The Economics of the Long Tail

Transcription

1 The Economics of the Long Tail Todd D. Kendall and Kevin K. Tsui Compass Lexecon and Clemson University October 20, 2008 Abstract Anderson (2006) argues that e-commerce and other new technologies improve e ciency by encouraging the entry of new producers and innovations, creating a long tail of niche products while reducing the market share of previously popular products. We study the strategic interaction between hits and niches in their pricing, entry, and innovation decisions using a model of product di erentiation with generalized cost structure. In contrast to the popular view, we show that improvements in information and communication technology can lead to either the long tail e ect or an opposite superstar e ect (Rosen, 1981), depending on (a) how the structure (not simply the level) of producer costs changes, and (b) how disparate are consumer preferences. These two factors also determine whether there is excessive or insu cient product diversity. Post-entry product and technology innovation incentives are ine cient in the long tail market structure because producers can soften price competition by engaging in excessive product di erentiation and adopting technologies with high variable costs. These results have implications on competitive policy, the paradox of choice, social fragmentation, and network neutrality. JEL Classi cations: L11, L86, M13, O31, K21 We acknowledge helpful comments and suggestions from Bill Dougan, Tim Perri, Ivan Png, Chad Syverson, Irina Suleymanova, Chuck Thomas, Bob Tollison, Julian Wright, and seminar participants at Clemson, National University of Singapore, the North American Summer Meetings of the Econometric Society 2007, and the Intertic Conference on Endogenous Market Structure and Industrial Policy. All remaining errors are our own. Correspondence may be addressed to Kevin K. Tsui, John E. Walker Department of Economics, Clemson University, ( ktsui@clemson.edu).

2 What changes in the future will be wrought by cable, video cassettes, and home computers? Sherwin Rosen I. Introduction The e ects of the internet on price levels and dispersion in various industries have been explored extensively. 1 Of equal interest, however, is the role of internet technology in changing the number and market shares of producers in these industries. An in uential trade book by Anderson (2006) considers this question and contends that e-commerce is creating a long tail of entry by individually-minor (through collectively important) niche suppliers in many industries, while reducing the relative importance of mainstream products. He argues for important normative e ects from increased entry, and in particular, the shift from the production of a few, monolithic hit products to the production of many separate niche products, both because it implies greater variety and satisfaction of niche preferences, and because it increases the likelihood that unknown, but talented individuals will enter markets where they can generate valuable innovations. 2 The long tail e ect is also related to important welfare debates on competition policy, cultural fragmentation, and network neutrality regulation. Theoretical and empirical research on the long tail e ect has reached con icting conclusions. Brynjolfsson, et al. (2007) and Emre, et al. (2007) both consider a decline in consumer search costs due to the introduction of e-commerce; however, the former authors argue for a long tail e ect, 3 while the latter argue that these cost reductions have actually had the opposite e ect, creating a superstar e ect in the sense of Rosen (1981), who argued that earlier communications technologies such as radio and television primarily served to increase the extent of scale economies among high quality suppliers. In this paper, we provide a uni ed theoretical framework to consider the e ects of the internet on industrial structure, e ciency, and innovation incentives. Our model is able to show how progress in information and communication technology may create long tails in some cases, and superstars in others, depending on how the structure (not simply the level) of producer costs changes with the introduction of the new technology, and how disparate are consumer preferences. In particular, we show that technological innovations that reduce xed costs relative to variable costs encourage entry by marginal producers, and thus generate long tail e ects in industries with plentiful horizontal di erentiation. By contrast, technologies that reduce variable costs relative to xed costs in highly vertically-di erentiated industries lead to strategic exclusion of marginal entrants, and thus, superstar e ects. Intuitively, high variable costs serve as a mechanism to soften price 1 See Ellison and Ellison (2005) for a review of the literature. 2 Today, millions of ordinary people have the tools and the role models to become amateur producers. Some of them will also have talent and vision. Because the means of production have spread so widely and to so many people, the talented and visionary ones, even if they re just a small fraction of the total, are becoming a force to be reckoned with (Anderson 2006, p. 65). 3 Technically, Brynjolfsson, et al. (2007) only argue for a short-run long tail e ect. They show that this e ect may be diminished in the long run as rms adjust their investments in the development of di erent products. 1

3 competition and customer-stealing among competing suppliers, while high xed costs reduce contestability by potential entrants. Therefore, it is unsurprising that the internet may have had di erent e ects in di erent industries, and the future direction of internet innovation may be to lengthen or shorten the tail in any given industry. With a better understanding of the long tail e ect, we can address several related welfare and regulatory issues. First, it is sometimes claimed that the internet has reduced the necessity for enforcement of competition laws in some industries, such as cross-ownership restrictions in radio and television (McKenzie and Lee, 2001, Crampton and Boudreaux, 2004). Our model implies conditions under which long tails and superstar e ects are e cient, and hence, when the internet may be a substitute (or complement) for antitrust enforcement. In particular, it is possible for technological change to generate excessive entry in some cases and insu cient entry in others. Second, Anderson (2006) argues that the increased variety of products available due to the internet has increased consumer welfare; however, Sunstein (2001) points out a darker side to the long tail social and cultural fragmentation. By providing a simple framework for distinguishing where internet technology creates long tails and generates excessive product di erentiation, our model can be a guide to where concern over fragmentation should rest. Finally, an important aspect of the debate over network neutrality legislation is the concern that broadband providers may raise costs to marginal entrants in internet application markets, and so reduce entry and innovation. Our model shows that the ability of network neutrality legislation to solve this problem depends on just how broadband providers would, in actuality, change the structure of costs, and how consumer preferences for internet applications are distributed. More generally, we demonstrate how niche product suppliers may innovate in order to gain access to an industry, and how incumbent producers may innovate in order to strategically exclude niche products. In many cases, we show that neutrality regulation would be counterproductive. Section II exposits our model and considers the e ects of exogenous technological change in generating long tail and superstar e ects. Section III shows how the model uni es previous theoretical and empirical ndings on the long tail e ect. Section IV considers the e ciency of market equilibria, and so addresses the general issue of how the internet a ects the value of competition laws, as well as addressing the paradox of choice and the problem of excessive social fragmentation. Section V studies producer incentives to innovate and the model s implications for network neutrality regulation, while Section VI concludes. II. A Model of Di erentiated Products with Fixed and Variable Costs of Production According to Anderson (2006), the internet reduces the cost of reaching niche pockets of consumers, and thus, the long tail is created as product selection switches from a few hit products to a multitude of varied niche products. To capture this idea, we present a model, the formal structure of which is an adaptation 2

4 of the duopoly model used in Davis, Murphy, and Topel (2004) (hereafter, DMT ). This duopoly setting is very simple, but it highlights the strategic interaction between incumbents and new niches in particular, their pricing, entry, and innovation decisions. The solution concept developed by DMT also enables us to focus on unique pure-strategy equilibria, which are useful for comparative analysis. We shall argue, however, that our key intuitions can be generalized to some standard oligopoly models with free entry, which suggests the robustness of these assumptions and our solution concept. Consumer demand in our model is more exible than in some other models, allowing for both vertical and horizontal product di erentiation, although this demand characteristic is not emphasized in DMT. More importantly, the major novelty here is to introduce a generalized cost structure in this framework, which highlights how a reduction in the costs of reaching niche consumers can have ambiguous e ects on entry, pricing, and innovation decisions, and how declines in cost interact with both vertical and horizontal di erentiation in consumer preferences, which we argue is crucial in understanding the nature and implications of the long tail. Moreover, introducing this generalized cost structure also allows us to study incentives for cost-saving technology innovation which are not considered in DMT. Subsection A exposits notation and describes the equilibrium concept we employ, while subsections B and C depict the properties of two possible types of equilibrium in the model. Subsection D supplies existence conditions for each type of equilibrium and illustrates how technological change can a ect these conditions. Subsection E illustrates the robustness of our major ndings in other theoretical frameworks. II.A. Theoretical Framework and Equilibrium Concept Consider a market with two single-product producers, each of whom sets a single price and maximizes pro ts. We will refer to them as the hit producer (h) and the niche producer (n), indicating their relative popularity in a market when both supply positive output, as discussed below. The production technology is de ned by xed costs F F; paid if a producer enters the market, and variable costs, V C(); where F and V are parameters which shift the cost structure. 4 We also assume that C() is increasing and convex, and thus, average variable cost, denoted C(), is increasing. To focus on the e ects of changes in the cost structure, we also assume for now that both producers have access to the same technology; however, our results are robust to this assumption, which will be relaxed in Section V when we study strategic technology innovation. There are N consumers, of which N f have fringe tastes, and N p = N N f have popular tastes. Denote the relative number of fringe customers by = N f =N p < 1. Consumers have unit demand, so that each of them will purchase at most one unit of either the hit or the niche product. 5 Let V p and V f be 4 For simplicity, we parameterize only the level of variable cost, but see note 16 below where we brie y consider shifts in the shape of the variable cost function. 5 Individual unit demand and constant population implies aggregate demand is inelastic when all consumers purchase from 3

5 the valuations of the hit product by popular- and fringe-taste consumers, respectively. Similarly, denote consumers valuations of the niche product by W p and W f. To distinguish consumers, assume that popular-taste consumers value the hit product more highly than fringe consumers, i.e., V p > V f : Thus, the majority of consumers (popular-taste) prefer the hit product. It is also natural to interpret these demand parameters in terms of the degree of vertical and horizontal di erentiation. An increase in (V p W p ) or (V f W f ) represents an increase in the hit s vertical di erentiation over the niche. Similarly, an increase in (V p V f ) or (W f W p ) represents an increase in horizontal di erentiation between the two products. Denote the producers chosen prices by P h and P n : Participation by popular-taste consumers requires V p P h or W p P n ; similarly, fringe consumer participation requires V f P h or W f P n : We will assume throughout that these constraints do not bind. We will also assume that each producer could feasibly sell to either consumer type and cover its costs: N i V i F F + V C(N i ) and N i W i F F + V C(N i ) for i = p; f. These assumptions make the problem non-trivial. The hit and the niche play a simultaneous price-setting game. After prices are selected, each consumer chooses to buy either the hit s product or the niche s. In the model, a supplier can choose not to enter the market by setting a su ciently high price that neither consumer type chooses to buy its product. We will focus throughout on potential entry by the niche, while assuming the hit always enters (the set of primitives for which this is true is broad: see DMT for a fuller analysis of entry incentives for incumbent suppliers). When producers compete in price under this exible demand speci cation and general cost structure, our model has no pure-strategy Nash equilibrium in general. Thus, we borrow a solution concept from DMT, price-cut immune (PCI) equilibrium, which assumes buyers always have the right to purchase at a previously announced price and hence producers are only ready to reduce their prices whenever undercutting and grabbing their rivals customers is pro table (see also Morgan and Shy (2000) and Shy (1996, 2001)). 6 In equilibrium, no seller has an incentive to lower its price in order to steal the rival rm s customers, although they may wish to raise prices. This equilibrium concept delivers unique pure-strategy equilibria. Pure strategy solutions may be preferred here, both because they are simpler and because traditional Bertrand solution concepts in such games are often subject to severe multiple equilibria issues (Baye and Morgan 1999) and are infeasible for many of the important applications to which the model may be applied. 7 DMT show that this equilibrium concept is a natural extension of the more standard Nash-Bertrand pricing equilibrium, some producers in equilibrium, but see section II.E for discussion related to relaxation of this assumption. 6 This solution concept is also known as undercut-proof equilibrium, which speci es a speci c type of conjectural variation behavior in which each rm assumes that the rival rm will alter its price only if such an action satis es two properties: (a) the undercutting rm will enlarge its market share by appropriating the customers of the rms it undercuts, and (b) such undercutting is pro table. 7 In addition, there are the usual concerns regarding the application of mixed strategy solutions (e.g., see Radner and Rosenthal, 1982, or Rubinstein, 1991). 4

6 and implies outcomes identical to those of Nash-Bertrand in many simple frameworks. 8 Formally, De nition 1 (Price-Cut Immune Prices). A set of prices P h ; P n is price-cut immune (PCI) if h (P h ; P n) h (P h ; P n) for all P h < P h and n (P h ; P n ) n (P h ; P n) for all P n < P n; where h and n represent the hit and the niche s pro ts, respectively. In other words, a set of prices is price-cut immune when, given all competitors prices, no individual producer wishes to cut its own price (although it may, however, wish to raise its price). If no producer wished to either cut or raise its price, these prices would correspond to the traditional Nash-Bertrand outcome. De ne i(p i ) as the set of all price-cut immune prices for producer i = h; n, given the price set by its competitor ( i ). Then De nition 2 (Price-Cut Immune Equilibrium). A PCI equilibrium is de ned as a set of prices P h ; P n such that and h (P h ; P n) = n (P h ; P n) = max h(p h ; Pn) P h 2 h(pn ) max P n2 n(p h ) h(p h ; P n ): One intuitive way of justifying this form of equilibrium is by assuming producers make binding price announcements (for example, through advertising), after which consumers perceive further price increases as reneging on a deal, although price reductions are, naturally, acceptable to consumers. When producers face di culty raising prices above previously announced levels, PCI equilibrium is a natural solution concept and forms an extension to ordinary Bertrand competition. 9 8 For example, in a standard model of Bertrand competition between two producers with di erentiated products, the unique PCI equilibrium is also the Nash equilibrium. For price competition between rms producing di erentiated brands, Morgan and Shy (2000) show that whereas a Nash- Bertrand equilibrium in pure actions never exists, a unique undercut-proof equilibrium always exists and has the following properties: (a) brands prices monotonically diverge when the brands become more di erentiated, and are identical when the brands become homogeneous; (b) the rm with the larger market share charges a lower price than the rm with the smaller market share but earns a larger pro t. The undercut-proof equilibrium also supports an upper bound on colluding prices in a dynamic meeting-the-competition price game. 9 Alternatively, Morgan and Shy (2000) argue that in an undercut-proof equilibrium environment, rms assume that rival rms are more sophisticated in that they are ready to reduce their prices whenever undercutting and grabbing their rivals customers is pro table. 5

7 In subsections B and C, we describe the properties of two possible types of PCI equilibria in our game. Subsection D supplies existence conditions for each, and illustrates comparative statics in the model. II.B. Equilibrium Type 1: The Long Tail Consider rst an equilibrium in which both the hit and the niche products are produced and sold in the market what we will refer to as a long tail equilibrium. In a stylized manner, this outcome corresponds to Anderson s (2006) notion that internet technology has introduced many new niche products into music, book, lm, and other industries, while reducing the market share of the incumbent products. More speci cally, we will focus on a sorting equilibrium in which popular-taste consumers purchase the hit product and fringe-taste consumers purchase the niche product. 10 A necessary condition for this equilibrium is that V p W p > V f W f, which we will assume for the rest of the analysis. In order for popular-taste consumers to buy the hit product, they must receive higher consumer surplus than they would receive by purchasing the niche product: P h P n + (V p W p ): (1) Similarly, for fringe-taste consumers to buy the niche product, it must be the case that P h P n + (V f W f ): (2) Also, in equilibrium, the hit must receive higher pro ts selling to popular-taste consumers exclusively, compared with cutting its price to P n + (V f W f ) in order to attract the fringe-taste consumers as well. This implies P h N p C(N p ) F F [P n + (V f W f )]N V C(N) F F; which can be rearranged as P h 1 N p f[p n + (V f W f )]N V [C(N) C(N p )]g : (3) Similarly, the niche producer prefers selling only to fringe consumers: P h (W p V p ) + 1 N f[p nn f + V [C(N) C(N f )]g : (4) Any pair of prices satisfying equations (3) and (4) is price-cut immune because neither supplier wishes 10 It is also possible under some parameterizations for the hit supplier to sell to fringe-taste consumers only and the niche supplier to sell to popular-taste consumers only (see DMT), but we ignore this possibility for simplicity here. 6

8 to cut its price to attract additional customers, given the other s price. Moreover, note that since V p W p > V f W f ; equations (1) and (2) cannot simultaneously bind. As an example, consider the case illustrated in Figure 1, Panel A, where we plot all four equations in P h -P n space. If there is a long tail equilibrium, it must lie strictly within the corridor formed by equations (1) and (2), since otherwise, all consumers would buy from only one of the two suppliers (or neither). Restricting ourselves to this space, we proceed to show that if an equilibrium exists in this region, it is at point e. Since equations (3) and (4) bind at point e, it is necessarily PCI. Then consider any niche producer price below Pn L. If this price were consistent with a long tail equilibrium, the hit s pro t-maximizing PCI response would be to set its price according to the minimum of lines (1) and (4), evaluated at the candidate niche price. But then the niche could do better and still be PCI by raising its price in order to make equation (3) bind. Similarly, consider a niche price above Pn L. Again, if this price were consistent with a long tail equilibrium, the hit must set its price in order to make equation (4) bind. But then the niche s price is no longer PCI. This argument illustrates that if there is a long tail equilibrium, point e, i.e., (Ph L; P n L ), is the only such equilibrium. Panel A represents a particular case in which when equations (3) and (4) bind, equations (1) and (2) automatically hold. This does not necessarily have to be so, and panels B and C illustrate cases in which it is not (and show the unique long tail candidate PCI equilibrium in each case as well). Essentially, cases like that in Panel A involve a su cient degree of horizontal di erentiation. 11 For simplicity, we will maintain this assumption throughout the rest of the paper, and leave the analysis of cases like those in Panels B and C to the Appendix, though as the Appendix shows, very little depends upon this assumption. Lemma 1 (Comparative Statics within a Long Tail Equilibrium). In any long tail equilibrium, (a) an increase in horizontal di erentiation between the two products raises the prices and pro ts of both producers, and (b) a uniform increase in variable costs raises the prices and pro ts of both producers. However, (c) an increase in xed costs has no e ect on prices, but reduces both producers pro ts. To prove this lemma, note that equations (3) and (4) form a system of two equations that imply prices in a long tail equilibrium given by Ph L = (1 + )(V p W p ) (V f W f ) + V [(1 + 2) C(N) C(N 1 + p ) C(N f )] 11 Equations (3) and (4) cross within the corridor formed by equations (1) and (2) when 2 1+ (V f W f ) (V p W p) V [C(N) 1+ C(N 1 f )] V [C(N) 1+ C(Np)] 1 1+ (Vp Wp) (V f W f ). Note that the term on the far left is decreasing, and the term on the far right is increasing, in the degree of horizontal di erentiation. 7

9 and P L n = (V p W p ) (1 + )(V f W f ) + V [(2 + ) C(N) C(Np ) C(N 1 + f )] : The hit producer s pro t can then be written as L h = Ph L N p V C(N p ) F F (1 + )(Vp W p ) (V f W f ) + V [(1 + 2) C(N) = (1 + ) C(N p ) C(N f )] N F F; and the niche producer s pro t is L n = P L n N f V C(N f ) F F = (V p W p ) (1 + )(V f W f ) + V [(2 + ) C(N) C(Np ) (1 + ) C(N f )] N F F: Lemma 1 follows from the expressions derived above. 12 It may seem surprising that rm pro ts are increasing in variable cost. What drives this result is the fact that, due to the assumed convexity of the cost function, price competition among producers is softened when variable costs are high because it becomes increasingly costly for each supplier to expand output to the other supplier s customers. 13 This implies that an improvement in technology that reduces total costs has ambiguous e ects on producer pro tability depending on how the cost structure is changed. For instance, a relative decline in variable costs makes xed costs more salient, reducing diseconomies of scale in production and creating greater competition to increase output and lower prices, and consequently lower pro ts. A relative decline in xed costs does the opposite, tending towards higher pro ts. Nothing in this subsection has shown that a long tail equilibrium must exist; we have only analyzed the uniqueness and properties of a long tail equilibrium if one exists. In the subsection D, we provide existence conditions, but rst, we consider a di erent equilibrium type altogether. II.C. Equilibrium Type 2: Superstars Now consider an equilibrium in which the hit producer sells to all consumers and the niche producer does not enter what we will refer to as a superstar equilibrium. 14 Though stylized, this equilibrium displays 12 In particular, part (b) is proved using the fact that C() is convex: since C(N) > C(N p) and C(N) > C(N f ), an increase in V raises Ph L, P n L, L h, and L n; similarly, an increase in F reduces L h and L n, but as no e ect on Ph L and P n L. 13 See Shaked and Sutton (1982) and Economides (1984) for instances of price competition softening through product di erentiation. 14 It is also possible for the niche producer to monopolize the market, and one could more generally endogenize the identity 8

10 the essential phenomena of Rosen (1981), in which market share and pro ts are concentrated among a small number of suppliers. In order for the hit to exclude the niche from entering the market, it must set P h such that the niche producer cannot pro tably sell to either type of consumer alone, nor to both. In order to sell to fringe-taste consumers, equation (2) implies that P n must be no higher than P h (V f W f ); in which case the niche producer would make pro t no greater than [P h (V f W f )]N f V C(N f ) F F: Thus, in a superstar equilibrium, this expression must be non-positive, i.e., the hit producer must set its price such that P h (V f W f ) + V C(Nf ) F F N : Similarly, to prevent the niche producer from pro tably selling to popular-taste consumers (and hence fringetaste consumers as well), the hit product cannot be sold at a price higher than P h (V p W p ) + V C(N) + F F N : If a superstar equilibrium exists, then the equilibrium price for the hit, Ph S, is the minimum of the above two values. 15 The pro t for the hit supplier in such an equilibrium is, therefore, 8 >< S h = >: (Vf W f ) V [ C(N) C(Nf )] N + F F (V p W p )N if (V f W f ) + V C(Nf ) + 1+ F F N (V p otherwise. W p ) + V C(N) + F F N Lemma 2 (Comparative Statics within a Superstar Equilibrium). In a superstar equilibrium, (a) an increase in the hit s vertical di erentiation over the niche raises its price and pro t, and (b) a uniform increase in either variable or xed costs raises the hit s price, but (c) pro ts are weakly decreasing in variable costs and weakly increasing in xed costs. Intuitively, pro ts are increasing in xed costs because xed costs reduce the entry threat from the marginal supplier, the niche (similarly, see Baumol, et al. 1982). Thus, just as in a long tail equilibrium, the e ect on pro ts from a decline in total costs depends on the relative decline in variable costs in comparison of the producer who becomes the superstar. Given our assumptions on the demand structure, however, it will always be the hit producer who monopolizes the market in any superstar equilibrium. 15 Thus, the niche s price in a superstar equilibrium is Ph S (V f W f ) = V C(Nf ) + 1+ F F, although at this price the N niche does not sell to any customers (recall our de nition of entry involved setting a price such that some customers buy the product). It can be checked that these prices do indeed form a PCI equilibrium: since the hit monopolizes the market at price Ph S, it has no incentive to lower prices below this level, and cannot increase pro ts while maintaining its superstar status above this price. Similarly, by construction, the niche would receive non-positive pro ts by lowering its price to attract either group of customers, so its maximum pro t level is zero, which it attains in the equilibrium. 9

11 with xed costs. However, the e ect is reversed from the long tail equilibrium: if variable costs decline relative to xed costs, the superstar producer becomes more pro table, not less. As an example, suppose V f W f and V p W p are positive, and for simplicity, let V = 0. This example is similar to Rosen s (1981) environment, in which vertical di erentiation is crucial. Then it can be seen from the above expression that even small di erences in supplier quality become magni ed into large di erences in pro ts, with the magni cation factor being the market size, N. Thus, Rosen s superstar income distribution also follows from our model. II.D. The Rise and Fall of Superstars In the previous two subsections, we have analyzed properties of each equilibrium type, but have not established the existence of either. In this section, we consider existence issues and illustrate how changes in technology, as well as demand characteristics, can lead to transitions between equilibrium types. In particular, we assume that new technology, de ned by changes in the parameters ( V ; F ), is exogenous. An alternative interpretation of this assumption is to view the e ects we observe here as long-run comparative statics, assuming that over a su ciently long time frame, lowest total cost technologies are always adopted; however, in Section V, we will explicitly study producers incentives to innovate (or adopt) new technology, and show that the results derived here remain valid. The main result of this section is summarized as follows: Proposition 1 (Determinants of Superstar and Long Tail E ects). Exogenous technological improvements that reduce variable costs relative to xed costs support superstar e ects, while those that reduce xed costs relative to variable costs support long tail e ects. Moreover, the tendency to shift towards a long tail equilibrium is greater when (a) the product is relatively horizontally di erentiated, (b) the size of the fringe customer group is relatively small, and (c) the initial xed costs are relatively large and the initial degree of diseconomies in production is relatively small. We will rst establish the existence and uniqueness of equilibria. Suppose that the niche producer chooses a price of Pn L ; as de ned by the long tail equilibrium in subsection B. If the hit producer then chooses the long tail equilibrium price Ph L ; equation (3) (which binds in a long tail equilibrium) implies that its pro t would be L h = [Pn L + (V f W f ) V C(N)]N F F: Alternatively, the hit producer could choose a price just low enough to exclude the niche producer and 10

12 move into a superstar equilibrium, receiving pro t S h = [P S h V C(N)]N F F [(V f W f ) + V C(Nf ) F F V C(N)]N N = [(V f W f ) + V C(Nf ) V C(N)]N F F + : F F Comparing these two expressions, it is straightforward to show that a necessary and su cient condition for the hit to have higher pro t under the long tail price response than the superstar price response is actually L n 0: In other words, when the niche producer makes pro ts in a long tail equilibrium, the hit prefers to price so as not to exclude the niche, and the long tail equilibrium exists (and is unique, as shown in subsection B). On the other hand, when the niche producer can make only negative pro ts under long tail pricing, the unique equilibrium is for the hit to become a superstar. Thus, the critical condition determining which type of equilibrium exists for any particular technology is the pro tability of the niche producer under long tail pricing. This analysis shows that movements between long tail and superstar equilibria can happen due to technological improvements that a ect the niche s pro tability. Recall that the niche producer s pro t in a long tail equilibrium, for a given technology, is L n = N (Vp W p ) (1 + )(V f W f ) + V [(2 + ) C(N) C(Np ) (1 + ) C(N f )] F F; This expression can be rearranged in the following linear form: V = m n F + b n where m n = ( )F [(2 + ) C(N) C(Np ) (1 + ) C(N f )]N and b n = (1 + )(V f W f ) (V p W p ) (2 + ) C(N) C(Np ) (1 + ) C(N f ) + ( ) L n [(2 + ) C(N) C(Np ) (1 + ) C(N f )]N : This expression de nes linear iso-pro t curves for the niche in V - F space, where the V -intercept is increasing in the niche s pro t level. In particular, by the analysis above, the iso-pro t curve de ned by L n = 0 divides the space between technologies that generate long tail and superstar equilibria, as in Figure 2. Above this zero-pro t line, the niche producer makes positive pro t in a long tail equilibrium, so any 11

13 technology in this region yields a long tail equilibrium. Below the zero-pro t line, the niche producer makes negative pro t if it enters, so any technology in this region yields a superstar equilibrium. The crucial aspect of the niche s zero-pro t line is that it is positively sloped. This is because the niche producer s pro t is increasing in variable costs and decreasing in xed costs, as shown in subsection B. Thus, suppose initially that the available technology generated cost structure a in Figure 2. This lies above the zero-pro t line, so the industry would initially be in a long tail equilibrium. Now consider a change in technology that lowers total costs, but reduces variable costs relative to xed costs, moving the cost structure from point a to point b. Under the new technology, the niche producer can no longer make pro t in any long tail equilibrium; thus, the industry evolves to a superstar equilibrium. Now suppose that total costs further decline through technological innovation to point c. In this case, xed costs have fallen relative to variable costs, and the industry moves back to a long tail equilibrium. Such dynamics can operate repeatedly as technology progresses, so that the industry moves back and forth between long tail and superstar e ects, even as total costs are declining throughout. What is relevant for the market structure is how each new technological innovation changes the mixture of variable and xed costs. Generally speaking, the niche producer s pro t can switch from negative to positive when technological improvement reduces xed costs relative to variable costs, and can switch from positive to negative when technological improvement reduces variable costs relative to xed costs. 16 This completes the rst half of the proof. To show the remaining equilibrium determinants mentioned in Proposition 1, note that from the demand side, the intercept, b n, shifts down when (V p V f ) or (W f W p ) increases. Therefore, an industry with more horizontal di erentiation will have a lower zero-pro t line, and hence a long tail equilibrium is more likely to prevail. Moreover, it is straightforward to show that the slope m n approaches in nity when becomes arbitrarily small. Hence, a larger market size for the fringe-taste consumers increases the incentives for the marginal rm to enter in order to serve that market. Finally, note that the slope of any iso-pro t curve, m n, is increasing in F and decreasing in the convexity of variable costs ( C(N) relative to C(N p ) and C(N f )). Hence, technological improvement is more likely to create superstars when initial xed costs are low or the initial degree of diseconomies is signi cant Throughout this discussion, we have considered uniform changes in variable costs. It is straightforward to generalize the analysis to allow for non-uniform changes. More generally, we can parametrize the variable cost function at di erent output level by 1 C(N), 2 C(N p), and 3 C(N f ). Then, the niche s long tail pro t is L n = (V p W p) (1 + )(V f W f ) + (2 + ) 1 C(N) 2 C(Np) (1 + ) 3 C(Nf )] N F F: Technological progress can reduce 1 ; 2 ; and 3 di erently. When the decline in 1 is small relative to the decrease in 2, 3 ; and F ; L n is likely to increase Therefore, a small (large) reduction in 1 relative to 2 ; 3 and F ; and hence an increase (decrease) in cost elasticity of output, tends to generate a long tail (superstar) e ect. 17 These two supply-side e ects are also consistent with Rosen s predictions. 12

14 II.E. Robustness Checks The model we have used to derive our central ndings is admittedly very simple, with only two competitors and two consumer types, and it employs a relatively non-standard solution concept. These features have allowed us to isolate the impacts of changes in the cost structure on the entry or exit of niche producers when both vertical and horizontal di erentiation are important, and will allow a clearer focus on the e ciency and endogenous technology innovation questions we address later. However, one may be concerned that these aspects of the model make our ndings ungeneralizable. To address this concern, consider the rst part of Proposition 1, which states that relative declines in xed costs lead to entry while relative declines in variable costs lead to exclusion. First, it is straightforward to see how changes in the cost structure are associated with entry or exit in a homogenous-good, free-entry Cournot model. 18 Therefore, our result is likely to hold even when consumers have elastic demands, because the key variable is the relative importance of xed versus variable costs rather than the level of total cost. As an alternative to Cournot, consider the e ect of changes in xed search costs in a hedonic competitive framework (Rosen, 1981). In the hedonic model, goods are vertically di erentiated, and the price of quality for a good with quality z can be written as p(z)+s z ; where p(z) is the market price of the good and s is a xed cost which does not depend on z. While Rosen pointed out that xed time and e ort costs in consumption are important components of s; and that these have increased with consumer earnings over time; we argue that xed time and e ort costs in acquiring information can be equally important and that the internet often reduce these costs signi cantly. Because consumers substitute imperfectly between quality and quantity, a decline in s in this model leads to a atter distribution of sales across producers of di erent qualities essentially, a long tail e ect. 19 Intuitively, a decline in indirect cost s leads consumers to switch towards lower quality products because they have less incentive to economize on the now lower xed costs. 20 Therefore, it is also true in a hedonic model that declines in xed information costs lead to long tails. Finally, we consider two models of horizontal product di erentiation, which explicitly model either consumer search or producer advertising. Anderson and Renault (1999) nd that product diversity rises with 18 Q For simplicity, assume linear demand (i.e., P = a Q) and quadratic variable costs (i.e., C(Q i ) = F + 2 i V ). When 2 the number of producers is xed at n; Cournot competition on quantities implies a unique Nash equilibrium in which each a producer sets Q i =. Under free entry, the number of producers is determined by the zero pro t condition. It is then 1+n+ V straightforward to show that n = 4 F 4 V F + 2a p (4 F + 2 V F ) 4 F which is decreasing in the xed cost F ; but increasing in the variable costs V provided the demand is su ciently high (in particular, a 2 > 8 F (2 + V )): In other words, a reduction in xed costs induces entry and hence reduces market concentration, whereas a reduction in variable costs discourages entry, leading to higher market concentration. 19 Empirically, Crain and Tollison (2002) nd evidence for this theory. They show that artist concentration in the music industry is positively correlated with earnings (and hence value of time). 20 This is similar to the famous Alchian-Allen theorem, although a decrease in s sh ts the supply of, but not the demand for, the good. 13

15 search costs, because market prices and hence pro tability are higher when it is more costly for consumers to search. Higher search costs therefore encourages product entry. This result seems to refute Anderson s (2006) thesis that one of the forces of the long tail is to connect supply and demand through lower search costs. However, it is important to note that the search costs in Anderson and Renault (1999) are best interpreted as variable costs, because each consumer has to incur that in order to learn the price as well as her match value for the product. In another paper, Grossman and Shapiro (1984) show that decreased advertising costs may reduce pro ts by increasing the severity of price competition. In a long run equilibrium, this implies exit for some products, and hence, a reduction in product diversity in the market. Grossman and Shapiro refer to this as an example of a potential cost-based facilitating practice, because it may be in the incumbent producers interests to raise advertising costs. Similarly, note the fact that the advertising cost in their model is essentially a variable cost in the sense that it costs more to expose the message to a larger fraction of the target population. Therefore, their result is also consistent with our implication that a reduction in variable costs can reduce pro ts and produce a superstar e ect through the exit of niche producers. Moreover, it can be shown that, if their model is revised to make the advertising cost xed instead of variable, decreased advertising costs create a long tail e ect in the sense that product diversity increases. 21 III. Unifying the Long Tail Literature According to Anderson (2006), the long tail e ect unleashed by the internet is composed of three forces: (1) a democratization of the tools of production (i.e., user-created content like homemade videos or blogs), (2) reductions in the costs of consumption due to this democratization (e.g., reading blogs is cheaper than reading a newspaper), and (3) closer connections between supply and demand from lower search costs. Previous literature, which we discuss below, has focused on (3) whether internet-related declines in the cost of information have created greater diversity in product o erings. In this section, we show that the literature s divergent views on this question can be reconciled by specifying how the structure of these costs has changed with the internet, and how horizontally or vertically di erentiated consumer preferences are in a given market. In our model, producers incur costs of production. In reality, because knowledge about potential demanders and suppliers, and characteristics of the goods are not perfect, various market institutions arise to facilitate and economize on the spread and acquisition of market information (Alchian, 1969). These institutions lead some information costs to be borne by consumers as explicit search costs, while others 21 In addition, our model may be usefully compared with those of Shaked and Sutton (1987) and Sutton (1991), who study the relationship between market concentration and cost structure in a class of models of vertical product di erentiation. They show that when sunk cost (a xed cost in their models) is endogenous, the market will remain concentrated regardless of market size. This result does not, however, hold when products are purely horizontally di erentiated. In our model, the long tail (superstar) e ect reduces (increases) market concentration. Although our focus is not on the e ects of changes in market size, we show that the long tail (superstar) e ect is more important for products which are horizontally (vertically) di erentiated when xed (variable) costs decline relative to variable ( xed) costs. 14

16 are internalized by rms (Robert and Stahl, 1993). 22 Because both types of information costs serve the same purpose (Janssena and Non, 2008), as well as because the internet may reduce costs in other aspects of production (such as Anderson s points (1) and (2) above), we lump all information costs together and assume their accounting incidence falls primarily on producers, either as xed or variable costs. 23 In particular, the classical reduced-form cost function speci cation in our model makes our results general and robust to the details of the production process, but more importantly, easy to apply in practice. In other words, our approach is not inconsistent with imperfect information. To the extent that private information can be made available at some reasonable cost (which is, in fact, paid in equilibrium), this cost may be treated as part of the production cost. 24 From a qualitative point of view, therefore, this version of imperfect information is a special case of our model. Quantitatively, the question is whether these costs of information are xed or variable. Recall that our model may be summarized as follows: declines in xed costs, especially in industries characterized by high degrees of horizontal di erentiation, are associated with long tail e ects, while declines in variable costs, especially in industries characterized by high degrees of vertical di erentiation, are associated with superstar e ects. Our model therefore provides a uni ed theoretical framework to consider the e ects of the internet on industrial structure, e ciency, and innovation incentives by identifying conditions under which a reduction in the cost of information through internet technology will lead to a long tail or a superstar e ect. We show that two factors generate the apparently contradictory ndings in previous literature: ambiguity about whether the cost reductions from new technologies are xed or variable, and incomplete accounting of the relative degree of vertical and horizontal di erentiation present in various industries. In particular, a close reading of the model in Brynolfsson, et al. (2007) reveals that search costs are xed therein. Thus, our ndings agree with theirs, which show that an internet-induced fall in search costs leads to a long tail e ect. Similarly, a close reading of Emre, et al. (2007) reveals that, in their model, search costs operate as a form of horizontal di erentiation. Thus, our ndings generalize the notion that a decline in search costs may also be associated with a superstar e ect. The empirical ndings of these papers and others in the long tail literature can also be reconciled with our model by noting that the structure of information costs depends on the nature of demand and the durability of information. Acquisition of information regarding the quality of a particular brand, for instance, is essentially a xed cost because customers only need to learn the information once, and can then buy many units of products with that 22 For instance, rms spend substantial resources on advertisements, window displays, sales clerks, specialist agents, brokers, in-store inventories, catalogues, correspondence, phone calls, market research, and so on, to provide useful product information to consumers. 23 While the accounting incidence is assumed to fall on producers, the economic incidence of these cost will, in general, be shared among producers and consumers in equilibrium. 24 The cost of making private information public is known as costly state veri cation (Townsend, 1979). 15

17 brand without having to learn much more about the brand s quality. On the other hand, acquisition of information about relative and absolute price levels is often a variable cost, especially if a product s price uctuates rapidly over time. These examples show that a new technology like e-commerce may reduce variable costs relatively to xed costs or vice-versa. Empirical examples from Brynjolfsson et al. (2007) (women s clothing) and Emre et. al. (2007) (travel agencies) can illustrate this point. Tastes in fashion tend to be idiosyncratic, and once a customer learns about a favorable brand or designer, she may become a repeat customer in the next season. Therefore, marketing costs in the case of women s clothing likely include an important xed component, which e-commerce can plausibly reduce. Knowledge about air travel prices, however, has a very high depreciation rate because of price discrimination, peak-load pricing, and frequent changes in prices and ight schedules. It is not di cult to imagine that online travel sites like Expedia.com and Travelocity.com have reduced the variable costs of airline ticket information in important ways. 25 Thus, our model shows that it is unsurprising that the internet has generated long tail e ects in women s clothing, but superstar e ects in travel agent services. Even within a single market, di erences in consumer preferences can create di erent e ects from the internet. In lm, Elberse and Oberholzer-Gee (2006) nd that the long tail e ect is more important in the Foreign and Adult movie genres, whereas the superstar e ect is more prominent for Children/Family titles. This is unsurprising if horizontal di erentiation is more important among the former groups than the latter, as seems plausible. Similarly, Crain and Tollison (2002) show that in the music industry, more diversity in consumer preferences is associated with a long tail e ect. Our model also provides a quali cation of Rosen s (1981) predictions regarding the e ects of information and communication technology, which supplies the quote that headlines this paper. Radio, television, and recording media technology improvements over the rst half of the 20th century emphasized relative declines in variable costs in comparison to xed costs. For instance, the invention of television lowered substantially per-consumer variable costs in the production of comedic and dramatic performances, relative to pre-existing stage and auditorium technology. However, the xed costs of performance did not decline much, and may have increased, since television studios, microphones, and broadcasting equipment represent substantial capital outlays. Thus, Rosen s model and ours predict that such technological innovation tends to create superstars. IV. Market E ciency: Competition Policy and Social Implications As in other models of entry under strategic competition, the number of rms in equilibrium may be ine cient (Mankiw and Whinston, 1986). Our model supplies conditions under which product entry is 25 Moreover, online travel sites may involve higher capital investment upfront than local bricks-and-mortar travel agencies, but at the same time can serve the entire national market; thus, the overall cost structure of the industry may have changed. 16