cost is constant in the possible demand range, so that the supply is not limited and therefore, buyers are not competing for products, but rather sellers are competing for each buyer. Then the market is equivalent to N separate markets with several sellers and one buyer. The price is normally set after a oneonone negotiations of a buyer and a seller. When the final price is set by the seller, the seller is uncertain about the private valuation of the buyer. The negotiations can be thought of as the process from which the seller extracts the signal x j of the buyer valuation. Naturally, the buyer knows its valuation, and seller needs to use its best guess of buyer s valuation to offer the price. During negotiations, by suggesting high prices, the seller may try to elicit the buyer valuation, and the buyer may try to respond in such a way that seller thinks the buyer is of low valuation. In any case, since the negotiations do not oblige neither buyer nor seller to commit, they can only be used by the seller as information for the final offer. The information obtain in the negotiations is used by the seller who makes the final take it or leave it offer. Hence, all the negotiations reduce to the signal x j of buyer valuation that the seller receives. 11
12 As it takes negotiations to find out the price of a seller, and the price depends on the signal x j that the seller receives during these negotiations, sellers can not find out the price the other sellers will set with certainty. In this example, the search cost is the cost of negotiating with the seller to obtain the best offer. 4.2 Retail Markets In a retail setting, stores differentiate from each other through a variety of factors such as store interior design, convenience, vertical contracts and reputation to sell a particular set of products at attractive prices, product assortment and the choice of brands, freshness (groceries), etc. This differentiation through product and physical store design are obvious examples. Other strategies, such as vertical contracts and switching costs, can also be considered as creating differentiation between stores. When retailers enter into different vertical contracts with manufactures, the contracts and resulting cost structure forces retailers to behave in a particular an predictable way that is observed by consumers and therefore retailers become differentiated. Switching costs contribute to the creation of segments of loyal consumers that may have systematic differences across stores, and again, lead to different and predictable pricing strategies pursued by the firms. Differentiation may also be created by using different strategy in making product information accessible to consumers. Zettelmeyer (2002) considers firms differentiating in that dimension in the online environment. Firms may also provide different product return policies. A larger variability of return policies on the Internet (Wood (2001)) is consistent with the predictions of this section. One might think that one store may check the other store s prices, and therefore get a better idea of whether its prices are being undercut. However, in a typical supermarket grocery shopping context, the decision of consumers whether to search often depends on their expectations of store prices on a bundle of goods, a bundle, contents of which may not even be known to the seller. Therefore, it is difficult for a store to observe if the other store is undercutting its prices. Furthermore, if there are other costs that consumers absorb (like ease of highway access, parking, checkout lines, etc.), it may not be clear which retailer is cheaper from a consumer point of view. 12
13 Segment 1 t Segment 2 V = V or V Firm 1 Firm 2 Figure 3: The case of homogeneous goods. 5 The Model with Homogeneous Goods I start with considering the model without product differentiation, followed with the model with exogenously set differentiation. The comparative statics between the two cases with defined timing and cost of product design will allow me to endogenize the product design. If both firms are located at the same point, we have a model with homogeneous goods (see Figure 3). Proposition 1. There is a unique symmetric equilibrium in the above model with homogeneous goods. In the equilibrium, consumers do not search, and the price is determined by the following rule: p(x) = { V if x = V or x =, min{v + 2s, V } otherwise. Proof. Existence. The above stated price rule is an equilibrium one because: if x = V, then the valuations are V and V + t, and by assumption of the model, firm prefers to receive demand of 1/2 with price V (from a random half of the buyers) to demand 1/4 with price V + t (from a random half of the buyers of higher valuation), which is the highest demand it can hope for at the price above V due to buyer valuations. At the same time, there is nothing to be gained by reducing price, since buyers do not search. The same analysis shows that p( ) = V is optimal. If x = V, the firm knows that consumer valuations are V and V + t. However, there is 1/2 chance that the other firm has signal, and hence sets price V. Let p be the price charged by the firm (after receiving signal x = V ). Then a consumer has to decide whether to search for a better price. Since the other price is V with probability of (at least) 1/2, the benefit of search for the buyer is at least 1 (p V ). 2 13
14 The buyer compares the benefit of search with the cost of search s, and searches if and only if the benefit of search outweighs the cost of search. This means that if the firm sets price above V + 2s, buyers will search. If buyers search, the demand is 0, as they find a better price (the price of the other firm is either V or V + t according to the equilibrium strategy). Therefore, price can not exceed V + 2s. Also, due to consumer valuations, price above V is suboptimal as it results in no profit. At the price of min{v + 2s, V } or below, consumers do not search and buy. Hence there is no reason for the firm to reduce the price below min{v + 2s, V }. Lastly, it is optimal for consumers not to search as far as the price does not exceed V + 2s. Hence the above is an equilibrium price strategy. Uniqueness. To see that the above equilibrium price is the unique symmetric equilibrium price strategy, note the following. 1) Lowest offered price can not be below V. This is due to the fact that if the firm charges an ε < s above the lowest possible price offered in an equilibrium, consumers will not search. If this price is below V, consumers will buy. Hence a firm that is considering to offer the minimal price below V is better off if it raises the price by ε < s, and hence no firm charges below V. 2) The price is set so that consumers do not search. If one consumer finds it optimal to search, then all do. If consumers search, there is at least 1/2 chance that they leave. By assumptions, a firm will not forego 1/2 demand for the maximal increase of price from V to V. 3) If x = V or x =, the firm sets p = V. The firm does not offer a higher price due to consumer valuations, since the demand has the same shape as monopoly due to no search by consumers and consumers do not search if p V by 2). 4) If x = V, the price is determined uniquely by the nosearch condition x V + 2s and valuation V of half of the consumers. The following proposition summarizes the properties of the equilibrium price. Proposition 2. In the above model with homogeneous goods, if 2s V V, 14
15 1. The expected equilibrium prices and profits are smoothly increasing in s 2. If s increases above a certain level, prices become monopolistic. 3. As s decreases to 0, prices approach the price under the lowest possible belief on consumer valuation. 4. Equilibrium price dispersion increases in s. 5. The aggregate (over possible valuations) buyer surplus is smoothly decreasing in s. 6. Social welfare does not increase in s. 5 Proof. The expected (before the signal x is known) equilibrium price is Ep = 3 4 V (V + 2s) = V + s 2, and the average across a priori possible consumer valuations buyer surplus is EBS = ( ) (V V 2s) 2 = V V 2s. 4 The first two claims of the proposition immediately follow from the above formulas. Social welfare in this model does not change with s, as price only affects the allocation of surplus. The equilibrium price dispersion is 0 in the case of low valuation (since signals are x = V or x = ) and possibly 2s in the case of high valuation. The apriori expected variance of price dispersion is (2s) 2 /4 = s 2, which increases in s. Prices become monopolistic as s becomes higher than V V. The last claim follows since when s 0, the highest possible price V + 2s approaches the lowest possible price V. 5 If the first search is free, then there is no impact of s on the social welfare, since prices in this model only affect the division of the surplus as even the monopoly price is such that all buyers buy. In a more general model with a possibility of some deadweight monopoly loss, social welfare would increase when prices decrease. This situation occurs when the model is extended to heterogeneous buyers, which will be considered in the next section. Also, if the first search is costly, then lower search costs would imply lower waste on search and therefore, higher social welfare. 15
16 Segment 1 t Segment 2 V = V or V Firm 1 Firm 2 Figure 4: Differentiated goods product preference space. It can also be noted from the proof of the equilibrium that the equilibrium price schedule in Proposition 1 remains an equilibrium price schedule if the number of sellers in the market is not restricted to two. Also note that the predictions of the model are consistent with general beliefs about the effects of search costs on the equilibrium prices, profits, and buyer surplus. The statements 13 of Proposition 2 indicate how Diamond paradox can be resolved if sellers don t have complete information about the demand. Kuksov (2002) shows how even a small amount of private uncertainty can resolve Diamond paradox if common knowledge is lacking. Empirical evidence in support of statement 4 of the above proposition in the online environment is conflicting (see Brynjolfsson and Smith (2000)). We will see in section 7 that if product differentiation is endogenous, there are conditions under which price dispersion decreases as search costs increase. We will also see that statements 4 and 5 may not hold if product design is endogenous. 6 Differentiated Products I model differentiated products by assuming that one firm s product is located at the ideal point of one segment of consumers and the product of the other firm at the ideal point of the other segment. In this case, the product/consumer space can be represented by the following diagram (Figure 4). In this model of differentiation, one consumer segment values one product at V or V and the other product at V + t and V + t respectively, and the other consumer segment values the first product at V + t or V + t and the other at V or V respectively. Therefore, a price differential of t is required for a given segment to consider the products as perfect alternatives. 16
17 Another form of differentiation one may consider is positioning of the product closer to the ideal points of consumers in a certain valuation case, i.e. moving the position of the product in the horizontal dimension of the above figure. Also, one can think of informative advertising or general product level research that shows comparative benefits of different products (as in pharmaceutic products) as changing the distance between the ideal points of different segments, i.e. increasing the value of t in the above figure. Both approaches lead to conceptually same conclusions as related to the effects of endogenous vs. exogenous product differentiation discussed below. The case of partial differentiation, where a firm moves its product a part of the way from the ideal point of one segment to the ideal point of the other segment requires consideration of asymmetric equilibria but leads to conceptually same conclusions. 6.1 Solution of the Model with Differentiated Products Proposition 3. There is a unique symmetric equilibrium in the above model with differentiated products. In the equilibrium, consumers do not search, and the price is determined by the following rule: p(x) = { V + t if x = V or x =, min{v + 2t + 2s, V + t} otherwise. Proof. The proof of this proposition follows the same proof as that of Proposition 1. Note two differences: the first is the minimal level of prices is raised to V + t. This is due to the fact that consumers search at the best fitting location first. This is the equilibrium behavior in any symmetric equilibrium since the expected (by consumers) price distribution at both stores is the same, and hence the better fitting firm provides a higher (by t) expected surplus. Secondly, in order to ensure no search by consumers in the case of high valuation (signal x = V ), it is enough to make a price differential of at most t + 2s (in contrast with the no differentiation case, where a price differential for no search had to be 2s). This is obtained as follows. In the case of differentiated products, a buyer compares the net utility of purchasing at the firm 1 with the possible net utility of a purchase at the firm 2 and the search cost s. Let V j be the valuation of a buyer at the firm j. As in the case of no 17
18 differentiation, if firm 1 received a signal x = V, there is probability 1/2 that the other firm received signal and sets price V + t. Also, the valuation of the buyer of the other product is t less than valuation of the product of firm 1 (as was noted before, buyers first search at the firm that provides better fit). Therefore the expected benefit of search is 1 2 ((V 2 V t) (V 1 p)) = 1 (p 2t V ). 2 In order that buyers would not search in the equilibrium, it is sufficient to set price such that the benefit of search above is no more than s. Hence, consumers don t search in the equilibrium if the price is as high as V + 2t + 2s, which is t + 2s higher than the other possible price (p( )). In this model, the assumption that once the price is known by the consumer, the consumer can search at a different firm at a cost of s and then return to the first firm at a zero cost becomes important for the equilibrium price formula. However, if the consumer is required to pay additional s to return, the results will be conceptually the same, since the only difference would be that min{v +2t+2s, V +t} is substituted by min{v +2t+3s, V +t} in the above formula for p(v ). Note that irrespective of consumer search, the prices are raised by t due to a better fit. The better fit leads to an increased social welfare, which is fully extracted by the firms. 6.2 Exogenously Differentiated Products: Results The implications of the model with (exogenously) differentiated products are similar to the implications of the model with homogeneous goods. Namely, we can formulate the following proposition. Proposition 4. In the above model with differentiated products, if 2s V V t, 1. The expected equilibrium prices and profits are smoothly increasing in s. 2. The aggregate (over possible valuations) buyer surplus is smoothly decreasing in s. 3. Social welfare does not increase in s. 18
19 4. Equilibrium price dispersion increases in s and t. 5. If s increases above a certain level, prices become monopolistic. 6. As s decreases to 0, prices approach the price under the lowest possible belief on consumer valuation. Proof. The proof follows from the formula for the equilibrium price rule just as in Proposition 2. Note that if t > V V (i.e. differentiation is higher than uncertainty about the valuation), then the prices do not depend on search costs and are as if firms would collude. 7 Endogenous Product Differentiation To model endogenous product differentiation, we have to allow firms to develop the products at a certain stage, and specify the possible product space and costs of positioning products at different locations in the product space. 7.1 The Model of Endogenous Product Design I model endogenous product design as follows. At the beginning, a generic product (in this case, generic just means a product that has already been developed and neither firm has proprietary rights on it) is available for both sellers for future sales. This product is located at the ideal point of one of the consumer segments. However, there is also an option to design another product that is located at the ideal point of the other segment. At the point the design decision must be made, both firms have the common prior on the buyer valuation parameter V. Either firm has the option to invest and develop the other product at a cost C. 6 After the decision on developing the product is made by the firms, both the firms and buyers learn about the existence and valuation of the new product 6 One can also consider an incumbent firm selling the generic product, and an entrant deciding whether to design a modification of the product or sell the generic product. The drawback of this approach is that one may argue that the incumbent is identified in buyer minds and hence an asymmetrical equilibrium may result. 19
20 (if it was designed). Then the firms simultaneously receive the signals x j of buyer valuation parameter V, and then, simultaneously decide on the prices. The assumption that the signal of consumer valuation x comes after the decision to design the product is due to time required for implementing the design and variability of consumer valuations. If product design would follow the signals of valuation, firms could use product design to convey information about their beliefs on consumer valuation to the other firm. The nature of the uncertainty of consumer valuation that is modelled here assumes faster changing beliefs. After the prices are set, buyer decisions follow, and profits realize. To see if a firm would invest in developing the product, one needs to compare the expected benefit of differentiation to the individual firm to the cost of differentiation C. 7.2 The Benefit of Differentiation Comparing the expected equilibrium price with and without product differentiation, we see that the expected benefit of differentiation is t/2 in case x = V or x =, and B(t, s, x) = 1 t if 2s > δ, 2 2t + δ 2s if 2s (δ t, δ), 2t if 2s < δ t, where δ = V V, x = V. This means that the expected (before receiving signal x) benefit of differentiation is t/2 if 2s > δ, EB(t, s) = t/2 + (δ 2s)/8 if 2s (δ t, δ), (1) 5t/8 if 2s < δ t. Thus we have the following proposition. Proposition 5. The expected benefit of differentiation in the above model is positive and nonincreasing function of the search cost s. In particular, the expected benefit of differentiation monotonously increases when s decreases when 2s (δ t, δ). 20
21 Proposition 5 can be restated as saying that buyer price search cost and product differentiation are substitutes. The result that the benefit of differentiation may increase and does not decrease when s decreases means that for a range of the cost of differentiation parameter C, lower s implies higher equilibrium product differentiation. This fact leads to important implications that are discussed in the following subsection. 7.3 Endogenous Product Design: Results The decision of a seller on whether to differentiate the product will, obviously, depend on the cost of differentiation. Suppose it costs C to design the differentiated product. Then a seller will be willing to design the product if and only if C < EB(t, s). Therefore, we have the following result Proposition 6. A seller is more likely to invest in product design if search cost s is smaller. In other words, a seller is willing to pay larger fixed cost to design the differentiated product if search costs are smaller. Proof. Since expected benefit of differentiation EB(t, s) is decreasing in s (see formula (1) or Proposition 5), product differentiation may only increase when s decreases. To see under which conditions on s and C it happens, note that in order for product differentiation to become equilibrium outcome from not an equilibrium outcome, s should change from a level s 1 such that C > EB(t, s 1 ) to a level s 2 such that C < EB(t, s 2 ). For this, one must have C (t/2, 5t/8), s 1 > 2t 4C + δ/2, and s 2 < 2t 4C + δ/2. The above proposition implies that in an economy with a number of industries or when many possibilities of differentiation exist, a decrease in buyer search costs for price in any range, may result in higher product differentiation as more and more products become differentiated. Let us now turn our attention to the effect of search cost s on equilibrium prices. Proposition 7. A decrease in search cost s has a direct effect of decreasing prices, and indirect effect of increasing prices through an increase in product differentiation. The resulting change in the equilibrium price can be either positive or negative. 21
22 Proof. The direct effect of search cost s on prices (keeping product differentiation constant) was discussed above (Proposition 4). The indirect effect is as follows. When s decreases, product differentiation increases, and the increase in product differentiation leads to higher prices. To see that this increase may more than offset the decrease in prices due to lower search costs, it suffices to consider the case when search costs are just above and below the level sufficient to induce product differentiation. Without the endogenous decision on product design, the equilibrium price with slightly lower search costs would be slightly lower. However, due to jump from not differentiated products to differentiated products, prices may increase by t + min{t, δ 2s}. To see exact conditions for increasing prices, consider C (t/2, 5t/8) and s changing from s 1 > 2t 4C + δ/2 to s 2 < 2t 4C + δ/2 (the conditions for equilibrium to change from a no differentiated to differentiated one). In this case, the equilibrium price changes from to p(x, s 1 ) = p(x, s 2 ) = { V if x = V or x =, min{v + 2s 1, V } otherwise, { V + t if x = V or x =, min{v + 2t + 2s 2, V + t} otherwise. The prices for the lower level of s are higher for all values of the signal x if s = s 1 s 2 < t. The above proposition suggests that the effect of search costs on prices may be different depending on the difficulty of product differentiation in a particular industry. One can expect that prices may increase as search costs decrease in an industry where a small change in the incentive to differentiate prompts firms to substantially increase differentiation. One could hypothesize that flower arrangement or apparel may be examples of such industries. The possibility of the paradoxical effect of lower search cost s on the equilibrium prices is not only due to better product fit, but also due to lower competition, as is demonstrated by the following counterintuitive possibilities for both seller profits and buyer surplus. Proposition 8. As s decreases, buyer s surplus may decrease, and equilibrium industry profits may increase. Furthermore, social welfare may decrease. 22
23 Proof. As was stated in the previous proposition, as s decreases, prices may increase. An increase in prices decreases buyer s surplus. The effect of prices on buyer surplus is partially mitigated by improved fit. However, it is easy to see that in the differentiated products equilibrium, each buyer is no better than in the nondifferentiated products equilibrium, and some buyers are strictly worse off. To see the possibility of increasing profits, note that if the decision on product differentiation is not cooperative, then the amount of differentiation is likely to be industry suboptimal, since differentiation by one seller has a positive externality for the other. In particular, in the current model, if the benefit of differentiation for one seller is EB(t, s), then (since the sellers are symmetric), the benefit of differentiation for both sellers together is 2EB(t, s). Hence, as the search costs decrease, the individual firm decision to design a differentiated product may trigger a more optimal for the industry product differentiation, and hence, increase industrywide profits (as opposed to the equilibrium with higher search costs). Further, social welfare may decrease as search costs decrease since the benefit from better fit of t/2 for an average consumer (benefit of t for half of consumers) with differentiation may be less than the cost of undertaken differentiation, which can be as high as 5t/8. The condition for a decrease in social welfare is exactly when equilibrium changes from a no differentiated to a differentiated one, because in that case C > t/2 is spend on differentiation and social benefit of differentiation is t/2. Hence, if the differentiation is caused by competition (i.e., when differentiation would not be an equilibrium outcome when s is extremely high, but is an equilibrium outcome with a given s), social welfare decreases. In other words, product differentiation caused by competition is socially suboptimal. The intuition of this result is that when a certain action of one firm (in this case, differentiation) has positive externality on other firms, an exogenous incentive urging firms to take that action may make all firms strictly better off. Besides the effect on the level of prices, decreasing search costs may have a counterintuitive effect on the price dispersion as well as the following proposition shows Proposition 9. As search cost s decreases, price dispersion may increase 23
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