Informative advertising by heterogeneous firms

Available online at www.sciencedirect.com INFORMATION ECONOMICS AND POLICY

Information Economics and Policy 20 (2008) 168–191 www.elsevier.com/locate/iep

Informative advertising by heterogeneous firms Emin M. Dinlersoz a,b,*, Mehmet Yorukoglu c a

b

Cornerstone Research, 1919 Pennsylvania Ave., N.W., Suite 600, Washington, DC, 20006, United States Department of Economics, University of Houston, 204 McElhinney Hall, Houston, TX 77204-5019, United States c The Central Bank of the Republic of Turkey, Istiklal Cad. 10, Ulus, 06100 Ankara, Turkey Received 3 February 2007; received in revised form 24 January 2008; accepted 25 January 2008 Available online 15 February 2008

Abstract This paper introduces a model to analyze the role of the cost of information dissemination in large markets where firms have varying degrees of intrinsic efficiency reflected in their marginal costs. Firms enter a market and discover how efficient they are. Those firms with high enough efficiency stay, others exit. Remaining firms then compete to attract consumers by disseminating information about their existence and their prices using a common advertising technology. The properties of the model’s equilibrium are analyzed. The model is then used to study the effect of the cost of information dissemination on the competitiveness of the market and key industry aggregates, such as price distribution and the distribution of firm value. Ó 2008 Elsevier B.V. All rights reserved. JEL classification: D80; L11; M37 Keywords: Information; Informative advertising; Price dispersion; Industry structure

1. Introduction This paper develops and analyzes a model of informative advertising by firms with varying degrees of efficiency which are reflected in their respective marginal costs. There are two major goals of this undertaking. The first one is to highlight the role of firm heterogeneity in markets where informative advertising is prominent. By explicitly recognizing the differences in intrinsic efficiency across firms, the paper investigates a critical aspect of the market provision of information that has not received much attention so far: the pecuniary externality imposed by more efficient firms on less efficient ones under competitive information dissemination. The nature of this ‘‘negative” externality depends on how efficiency is distributed across firms and the type of the advertising technology. The analysis emphasizes the effect of the interaction between firm heterogeneity and advertising technology on equilibrium distributions of price, firm value, and the amount of advertising. * Corresponding author. Present address: Cornerstone Research, 1919 Pennsylvania Ave., N.W., Suite 600, Washington, DC, 20006, United States. E-mail addresses: [email protected], [email protected] (E.M. Dinlersoz).

0167-6245/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.infoecopol.2008.01.002

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The second goal is to use the model to study the effects of an exogenous reduction in the cost of information dissemination in a market with many different types of firms. The role of consumer information has attracted renewed attention with the diffusion of e-commerce. Media revolutions over the course of history, such as newspaper, radio, television and most recently the Internet, have given way to easier and cheaper information dissemination.1 Firms now have access to more efficient technologies to reach and inform consumers. Because a firm’s success depends critically on how effectively it spreads information about itself, improvements in information technologies have had profound effects on competition among firms. Recent research on the economics of the Internet has focused mostly on the implications of reduced search costs for consumers.2 However, firms’ increasingly intense efforts to reach consumers by releasing information through online advertising have received less attention, despite the fact that Internet advertising is a major tool of competition for Internetbased firms and search engines. Major search engines, such as Yahoo! and Google, have been competing for advertising revenues by introducing new ways of making consumers click on on-line ads.3 Using the model, the effect of continuing improvements in advertising technologies on industry structure is analyzed. The model is stylized to study the interaction between firm heterogeneity and the cost of information. A large competitive market is considered, where firms differ only with respect to their marginal costs.4 Firms enter the market as long as it is profitable to do so. After entry, each firm learns its intrinsic efficiency: a more ‘‘efficient” firm has a lower marginal cost compared to a less efficient firm.5 Those entrants that are not efficient enough exit. Remaining firms offer a homogeneous good for sale and compete by choosing prices, but need to make themselves known to consumers before any sales can be made. Firms are endowed with a common ‘‘information technology”, also referred to as ‘‘advertising technology”, that enables them to spread information about their existence and their attributes. Information dissemination is equivalent to informative advertising: only the information about the existence, location, and price of a firm is conveyed, and there is no persuasive, goodwill, or signaling content of an ad. For simplicity, consumers are assumed to be passive information filters. They do not engage in search and make their purchases based on the information they receive randomly.6 The model sketched above contains certain special elements that facilitate the analysis of the role of information in markets with heterogeneous firms. First, the focus is on a large economy with many firms and many consumers where it is critical for firms to make themselves known to consumers. Continuing improvements in information dissemination technologies affect many large sectors of the economy, making it appropriate to adopt a large market framework. An individual firm is by assumption ‘‘small” with respect to the rest of the industry, and it takes the industry aggregates as given. This assumption comes at the expense of ignoring a single firm’s actions on the rest of the industry, but allows for a simpler analysis. Second, the model explicitly considers firm entry and exit and the endogenous determination of industry size, albeit in a one-shot setting. The differences in entry rates and threshold efficiency levels for survival across economies with different costs of information dissemination are investigated. Finally, specific attention is paid to the role of information technology. A general advertising technology that generates decreasing returns to advertising outlays is considered.7 Comparative statics exercises are performed with respect to the advertising technology to analyze how a reduction in information cost affects the distributions of key variables, such as price and firm value. The model is closely related to the static models of informative advertising in homogeneous-good industries. In particular, the model draws upon the work of Butters (1977), who introduced an early version of these 1

See Chandler and Cortada (2000) for an excellent discussion of the information’s role in shaping firm and industry structure in the US. See, e.g., Brown and Goolsbee (2000). 3 Research by eMarketer predicts that online advertising market will grow to $25 billion in 2010 from its current level of $15.9 billion (see Guth, 2006). 4 Like Stegeman (1991), we use the term ‘‘competitive” to emphasize that each firm is small with respect to the industry and has no influence on industry aggregates by itself. However, a firm can set its own price and influence its demand, taking as given the aggregate distribution of prices in the market. Thus, the way we use the term ‘‘competitive” is different from the general textbook definition of a competitive industry. 5 As described later, all firms have the same fixed cost of operating in the industry. Thus, a more efficient firm is also the one with a lower average total cost, net of advertising cost. 6 Consumer search and advertising are jointly investigated by Robert and Stahl (1993) in a framework with identical consumers. 7 However, no attempt is made to replicate the specific nature of returns to advertising in a particular advertising medium. 2

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models, and Stegeman (1991), who considers the role of informative advertising in a large, competitive economy with an emphasis on welfare. The present paper differs from those papers in two main dimensions: (i) firms are heterogeneous, and (ii) entry, exit, and endogenous determination of industry size are considered. Implications of firm heterogeneity have so far not been studied in detail in the context of advertising, even though they have been considered in theoretical models of consumer search.8 Compared to the homogeneous firm environment, one advantage of the approach here is that, for any exogenously given distribution of firms’ marginal costs and an advertising technology, firms adopt pricing and advertising strategies that are uniquely determined by their efficiency, which also lead to a unique distribution of firm value. As a result, the effect of changes in advertising cost on firm value distribution can be analyzed. Firm value distribution is degenerate in both Butters (1977) and Stegeman (1991) because there is no firm heterogeneity.9 Moreover, how industry size is determined, i.e. how large the mass of firms in the industry is and which types of firms actually survive, has received little attention in previous work, including Butters (1977), Stegeman (1991) and Ireland (1993). The present paper analyzes these issues explicitly. Finally, when firms have identical marginal costs, the model reduces to that of Butters’s (1977) with a continuum of firms. Firm heterogeneity does not distort the social optimality of advertising, a result that emerges in Butters (1977) but does not hold in all models of informative advertising. The main findings can be summarized as follows. In the extreme case of free advertising, the model is equivalent to the case with perfect consumer information about all prices. In this case, post-entry price competition has the familiar Bertrand outcome: the most efficient firm type has price equal to marginal cost, and all other firm types make no sales. When the advertising cost is sufficiently high, all firms charge monopoly price, as there is no or little overlap in firms’ advertising reach. Of more interest are equilibria where advertising cost is moderate. In such equilibria, more efficient firms set lower prices, advertise more intensely, attract more consumers, and generate higher sales. These equilibria also exhibit dispersion in prices, advertising levels, and firms’ market values. The maximum price charged is always the monopoly price, whereas the minimum price depends on the advertising technology and the distribution of marginal cost. Many important properties of equilibrium depend on the interaction between the distribution of marginal cost and the advertising technology. Markup and advertising intensity, as measured by the advertising expenses-to-sales ratio, can be nonmonotonic functions of marginal cost. There are two main effects of a lower cost of information. The direct effect is a decline in a firm’s cost of advertising and an increase in each firm’s incentives to advertise. This effect acts to increase firm value. However, there is also an indirect effect or a pecuniary externality: the change in the number of ads sent by all firms that have lower marginal costs and, hence lower prices, than a given firm. If the number of ads sent by more efficient firms is sufficiently higher, then the indirect effect can overcome the direct effect, leading to a decline in a firm’s value. When lower information costs lead to a sufficient increase in the total amount of advertising, the probability of exit, average productivity, and average firm value all increase. Less efficient firms raise their prices to be able to survive. The range of price and the range of firm value always increase as advertising cost falls. Lower cost of advertising can either enhance entry or act as an entry barrier, depending on how the lower cost affects the post-entry distribution of firm value. Social welfare is also higher in an economy with lower information costs. However, the direction of change in certain key variables, such as markups, advertising intensities, and the average and the variance of prices, depend on the distribution of marginal cost across firms and the nature of the change in the advertising technology. At a broad level, this paper is part of the literature on the economics of information, initiated mainly by Stigler (1961). Existing work involves some form of consumer search or advertising by firms, or both. Some examples in the consumer search literature include Salop and Stiglitz (1977), Reinganum (1979), Wilde and Schwartz (1979) and Burdett and Judd (1983). In particular, Reinganum’s (1979) model analyzes the implications of consumer search when firms are heterogeneous with respect to marginal cost, as in the present model. In the advertising literature, closely related papers are Butters (1977), Grossman and Shapiro (1984), 8

See, e.g., Reinganum (1979). It should be noted that heterogeneity per se is not needed to generate price dispersion, which emerges even in a homogeneous firms framework, as in Butters (1977) and Stegeman (1991). But all firms make the same profit in these models, leading to a degenerate firm value distribution. 9

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Stegeman (1991), Ireland (1993), Robert and Stahl (1993) and Stahl (1994). In terms of the effects of firm heterogeneity on advertising, the closest work is that of Grossman and Shapiro (1984), who consider firms that are differentiated with respect to their location in product space. However, even though this feature introduces firm heterogeneity trivially with respect to the location attribute, only the symmetric equilibrium is analyzed, so different firms effectively adopt identical pricing and advertising strategies in equilibrium. The rest of the paper is organized as follows. Section 2 presents the model. Section 3 defines the equilibrium and studies its properties. Comparative statics with respect to the information technology is performed in Section 4. Section 5 concludes. The proofs of the results that are not obvious are in Appendix A. 2. The model Consider an industry with a large number (a continuum) of firms offering a homogeneous good for sale to a large number (a continuum) of consumers. As in Stegeman (1991) and Hopenhayn (1992), an individual firm is assumed to be negligible with respect to the rest of the industry. Thus, a firm has no influence on industry aggregates by itself and takes these aggregates as given. This assumption simplifies the setup by removing any effect of the number of ads sent by the firm on its pricing decision, as shown below. All decisions take place over time collapsed into a single period, as in Fig. 1. There is a continuum of ex-ante identical potential entrants. At the beginning of the period, potential entrants decide whether to enter the industry. Upon entry, firms’ marginal costs are revealed. Firms then decide whether to stay in the market. Those that stay choose their prices and advertising outlays. Firms commit to the prices they advertise. Consumers learn about firms and their prices only through advertising by firms. 2.1. Consumers The mass of consumers, or the market size, is normalized to unity. Consumers receive ads randomly and independently. It is assumed that no consumer ends up receiving more than one ad from the same firm and each ad is observed by some consumer with probability one. These assumptions remove the need to account for duplicate ads to a consumer and ads that reach no consumer, without compromising on the basic nature of informative advertising. Let WðiÞ be the probability that a consumer receives an integer number of i P 0 ads. As in Butters (1977) and Stegeman (1991), if there is a total of A ads per consumer in the economy, the probability that a consumer receives no ads is eA .10 A consumer is either uninformed, or informed of one or more firms as a result of advertising. An ad contains a vector of variables that describe the corresponding firm’s attributes, such as price, location and hours of operation. For simplicity, the only payoff-relevant variable in an ad is price. A consumer has a unit demand with net surplus function  s  p if p 6 s U ðpÞ ¼ 0 otherwise; where s > 0 denotes the gross consumer surplus and p > 0 denotes the price. A consumer visits the firm that offers the maximum net surplus among all firms from which he receives ads. 2.2. Firms Firms enter the industry by incurring a (sunk) entry cost of j > 0. The role of this positive entry cost is to limit the size of the industry.11 Firms then learn their (constant) marginal costs, which are independently and identically drawn from a continuous cumulative distribution function vðcÞ with a density dvðcÞ defined over the interval ½c; c, where s > c > 0 and c > 0. The distribution of the marginal cost is known to all potential 10 If there is a total of n consumers and A ads per consumer, the probability that a consumer receives no ads is ð1  1=nÞAn , which converges to eA as n becomes large. 11 If the entry cost is zero, an unbounded mass of firms can enter the industry.

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Fig. 1. The timing of decisions for firms and consumers.

entrants. It is also assumed that the frequency distribution of firms’ marginal cost drawn from v matches the actual distribution v itself.12 A firm that stays in the market incurs a fixed cost of operation, f > 0, which can be avoided only if the firm exits. Because the entry cost is sunk, without a positive fixed cost all firms that enter would stay in the market even when they make zero variable profit. It would then be impossible to talk about a survival threshold. The value of exit is normalized to zero. Thus, a firm with a marginal cost that renders negative profits net of fixed cost exits the industry. When indifferent between exiting and staying, a firm is assumed to stay. In the discussion below, a firm with a lower marginal cost than another firm will sometimes be referred to as a ‘‘more efficient” firm.13 The advertising technology, U, is exogenously given and common to all firms.14 For any a 2 ½0; 1Þ, UðaÞ gives the total cost of sending a ads. The technology satisfies the following assumption. Assumption 1 (i) U is twice continuously differentiable and strictly convex: U0 > 0 and U00 > 0 on ð0; 1Þ, (ii) There is no fixed cost of advertising: Uð0Þ ¼ 0, and (iii) Advertising cost does not increase steeply around zero: lima!0 U0 ðaÞ ¼ 0. These assumptions on the advertising technology capture the basic empirical regularity that the effectiveness of advertising is subject to diminishing returns, consistent with the empirical evidence on diminishing returns to advertising reviewed in Sutton (1991). Assumption 1(i) implies that sending an ad becomes increasingly costly at the margin as the number of ads increases. From an individual firm’s perspective, there is a very large pool of consumers. By assumption, each ad reaches a new consumer and the probability of sale resulting from an ad is independent of the number of ads sent by the firm. In the absence of any constraints on the advertising technology, a firm can reach an arbitrarily large number of consumers. Some form of decreasing returns to advertising is therefore needed to guarantee that no firm ends up reaching an arbitrarily large number of consumers. One possible interpretation of convex advertising cost is that, since each ad from a firm is assumed to reach a distinct consumer, as the number of ads sent increases it becomes increasingly costly to locate and inform a consumer who has not yet received an ad from the firm.15 The way decreasing returns is introduced here is different in form, but same in spirit, compared to that in Butters (1977) and Stegeman (1991). In both studies, the decreasing returns arise because there is a positive probability that a consumer receives more than one ad from the same firm. Furthermore, the marginal cost of advertising is constant. As a result, the cost of reaching a given fraction of consumers is a strictly convex function. Here, each additional ad reaches a consumer who has not yet received an ad from the firm, by assumption. The marginal cost of finding such a consumer is assumed to be increasing in the number of ads sent, or equivalently, in the number of consumers reached.

12 As in other models with a continuum of firms (e.g., Hopenhayn, 1992), there are technical problems associated with this matching of the two distributions, i.e. problems associated with the applicability of ‘‘the law of large numbers” for the case of a continuum of i.i.d. random variables. Solutions have been offered to these problems (see, e.g., Judd, 1985). For instance, one can assume that firms’ marginal costs are correlated in some dimension. Since independence of marginal cost across firms does not have a specific role in our setup, such an assumption can be adopted here without any effect on our results. 13 Efficiency is usually defined with respect to the average cost, not marginal cost. Because all firms face the same fixed cost and the same advertising technology, a more efficient firm also has a lower average cost. 14 An extension to heterogeneous advertising costs is discussed later. 15 Note that this process does not necessarily imply that firms target a specific set of consumers.

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Assumption 1(ii) is made for simplicity. Any fixed cost of advertising can be included in the fixed cost, f. Finally, Assumption 1(iii) ensures that all firms in the industry advertise regardless of their type. The post-entry profit for a firm with cost c is given by Pðp; a; cÞ ¼ mðp; aÞðp  cÞ  UðaÞ  f ;

ð1Þ

where mðp; aÞ is the number of customers the firm acquires given its price p and the number of ads a. The function m can be written more explicitly as mðp; aÞ ¼ asum1 i¼0 WðiÞZðp; iÞ:

ð2Þ

In (2), WðiÞ is the measure of consumers in the market who have i firms in their information set, which is equal to the probability that a consumer receives i ads. The function Zðp; iÞ is the probability that a consumer with i ads does not have an ad with price lower than p. Note that Eq. (2) embeds the assumption that a firm is small and ignores the effect of its ads on the total number of ads. A firm takes as given the mass of consumers who have i ads as a result of the collective advertising made by all other firms, where i P 0. i Because a consumer receives ads independently, the probability Zðp; iÞ can be written as ½1  QðpÞ , where QðpÞ is the fraction of all ads with price less than or equal to p. Then, the total number of ads with price p or less is AQðpÞ. Therefore, one can write mðp; aÞ ¼ aeAQðpÞ ¼ azðpÞ;

ð3Þ

where zðpÞ ¼ eAQðpÞ is the probability of sale for an ad, or equivalently, a consumer’s demand at price p, conditional on consumer having an ad from a firm with price p. The dependency of the probability of sale on cumulative advertising made by firms with price less than p highlights the precise source of the pecuniary externality created by advertising. The more the fraction of ads priced less than p, the lower the probability of sale. The fraction of ads priced less than p is determined by both the distribution of the marginal cost and the advertising technology. As discussed below, this ‘‘negative externality” is key to understanding some important features of the model. A firm’s value after entering and learning its marginal cost is given by   V ðcÞ ¼ max 0; max Pðp; a; cÞ ; p;a

which reflects a firm’s two options: exit, in which case the value is zero, or stay in the industry and choose price and advertising level to maximize profits. Finally, entry to the industry is unrestricted, leading to the free entry condition Z c V ðcÞ dvðcÞ 6 j: ð4Þ c

In other words, firms enter until the expected post-entry profit equals the entry cost. There is positive entry if (4) holds as an equality, and no entry otherwise. 3. Equilibrium Before the formal definition of the equilibrium, it is instructive to discuss two polar cases. In the case of very high advertising costs, i.e. when U is a very steep function, each firm can reach only a very small number of consumers, and the probability that a consumer receives ads from more than one firm is negligible. In other words, the reach of advertising by firms is very limited. No firm has any incentive to lower its price below the monopoly price s to attract consumers who also have ads from other firms.16 16

To see this formally, note that if charging monopoly price is optimal for the most efficient firm type, it must also be optimal for all other firm types. The most efficient firm type has the highest markup at any given price compared to other firm types and therefore has the highest incentive to reduce its price to steal consumers away from other firm types. As a result, if it is not profitable for the most efficient firm type to reduce price below the monopoly level, it cannot be profitable to do so for other firm types. By Assumption 1, for any given monopoly price s there exists an advertising technology with a steep enough marginal cost function U0 such that the monopoly pricing is adopted by the most efficient firm type and therefore by all other surviving firms.

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The other polar case occurs when UðaÞ ¼ 0 for all a P 0 (free advertising). This extreme case is ruled out by Assumption 1. In this case, each firm in the market reaches all consumers, and the standard result of Bertrandcompetition under perfect consumer information applies to post-entry competition. The most efficient firms charge prices identical to their marginal cost and make zero profit, and all other firms have zero sales. With positive entry or fixed costs, this leads to an empty industry. For the rest of the paper, advertising cost is assumed to be low enough for firms to be in a competitive region where a sufficiently large mass of consumers are aware of more than just one firm and firms compete in prices, leading to price dispersion. 3.1. Definition and properties of equilibrium Let an asterisk (*) denote equilibrium variables and functions. Formally, an equilibrium can be defined as follows: Definition 1 (Equilibrium). An equilibrium is a set of pricing and advertising policies fp ðcÞ, a ðcÞg for firms, an entry mass M  , and an exit threshold c such that (i) firms maximize their profits by adopting the pricing and advertising policies p ðcÞ and a ðcÞ, (ii) consumers maximize their surplus by choosing the lowest price firm among the ads they receive, (iii) all firms with cost c > c exit, where c ¼ inffc 2 ½c; c : V  ðcÞ ¼ 0g, (iv) M  is the mass of entrants that satisfies the free entry condition (4), and (v) the resulting cumulative distribution of ads across prices, Q ðpÞ, is consistent with conditions (i) through (iv). Note that condition (v) of Definition 1 is needed for an individual firm’s advertising and pricing policies to be consistent with the aggregate distribution of ads in the economy generated by firms’ policies and entry and exit decisions. The exit threshold and the entry mass imply an equilibrium measure of firms, l ðcÞ ¼ M  vðcÞ for all c 2 ½c; c , where l ðcÞ is the mass of firms with marginal cost c or less. The cumulative distribution of marginal cost in equilibrium is vðcÞ=vðc Þ. The total mass of firms in the industry is M  vðc Þ, and the mass of exiting firms is given by M  ð1  vðc ÞÞ. The total mass of consumers R cwho purchase is equivalent to the mass  of consumers who receive at least one ad, 1  eA , where A ¼ M  c a ðcÞ dvðcÞ is the total number of ads sent by all firms. Assuming for the time being that an equilibrium exists, the characteristics of the equilibrium cumulative distribution of ads across prices, Q , can be established. All firms cannot charge the same price, otherwise one of the firms with cost lower than that common price could reduce its price slightly and steal a positive mass of consumers from other firms, resulting in a net increase in profit. Therefore, there must be price dispersion in equilibrium and Q is non-degenerate. The maximum price observed in equilibrium must be s. If the maximum price exceeds s then the corresponding firm obtains no sales. If, on the other hand, maximum price observed is less than s, then any firm charging this price can raise its price up to s without losing any customers. Furthermore, Q must be continuous and strictly increasing over some interval ðpmin ; sÞ, where pmin is the minimum price observed in equilibrium. If Q is not continuous, it must have a mass point at some price. Then, one of the firms charging that price can reduce its price infinitesimally and steal a positive mass of consumers from other firms charging the same price, which leads to a discrete jump in the firm’s profit. To see that Q is strictly increasing, note that if Q is constant over some interval, say, ½p1 ; p2   ½pmin ; s, then any firm charging price p1 could increase its price to p2 , without reducing its probability of sale. Given the properties of Q , the equilibrium behavior of firms can be analyzed. The equilibrium probability of sale z ðpÞ is strictly decreasing in p, because Q ðpÞ is strictly increasing in p. As shown below, in equilibrium every firm sends a unique amount of ads at a unique price determined by the firm’s marginal cost. Therefore, the density, q ðpÞ, of ads at price p exists and it is strictly positive at any advertised price. The derivative of   z ðpÞ is then z0 ðpÞ ¼ A eA Q ðpÞ q ðpÞ < 0. Given an equilibrium distribution Q , each firm type c chooses a unique price and a unique advertising level. Proposition 1. The profit function P ðp; a; cÞ is maximized at a unique advertising level a ðcÞ 2 ð0; 1Þ, and at a unique price, p ðcÞ 2 ðc; s.

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Proposition 1 implies that an incumbent firm’s optimal choices of price, p ðcÞ, and advertising, a ðcÞ, are characterized by the following first order conditions17 z0 ðpÞðp  cÞ þ z ðpÞ ¼ 0; 

0

z ðpÞðp  cÞ  U ðaÞ ¼ 0:

ð5Þ ð6Þ

Observe from (5) that a firm’s pricing decision is independent of the number of ads the firm sends by itself; what matters is the collective advertising made by other firms. The decoupling of the firm’s price choice from its own advertising is a result of the assumption that an individual firm is small with respect to the rest of the economy and cannot influence the distribution Q by itself. From (5) and the definition of z ðpÞ, a type c firm’s markup is given by p ðcÞ  c ¼ 

z ðp ðcÞÞ 1 ¼ : z0 ðp ðcÞÞ A q ðp ðcÞÞ

ð7Þ

From (7), markup at marginal cost c is inversely related to the amount of advertising at price p ðcÞ, and therefore, to the equilibrium mass of type c firms and the amount of ads sent by each such firm. In this sense, mark ups depend on the ‘‘local” intensity of information release to the market. Furthermore, relative markup, p pðcÞc  ðcÞ , follows the familiar inverse elasticity rule.18 A number of important properties of firm behavior in equilibrium can be summarized as follows. Proposition 2 (i) (ii) (iii) (iv)

A A A A

firm’s firm’s firm’s firm’s

price, p ðcÞ, is strictly increasing in c, amount of advertising, a ðcÞ, is strictly decreasing in c, ~  ðcÞ  m ðp ðcÞ; a ðcÞÞ, is strictly decreasing in c, number of customers, m    ~ ðcÞp ðcÞ, is strictly decreasing in c. sales, r ðcÞ ¼ m

An implication of part (i) of Proposition 2 is that the minimum price in equilibrium is the one charged by the most efficient firm, i.e. pmin ¼ p ðcÞ ¼ c þ U0 ða ðcÞÞ, by (6) and the fact that z ðp ðcÞÞ ¼ 1, i.e. the probability of sale at the lowest price is one. The maximum price, s, is charged by the marginal firm, i.e. p ðc Þ ¼ s. While a firm’s price is strictly increasing in its marginal cost, markup, p ðcÞ  c, need not be. Noting that in equilibrium the density of ads at marginal cost c is q ðp ðcÞÞ ¼ ðM  a ðcÞ dvðcÞÞ=A , the markup in (7) can be written as p ðcÞ  c ¼

1 : M  a ðcÞ dvðcÞ

The markup for type c firms is inversely related to the total mass of firms, advertising made by a type c firm, and the density of type c firms. The rate of change in markup therefore depends on the distribution of the marginal cost and the advertising technology. It is easy to verify that a sufficient, but not necessary, condition for markup to be strictly increasing in c is the density of marginal cost to be non-increasing, i.e. d2 vðcÞ 6 0. This condition is satisfied by distributions with non-increasing density, including exponential, uniform, and some types of log-normal distribution.19 However, relative markup need not be monotonic even when markup is monotonic. Because markup is a function of the level of advertising a ðcÞ, it depends on the advertising technology. For the most efficient firm type, the markup is given by p ðcÞ  c ¼ U0 ða ðcÞÞ: 17 18

Except for price p ¼ s, where the profit function is not continuous. Over the range ðpmin ; sÞ, p ðcÞ  c z ðp ðcÞÞ 1 ¼  0  ¼ ;  p ðcÞ z ðp ðcÞÞp ðcÞ eðp ðcÞÞ

where eðp ðcÞÞ ¼ A q ðp ðcÞÞp ðcÞ is the elasticity of demand at p ðcÞ. 19

Note that all distributions with non-increasing hazard rate are also in the class of distributions with non-increasing density.

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At the extreme when advertising is free, i.e. UðaÞ ¼ 0 for all a, the markup of the most efficient firm type is exactly zero. When advertising is relatively flat and close to this extreme of free advertising, markups for the most efficient firm type is close to zero, whereas the marginal firm surviving has a positive markup. Thus, when U is a relatively slow-rising function, markup is strictly increasing in marginal cost. On the other hand, when U is very steep and the monopoly pricing prevails, markup is a strictly decreasing function of marginal cost as each firm charges s. In general, for steeper U, the total number of ads in the market is low and the survival threshold is high, implying a markup that can be strictly decreasing in marginal cost. Another object of interest is a firm’s advertising intensity defined by the ratio of the advertising expenses to  ðcÞÞ sales, Uða . This ratio has been frequently used in the empirical literature to measure the relative importance  r ðcÞ of advertising across firms or industries. For instance, some earlier work, e.g., Comanor and Wilson (1974), found that firms with larger sales tend to spend proportionally more on advertising, but this positive association is reversed in some industries with heavy overall advertising expenditures. More recently, Sutton (1991) used industry-wide advertising intensity measures to assess the significance of advertising and its role in industry concentration.20 In the model, a firm’s advertising intensity depends both on the distribution of marginal cost and on the advertising technology. Intuitively, when advertising entails a very low marginal cost, this ratio can be lower for more efficient firms, which have very large sales compared to less efficient firms. On the other hand, when advertising cost is very high, less efficient firms have high advertising expenditures and very low sales, and the ratio can be lower compared to more efficient firms. The nature of the dependency of advertising intensity on efficiency therefore is in part determined by the advertising technology. The raw average of equilibrium prices is given by Z c 1  praw ¼ p ðcÞ dvðcÞ: vðc Þ c While  praw is generally used to measure average price in a market in the absence of any information on firms’ market share, it does not take into account the differences in the number of ads released into the market by different firms. A randomly selected consumer is more likely to observe ads from more efficient firms than less efficient ones. Therefore, the distribution of raw price first-order stochastically dominates that of advertised price, also implying that the average advertised price, pad , is lower than praw . Yet, pad does not properly reflect the allocation of consumers across firms, because not all ads turn into sale and most of the transactions take place at low prices. The average transaction price is Z c   ptrans ¼ p ðcÞw ðcÞ dvðcÞ; ð8Þ c 

~  ðcÞ=ð1  eA Þ. It can be where the weights are the firms’ shares of total consumers who purchase, w ðcÞ ¼ m shown that the advertised price is stochastically higher, in a first order sense, than the transaction price, and ptrans <  pad . The variances of the prices, however, cannot be ranked unambiguously.21 3.2. Existence and uniqueness of equilibrium Under certain conditions, a unique equilibrium with positive entry and non-degenerate price distribution exists when advertising cost is moderate.22 Since each firm takes the aggregate distribution of ads as given, the existence of equilibrium requires the existence of an advertising policy a ðcÞ by firms such that given the distribution Q ðp ðcÞÞ of ads across prices generated under this policy, the advertising policy a ðcÞ is opti20 21

R c R c The industry advertising intensity is given by the ratio of total advertising expenses to total sales ð c Uða ðcÞÞ dvðcÞÞ=ð c r ðcÞ dvðcÞÞ. For instance, the difference between the variances of the raw and transaction price is   h 2  2 i Varðptrans Þ  Varðpraw Þ ¼ E½p2trans   E½p2raw  þ praw  ptrans :

The term in brackets is positive, but the term in parentheses is negative, because ptrans is stochastically lower than praw . 22 Note that there is no price dispersion in the polar cases discussed earlier: when advertising is very costly price distribution is degenerate at s, whereas when advertising is free, the distribution is degenerate at c.

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mal for firms. Therefore, a fixed point argument is needed to establish existence of equilibrium. Positive entry and exit in equilibrium is possible only if the entry cost is low enough compared to the expected profit from entry. The following theorem details these arguments. Theorem 1. Under sufficiently low advertising cost and given all other parameters of the model except j, there is some j0 > 0 such that there exists a unique equilibrium with positive entry and exit and non-degenerate price distribution as long as the entry cost, j, is less than j0 . 3.3. Social welfare and equilibrium Equilibrium does not necessarily coincide with social optimum in most models of informative advertising. Two opposing effects lead to this discrepancy. A firm usually does not appropriate all the surplus from a sale, which induces under-advertising relative to the socially optimal level, and a firm can steal consumers away from firms with higher prices, which causes over-advertising. Stegeman (1991) shows that, in a setting where consumers are heterogenous with respect to their reservation prices and firms are identical, the first effect generally dominates. However, there are cases where the two effects exactly cancel each other out and the social optimum is achieved, as in Butters (1977) with identical firms and consumers. The model here adds firm heterogeneity to an otherwise similar setting to Butters’s (1977). With heterogenous firms, in addition to the two effects mentioned above, a third effect comes into picture: the expected social surplus from an ad is higher for more efficient firms. Therefore, the social planner has an incentive to send more ads from more efficient firms compared to less efficient ones.23 Nevertheless, this third effect does not distort the social optimality of competitive advertising. In equilibrium, more efficient firms recognize their cost advantage, and they charge lower prices and send more ads compared to less efficient ones. This extra incentive to over-advertise coincides with the social planner’s desire to send more ads from firms with higher efficiency. Let the superscript ‘‘S” identify the variables and functions related to the social planner’s problem. The social planner’s task is to choose the total measure of firms M s , the marginal firm cs , and an advertising policy as that specifies the number of ads as ðcÞ each incumbent firm type c 2 ½c; cs  should send, so as to maximize the social surplus max W ðas ; M s ; cS Þ ¼ Rðas ; M s ; cs Þ  Cðas ; M s ; cs Þ:

as ;M s ;cs

ð9Þ

In (9), the function R gives the total gross surplus. Since every informed consumer purchases, the total surplus is simply the gross surplus per consumer times the mass of consumers who receive at least one ad ! R cs s M S a ðcÞ dvðcÞ s s s c Rða ; M ; c Þ ¼ s 1  e : The function C in (9) gives the total social cost Z cs Z Cðas ; M s ; cs Þ ¼ M S cas ðcÞzs ðcÞ dvðcÞ þ M s c

cs

Uðas ðcÞÞ dvðcÞ þ M s vðcs Þf þ M s j;

ð10Þ

c

where the first term is the total variable cost of sale to all consumers who purchase, the second term is the total advertising cost, the third term is the total fixed cost of firms with marginal costs less than cs , and the fourth term is the total entry cost. The social planner’s choice of advertising for each firm generates a cumulative diss tribution of ads, Qs , across marginal cost levels. In other words, of ads that are sent from R c Qs ðcÞ is the fraction R cs s firms with marginal cost less than or equal to c, i.e. Q ðcÞ ¼ ð c a ðxÞ dvðxÞÞ=ð c as ðxÞ dvðxÞÞ for c 2 ½c; cs . Finally, in (10), zS ðcÞ is the probability that a consumer purchases from a firm with marginal cost c, i.e. R cS s S zs ðcÞ ¼ eA Q ðcÞ , where As ¼ M s c as ðcÞ dvðcÞ.

23 The strict convexity of the advertising cost implies that as the number of ads sent by a firm type increases, a critical level of marginal cost of advertising will be reached where the social planner would like to switch to the firm type with the next highest efficiency. Therefore, it is not desirable for the social planner to send ads only from the most efficient firm type.

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At the social optimum, social planner’s marginal benefit and marginal cost from sending an ad from firm type c must balance each other out zs ðcÞðs  cÞ ¼ U0 ðaÞ;

ð11Þ

If the additional ad from firm c is received by a consumer with no information, the social benefit is ðs  cÞ. If the extra ad is received by a consumer with i > 0 ads with the lowest marginal cost q, then the social welfare increases by an amount maxf0; ðq  cÞg. Therefore, Z cs 1 X s s s z ðcÞ ¼ W ð0Þðs  cÞ þ W ðiÞ maxf0; ðq  cÞghðq; iÞ dq; c

i¼1

where hð; iÞ is the density of the minimum of the marginal costs of i firms the consumer is informed of. The optimality condition for the mass of entrants, M s , is given by Z cs Z cs zs ðcÞaS ðcÞðs  cÞ dvðcÞ ¼ Uðas ðcÞÞ dvðcÞ þ vðcs Þf þ j; ð12Þ c

c

where the left hand side is the marginal addition to total social surplus due to an extra firm, whereas the right hand side is the expected total social cost. Finally, the marginal firm type operating in the industry, cs , is determined by the condition as ðcs Þzs ðcs Þðs  cs Þ  Uðas ðcs ÞÞ ¼ f ;

ð13Þ

where the left hand side is the social benefit from operating a type cs firm, and the right hand side is the fixed cost. In arguing that equilibrium is socially optimal under the conditions of Theorem 1, the first step is to show that the model reduces to that of Butters’s (1977) when firms have identical marginal costs. In this case, equilibrium maximizes social welfare, as was shown by Butters (1977) and Stegeman (1991). With identical firms, the firm with the highest price, s, captures all the surplus from a sale and cannot steal consumers away from any other firm, and therefore, its advertising level is socially optimal. Because an ad from a firm with price p < s creates the same social surplus as a firm charging price s and each firm sends the same number of ads, every firm’s advertising is socially optimal. The second step is to study an equilibrium with an arbitrarily large number of different marginal costs. In this case, firms with different marginal costs send different number of ads, but the amount of advertising is still socially optimal given a firm type. It is shown that a more efficient firm’s incentive to send more ads than less efficient ones coincides with the social planner’s incentive to send more ads from more efficient firms. The entire process is formalized in the proof of the following theorem. Theorem 2. Social welfare is maximized in equilibrium. The correspondence between market equilibrium and social optimum suggests a computational algorithm that can be used to solve for the equilibrium. This algorithm, which is later used to compute examples of equilibria, is described in Appendix B. 4. The role of information technology In this section, the role of the cost of information is studied by comparing two economies with different advertising costs. The goal is to characterize the response of key industry aggregates, such as price dispersion, the distribution of firm value, markups, and advertising intensities to a decline in the cost of information. 4.1. Comparative statics Consider two economies that differ only in the cost of disseminating information. In the second economy it is cheaper to spread information, on the margin, than in the first economy: U01 ðaÞ > U02 ðaÞ for all a > 0. Under Assumption 1, U01 ðaÞ > U02 ðaÞ for all a > 0 also implies U1 ðaÞ > U2 ðaÞ for all a > 0. For tractability, a decline

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in the cost of information will be represented by a ‘‘smooth” change in the advertising technology. Assume that Uð; hÞ is continuously differentiable with respect to a parameter set h, and that for some h 2 h oU0 ða; hÞ >0 oh

for a > 0;

for all values of h for which U is differentiable with respect to h. A lower marginal cost of information in economy 2 compared to economy 1 can then be obtained by allowing a lower value of h for economy 2, i.e. h1 > h2 . An example of a family of advertising technologies with the desired properties is Uða; hÞ ¼ vau ;

ð14Þ

where h ¼ fv; ug, with v > 0 and u > 1. There are two main effects of a lower cost of information. The direct effect is a decline in a firm’s cost of advertising and an increase in each firm’s incentives to advertise. This effect acts to increase firm value. However, there is also an indirect effect or a pecuniary externality: the change in the number of ads sent by all firms that have lower marginal costs and, hence lower prices, than a given firm. If the number of ads sent by more efficient firms is sufficiently higher, then the indirect effect can overcome the direct effect, leading to a decline in a firm’s value. The magnitude of the direct effect depends on the type of change in the advertising technology. If the advertising cost declines more for lower levels of advertising than higher levels, less efficient firms can benefit more from the decline. The indirect effect also depends on the change in the advertising technology. If the advertising cost declines much more for higher advertising levels than lower advertising levels, then less efficient firms are hurt more by the decline in advertising cost. The magnitude of the indirect effect also depends on the distribution of marginal cost. If there is a high fraction of firms with low marginal costs, then a lower information cost implies a substantial increase in the number of low-priced ads, adversely affecting firms with high marginal costs. Nevertheless, some important effects of lower information costs can be stated without having to make any assumptions on the distribution of marginal cost and the type of change in the advertising technology. Proposition 3. Suppose that, for two otherwise identical economies, advertising technologies U0i ðÞ ¼ U0 ð; hi Þ, i ¼ 1; 2, satisfy Assumption 1, and that h1 > h2 , i.e. the marginal cost of advertising is lower in economy 2 compared to economy 1. Then, in the low-information-cost economy (economy 2): (i) The maximum firm value and the range of market values are higher, (ii) The minimum price is lower and the range of prices is higher, (iii) Social welfare is higher. Because only the direct effect applies to the most efficient firm type, the value of that firm type increases as a result of lower information cost. As a result, the range of market values increases because the marginal firms have always zero value. The range of prices increases because the marginal firm type always charge s, whereas the most efficient firm type always reduces its price in response to a decline in advertising cost. An important issue is the effect of lower information costs on the survival probability and the equilibrium distributions of marginal cost and firm value. A simple necessary condition for the marginal firm to be more efficient in economy 2 compared to economy 1 can be stated without any further restrictions. Proposition 4. If the marginal firm in economy 2 is more efficient than that in economy 1, then the total number of ads in economy 2 must be higher, i.e. c2 < c1 implies A2 > A1 . The reverse of the claim in Proposition 4 is not true. It is not enough that the total number of ads is higher in economy 2; it must increase sufficiently for the marginal firm to be more efficient. Clearly, the increase in the total number of ads (the indirect effect) must be large enough to offset the decline in advertising cost (the direct effect). To see this, let P ðc Þ be the profit of the marginal firm in economy 1. By the envelope theorem dP ðc Þ dA  ¼ a ðc ÞeA ðs  c Þ  Uh ða ðc ÞÞ; dh dh . Thus, where Uh  oU oh

dP ðc Þ dh

< 0 if

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dA Uh ða ðc ÞÞ >    A : a ðc Þe ðs  c Þ dh

ð15Þ

In other words, for the marginal firm’s profit to decline, total number of ads must increase sufficiently as h declines. The following example illustrates these effects explicitly. Example 1. Consider the advertising technology in (14). The first order condition for advertising for the marginal firm c is 

eA ðs  c Þ ¼ vuau1 ; which yields 





a ðc Þ ¼



eA ðs  c Þ vu

1 u1

:

The profit for the marginal firm is then i uh u 1  1  P ðc Þ ¼ vu1 eA ðs  c Þ u1 uu1  uu1  f ¼ 0;

ð16Þ

which yields 

A

c ¼se v

1 u

!u1 u

f 1

u

uu1  uu1

;

ð17Þ

From (17), the marginal firm is more efficient (c is lower) when A is higher. Therefore, while a decrease in v has a direct effect of increasing the profits of the marginal firm, if the indirect effect (the increase in A ) is large enough, the marginal firm must be more efficient. Now, suppose that the parameter v decreases, so that the cost of advertising is lower. Condition (15) then yields dA 1 : > uv dv

ð18Þ

The right hand side of (18) is positive. Therefore, the total number of ads must increase sufficiently for the marginal firm to be more efficient when v is lower. The following result can now be stated. Proposition 5. Suppose that, as a result of lower advertising costs, the marginal firm is more efficient in economy 2, i.e. c2 < c1 . Then, in economy 2: (i) The marginal cost is lower in a first-order stochastic sense, (ii) The average marginal cost is lower, (iii) The average firm value is higher. Proposition 5 requires only a sufficient increase in the total amount of information released to the market by firms, but does not place any restrictions on how this increase is distributed across firms. Efficiency is higher in a first order stochastic sense purely due to a selection effect, i.e. the survival threshold is lower in economy 2. As a result, the average market value of firms is also higher. Next, consider the response of industry concentration. The following measure of concentration designed for an industry with infinitesimal firms is used.24 24

Common industry concentration measures, such as a four-firm or an eight-firm concentration ratio, are not meaningful in this context because individual firms have ‘‘zero measure” with respect to the rest of the industry.

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F ðcÞ ¼

Z c

c 

~ ðxÞ dvðxÞ m

!, Z

181

!

c 

~ ðxÞ dvðxÞ : m

c

F  ðcÞ is the fraction of total customers served by firms with a marginal cost of at most c, or equivalently, the ~  . Since a firm’s number of customers and sales are monotonically related to its cumulative distribution of m  marginal cost, F ðcÞ is equivalent to the share of customers accounted by firms with size greater than or equal ~  ðcÞ, and to the fraction of customers accounted by firms with sales of at least r ðcÞ. If the decline in inforto m mation cost is such that there is a sufficient increase in the number of ads sent by firms with low marginal costs, both the number of customers and the sales of these firms increase. At the same time, given more intense advertising by more efficient firms, less efficient firms’ number of customers and sales tend to decrease. In such cases, industry concentration increases. The effects of the decline in information cost can be demonstrated under plausible functional forms for the advertising technology. The simulations in the next section illustrate some properties of equilibrium by using a specific advertising technology. The equilibrium solution algorithm is described in Appendix B, which is based on the correspondence between the social optimum and the market equilibrium (Theorem 2). 4.2. Simulations Consider the following parameterization of the model: s ¼ 4, vðcÞ is uniform over [1,5], j ¼ 1, f ¼ 0:1, and Uða; hÞ is chosen as in (14). Uniform distribution is clearly a special case, but simplifies the demonstration of key points by eliminating the dependence of the results on the variations in the density of firms across marginal cost levels. The effects of the advertising technology can thus be isolated. Under uniform distribution, markup is an increasing function of marginal cost, as discussed earlier.25 Comparative statics is carried out with respect to two parameters: v and u. Changes in these parameters lead to results that differ in important ways. A decrease in v scales down the marginal cost of advertising uniformly for all levels of a. Thus, the ratio of the marginal cost in the low-v-economy to the marginal cost in the high-v -economy is constant for all a > 0. On the other hand, a decrease in u makes this ratio a strictly decreasing function of a for all a > 0. Lower u thus allows more efficient firms to increase the amount of ads they send much more compared to the case with lower v. As demonstrated below, the resulting increase in the number of ads sent by more efficient firms has a more adverse effect on relatively less efficient firms compared to the case of lower v. Simulation 1. Let v ¼ 0:2, 1, and 2, corresponding to low, medium, and high-information-cost economies, and let u ¼ 2. Fig. 2 displays the pricing policy. Price is monotonic in marginal cost, as was shown in Proposition 2. More efficient firms lower their prices considerably as advertising cost declines. Firms with lower efficiency, on the other hand, increase their prices to be able to survive. Note also that there is a ‘‘pivotal” firm for any pair of advertising technologies, whose price remains constant in response to a decline in the advertising cost. Such a firm always exists as long as the marginal firm is more efficient in response to a decline in the advertising cost. Fig. 3 contains the post-entry profit or firm value as a function of marginal cost. The marginal firm has a lower marginal cost as the advertising cost declines, because in this parameterization the decline in the values of the firms with low efficiency due to an increase in the total number of ads overwhelms the increase in their values due to lower cost of advertising. As a result, as the advertising cost declines, marginal cost becomes stochastically lower. Relatively more efficient firms have higher profits for all three technologies considered. Note that for any pair of advertising technologies there exists a firm type whose value does not change as advertising cost declines. The existence of such a firm is guaranteed by free entry. That is, it is impossible for the values of all firms to increase as the advertising cost declines, for otherwise the expected firm value before entry would exceed the entry cost and the free entry condition (4) would be violated.

25

Note also that the parameters are chosen so that the extreme cases of Bertrand outcome and monopolistic competition do not arise.

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Fig. 2. Optimal pricing policy (Simulation 1).

Fig. 3. Firm value as a function of marginal cost (Simulation 1).

Simulation 2. Consider now the exercise in Simulation 1 for different values of u, keeping v constant. Successively higher advertising cost is now represented by u ¼ 1:5, 2, and 3, where v is held at 0.2.26 As shown in Fig. 4, prices are once again lower for relatively more efficient firms in the low-information-cost economy, and such firms cut their prices as the information cost declines. Exit thresholds are now much lower compared to Simulation 1. Therefore, firms are on average more efficient for each of the three technologies, compared to Simulation 1. Note also that less efficient firms tend to raise their prices much more compared to Simulation 1, because more efficient firms send a much larger number of ads at lower prices, implying a 26

Note that any given pair of these technologies satisfies the assumptions stated in the hypothesis of Proposition 6 only for a P 1. If sufficient number of firms send ads in the interval (0,1] in equilibrium, then the total number of ads can be lower for the low-informationcost cases, leading to higher survival threshold. However, this effect does not emerge in the current parameterization and the survival threshold is lower.

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Fig. 4. Optimal pricing policy (Simulation 2).

Fig. 5. Firm value as a function of marginal cost (Simulation 2).

tougher competition compared to Simulation 1. As Fig. 5 indicates, the range of firm values is wider for each of the three advertising technologies compared to Simulation 1. Also, compared to Simulation 1, firm value starts to increase more steeply as the marginal cost declines, as the slopes of the firm value function indicate. The simulation results provide some insight into the nature of the equilibria that can be generated by the model. It should be emphasized that the analysis relates industry structure to an exogenously given advertising technology, fixing other parameters of the model. Therefore, the relationship between any two endogenous variables is generated entirely by the exogenous changes in the technology. The model does not embed any role for an endogenous escalation of advertising outlays by firms in a strategic effort to affect industry structure or deter entry, given an advertising technology. Such affects are the focus of research elsewhere, e.g., Sutton (1991). From the perspective of the present model, differences across industries in concentration, profitability, and advertising intensity result from the differences in the type of media used for advertising, controlling for

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other exogenous industry characteristics. An implication is that cross-sectional industry studies should control for the type of advertising media used in industries. For instance, an industry using mainly a low-cost medium to advertise may be more concentrated than an industry using a high-cost medium, and the former could have lower overall advertising expenditures, implying a negative correlation between industry concentration and industry advertising intensity. 5. Conclusions This paper developed a model of informative advertising by firms that differ in their marginal costs of sale. The model was used to study the broad implications of exogenous changes in information costs. Specific consideration was given to the implications of idiosyncratic differences in efficiency across firms on the allocation of consumers across firms through advertising. The amount of advertising by firms with higher efficiency imposes a negative externality on less efficient firms. The consequences of this externality were analyzed. The nature of equilibrium pricing changes from a Bertrand outcome in the case of free advertising to monopoly pricing in the case of sufficiently high advertising costs. In between these two cases, there is a range of equilibria whose properties were analyzed in detail. In such equilibria, more efficient firms set lower prices, advertise more intensely, acquire more customers, and make higher sales. Equilibria entail continuous distributions of prices, markups, advertising levels, and firms’ market values, all of which depend on the cost of advertising and the distribution of marginal cost. When firm heterogeneity is recognized, a fall in the cost of information does not have straightforward implications on the dispersion of key variables. Under certain conditions, it is possible to make statements about the changes in equilibrium distributions of price and firms’ market values. Some caveats are in order. First, firms are by construction small and ignore the effect of their actions on industry aggregates. It is desirable to also consider the case where firms are ‘‘large” and strategic moves by firms is important. For instance, a firm may choose not to advertise heavily so as not to trigger an aggressive response from its rivals. Second, and relatedly, the small firm assumption leads to the separation of a firm’s pricing and advertising decisions. Such separation is not usually possible. Third, a consumer’s demand function is rectangular. Nevertheless, most results, including the welfare result (as shown in Stegeman (1991, p. 271)), can be extended to the case with a downward sloping demand function. However, the social optimality of advertising is not robust to modifications of some other assumptions, such as the homogeneity of demand functions for consumers. As Stegeman (1991) shows in detail, deviations from some of the assumptions can overturn the welfare result. With the ongoing diffusion of online advertising and its potentially adverse effect on traditional advertising media, an important issue for future research is the nature of substitution by firms among information technologies with different effectiveness and reach. An analysis of how firms use media of different types simultaneously can be done by endowing firms with multiple information technologies. Another extension, studied in Dinlersoz and Yorukoglu (2007), is a multi-period version of the model, where each firm accumulates a customer base through advertising subject to random shocks to its marginal cost. The dynamic framework has important implications on firm growth and can account for certain important empirical regularities pertaining to firm and industry dynamics. Acknowledgements We thank the editor, Tommaso Valletti, an associate editor, and anonymous referees for helpful suggestions. We also thank Roger Sherman and numerous seminar and conference participants for comments. Appendix A. Proofs Proof of Proposition 1. P is strictly concave in a because mðp; aÞ is linear in a and U is strictly convex. Thus, it is maximized at a unique advertising level a ðcÞ for any given p. Since all prices in ½pmin ; s are charged in

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equilibrium, there exists a marginal cost for which the corner price s is optimal. All other prices are interior solutions and satisfy the first order condition. For uniqueness, suppose, to obtain a contradiction, that for any given firm with cost c < c, there are two prices p1 and p2 2 ðpmin ; sÞ that are both optimal. Without loss of generality, p1 < p2 . Since the derivative of the profit function with respect to price is zero at both p1 and p2 , there must exist, by the continuity of the derivative and the intermediate value theorem, a price p0 2 ðp1 ; p2 Þ such that z0 ðp0 Þðp0  cÞ þ z ðp0 Þ ¼ 0:

ð19Þ

Since all prices in ½pmin ; s are observed in equilibrium, there must then a exist a firm c0 6¼ c for which price p0 is optimal. For this firm, p0 satisfies the first order condition z0 ðp0 Þðp0  c0 Þ þ z ðp0 Þ ¼ 0: 0

0

ð20Þ

0

But because p  c 6¼ p  c , (19) and (20) cannot hold simultaneously. Thus, there cannot be more than one interior maximizer. h Proof of Proposition 2. Parts (i) and (ii). An application of the Implicit Function Theorem to the first order conditions (5) and (6) yields z0 ðp ðcÞÞ ; 2z0 ðp ðcÞÞ þ z00 ðp ðcÞÞðp ðcÞ  cÞ z ðp ðcÞÞ a0 ðcÞ ¼  00  : U ða ðcÞÞ Because p ðcÞ is an interior maximizer, the second order condition must hold: 2z0 ðp ðcÞÞþ z00 ðp ðcÞÞðp ðcÞ  cÞ < 0. Since z0 ðp ðcÞÞ < 0, it follows that p0 ðcÞ > 0. Because z ðp ðcÞÞ > 0 and ~  ðcÞ ¼ a ðcÞz ðp ðcÞÞ. U00 ða ðcÞÞ > 0 by Assumption 1, it also follows that a0 ðcÞ > 0. Part (iii). Note that m   ~ ðcÞ is strictly decreasing. Part (iv). Using Parts (i) and (ii), and the fact that z is decreasing imply that m ~  ðcÞ ¼ a ðcÞz ðp ðcÞÞ, the derivative of sales r ðcÞ is m p0 ðcÞ ¼

a0 ðcÞz ðp ðcÞÞp ðcÞ þ a ðcÞz0 ðp ðcÞÞp0 ðcÞp ðcÞ þ a ðcÞz ðp ðcÞÞp0 ðcÞ:

ð21Þ

Rearranging the first order condition (5) for price and substituting it in (21), a0 ðcÞz ðp ðcÞÞp ðcÞ þ a ðcÞz0 ðp ðcÞÞcp0 ðcÞ < 0; which follows directly from parts (i) to (iii).

h

Proof of Theorem 1. Given an exit threshold ~c 2 ½c; c and an entry mass M 2 ½0; 1Þ, consider an arbitrary (neither necessarily optimal nor part of an equilibrium) continuous advertising function aðc; ~c; MÞ : ½c; ~c ! Rþ , which specifies the number of ads sent by each firm type c 2 ½c; ~c. Given the pair f~c; Mg, let QðpÞ be the distribution of ads across prices pðc; ~c; MÞ optimally chosen by each firm type c 2 ½c; ~c under the advertising function aðc; ~c; MÞ. From the discussion in Section 3, under moderate advertising cost, Q is unique, continuous, and strictly increasing over ðc; ~cÞ, and pðc; ~c; MÞ is unique, continuous, and strictly increasing in c for c 2 ðc; ~cÞ. Moreover, pðc; ~c; MÞ 2 ½pðc; ~c; MÞ; s and pð~c; ~c; MÞ ¼ s. Let A denote the space of continuous, bounded advertising functions, a : ½c; ~c ! Rþ , endowed with the sup-norm. Given the pair f~c; Mg, let T: A ! A be the operator that matches any advertising function a 2 A to the advertising function T ða; ~c; MÞ 2 A that results from the firms’ optimal choices of advertising under the distribution Q generated by the function a. Using the first order condition for advertising, T can be defined pointwise at any c 2 ½c; ~c as Rc   M aðx;~c;MÞ dvðxÞ 01 c T ða; ~c; MÞðcÞ ¼ U e ðpðc; ~c; MÞ  cÞ : For existence, the following are shown.

h

Lemma 1. For a given pair f~c; Mg, T has a fixed point a ðc; ~c; MÞ, which is strictly decreasing in c and strictly decreasing in M.

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Lemma 2. For a given configuration of the model’s parameters, there exists some j0 > 0 such that, given j < j0 , the exit rule and the free entry condition hold for a unique pair fc ; M  g and for a corresponding fixed point a ðc; c ; M  Þ, where c 2 ðc; cÞ and M  > 0. Lemmas 1 and 2 imply existence of an equilibrium with positive entry and exit. For uniqueness, it needs to be shown, in addition, that Lemma 3. Given the pair fc ; M  g identified in Lemma 2, there exists a unique fixed point of T, a ðc; c ; M  Þ, for which fc ; M  g satisfies the free entry condition and the exit rule. Proof of Lemma 1. The first order condition for advertising is 0 zðpðc; ~c; MÞÞðpðc; ~c; MÞ R  cÞ ¼ U ðaðcÞÞ;

where zðpðc; ~c; MÞÞ ¼ e

M

c

c

aðx;~c;MÞ dvðxÞ

. By Proposition 1, there is a unique solution aðcÞ for all c. Thus,

T ða; ~c; MÞðcÞ ¼ U01 ðzðpðc; ~c; MÞÞðpðc; ~c; MÞ  cÞÞ: Let Gðc; ~c; MÞ ¼ zðpðc; ~c; MÞÞðpðc; ~c; MÞ  cÞ: Then, T ðaÞ  ðU01  GÞðaÞ. By Assumption 1, U01 is continuous. G is also continuous in c. Therefore, T is a continuous operator that maps a compact space, A, onto itself, and thus has a fixed point a ðc; ~c; MÞ for any given f~c; Mg, by Schauder’s fixed point theorem (see, e.g., Theorem 3.2 in Granas and Dugundji (2003)). Note also that T maps any a 2 A into a function T ðaÞ 2 A that is strictly decreasing in c, because ðU01  GÞðaÞ is a strictly decreasing function of c (by Assumption 1 and Proposition 1). Therefore, any fixed point of T must also be a strictly decreasing function of c, which is required for any advertising function aðcÞ to be part of an equilibrium. Finally, a ðc; ~c; MÞ is strictly decreasing in M because ðU01  GÞðaÞ is strictly decreasing in M for any c. h Proof of Lemma 2. Let Pð~c; ~c; MÞ be the profit of firm type ~c given the pair f~c; Mg and the fixed point a ðc; ~c; MÞ R ~c  M a ðx;~c;MÞ dvðxÞ  c ðs  ~cÞ  Uða ð~c; ~c; MÞÞ  f : Pð~c; ~c; MÞ ¼ a ð~c; ~c; MÞe It is easy to show that Pð~c; ~c; MÞ is continuous in ~c and M, strictly decreasing in ~c, and strictly decreasing in M. Let M 1 ð~cÞ be the mass of entrants such that the optimal exit rule is satisfied by firm type ~c, i.e. M 1 ð~cÞ is the solution to Pð~c; ~c; M 1 ð~cÞÞ ¼ 0. It can be verified that M 1 ð~cÞ is continuous and it is strictly decreasing in its argument because Pð~c; ~c; MÞ is strictly decreasing in ~c, i.e. the higher ~c, the smaller the mass of entrants needed to satisfy the optimal exit rule. Similarly, let Pðc; ~c; MÞ be the profit of a firm with marginal cost c given the pair f~c; Mg and the fixed point a ðc; ~c; MÞ. Let M 2 ð~cÞ be the mass of entrants that satisfies the free entry condition given ~c and the fixed point a ðc; ~c; M 2 ð~cÞÞ. M 2 ð~cÞ is defined by Z ~c Pðc; ~c; M 2 ð~cÞÞ dvðcÞ ¼ j: c

Again, it is easy to show that M 2 ð~cÞ is continuous, and strictly increasing in ~c. Next, consider the behavior of M 1 ð~cÞ and M 2 ð~cÞ at the boundary points c and c. Note that M 1 ðcÞ > 0, because Pðc; R c c; MÞ > 0 for all M > 0 and Pðc; c; MÞ is strictly decreasing in M. On the other hand, M 2 ðcÞ ¼ 0, because c Pðc; c; MÞ dvðcÞ ¼ 0, i.e. expected profit from entry is zero when even the most efficient firm type cannot make any positive profit, and hence the entry mass is zero. Therefore, M R c1 ðcÞ > M 2 ðcÞ. Note, next, that ~ ~ ~  Pð~ c ; c ; MÞ < Pðc; c ; MÞ for all c < c , which implies Pð c ; c ; MÞ < c; MÞ dvðcÞ. Let j0 ¼ c Pðc;  R c R c 0 c; M 1 ðcÞÞ dvðcÞ. Notice that j > 0, because c Pðc; c; M 1 ðcÞÞ dvðcÞ > Pðc; c; M 1 ðcÞÞ ¼ 0. Then, for c Pðc;  any j < j0 , M 1 ðcÞ < M 2 ðcÞ. Together with M 1 ðcÞ > M 2 ðcÞ, this implies that M 1 ð~cÞ and M 2 ð~cÞ intersect only once at an interior point c 2 ðc; cÞ. The corresponding entry mass is M 1 ðc Þ ¼ M 2 ðc Þ ¼ M  > 0. Thus, there

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187

exists a unique pair fc ; M  g that satisfies the free entry condition and the optimal exit rule. It follows that there exists an equilibrium with positive entry and exit. h Proof of Lemma 3. Suppose that, given fc ; M  g, there exist two fixed points, a1 ðc; c ; M  Þ and a2 ðc; c ; M  Þ, such that a1 ðc0 ; c ; M  Þ 6¼ a2 ðc0 ; c ; M  Þ for some firm type c0 . The first order condition for advertising by firm type c implies R c    M  ai ðc;c ;M Þ dvðcÞ c ðs  c Þ ¼ U0 ðai ðc ; c ; M  ÞÞ; ð22Þ e for i ¼ 1; 2. But the exit rule and the first order condition in (22) then yield Pi ðc Þ ¼ ai ðc ; c ; M  ÞU0 ðai ðc ; c ; M  ÞÞ  Uðai ðc ; c ; M  ÞÞ  f ¼ 0;

ð23Þ 

for i ¼ 1; 2. Note that the right hand side of (23) is a strictly increasing function of ai ðc ; c ; M Þ, by Assumption 1. Therefore, the solution ai to (23) must be unique. Consequently, a1 ðc ; c ; M  Þ ¼ a2 ðc ; c ; M  Þ. Without loss of generality, assume a1 ðc0 ; c ; M  Þ > a2 ðc0 ; c ; MR  0Þ for some c0 2 ðc; c Þ.RBecause Pi ðcÞ is a strictly increasc c0 ing function of ai , P1 ðc0 Þ > P2 ðc0 Þ. This implies c a1 ðc; c ; M  Þ dvðcÞ < c a2 ðc; c ; M  Þ dvðcÞ, i.e. the total number of ads sent by firms with cost less than c0 (and hence with lower prices) must be higher under the advertising policy a2 , because lower profits imply that the number of ads sent by firms withcosts lower than c0 is higher, and vice versa.27 It follows that P1 ðcÞ > P2 ðcÞfor all c > c0 , because, under a2 , all such firms also face a higher number of ads from firms with marginal cost c0 or lower. Therefore, P1 ðc Þ > P2 ðc Þ, contradicting the fact that firm type c breaks even under both advertising policies. As a result, the fixed point a must be unique. This completes the proof of Lemma 3 and Theorem 1. h Proof of Theorem 2. In an environment where a continuum of firms have identical marginal costs as in Butters’s (1977), equilibrium advertising by each firm is socially optimal. This result was shown previously by Butters (1977) and Stegeman (1991) in very similar setups, and it can be shown to apply here with some modification. For brevity, the reader is referred to those papers for the details. The result is now extended to the case of an arbitrary number n P 2 of firm types, where the marginal costs of firms differ across the two types and there is a continuum of firms of each type. Suppose that there are n P 2 discrete marginal cost levels c1 ; . . . ; cn , where ci > ci1 , i ¼ 2; ::; n and c1 ¼ c and cn ¼ c . Consider a competitive equilibrium where there is a continuum of firms mass M i at each cost level ci , such that the total mass of firms is M  . It can be verified, using arguments similar to those in the discussion of the properties of equilibrium (Section 3.1), that firms of a given type charge prices in a compact interval, the intervals do not overlap across firm types, and there is no gap between two consecutive intervals. In other words, type cn firms will some interval ½s  Dn1 ; s and type ci firms will charge prices in some P charge prices Pin nj compact interval ½s  nj1 D ; s  i i¼1 i¼1 Di , i ¼ 1; . . . ; n  1. Suppose that social planner’s choices of entry mass and the exit threshold coincide with the corresponding levels in competitive equilibrium. Social planner’s first order condition for advertising by a type cj firm is given by " # 1 n X X   ~ W ðiÞ ð24Þ W ð0Þðs  cj Þ þ hðck ; iÞ maxð0; ðck  cj ÞÞ ¼ U0 ðaÞ; i¼1

k¼2

where ~ hðck ; iÞ is the probability that ck is the lowest cost among i ads received by a consumer. For a cost cn firm this yields W ð0Þðs  cn Þ ¼ U0 ðaÞ: Note that all firms with the same type choose to send the same number of ads. Using the first order condition for advertising (6), a firm’s equilibrium profit can be written as a function of ads 27

To see this, let Aðc0 Þ ¼ AQðpðc0 ÞÞ be the number of ads sent by firms with costs c0 or lower. Then, by the envelope theorem 0 ¼ mðpðc0 Þ; aðc0 ÞÞðpðc0 Þ  c0 ÞeAðc Þ < 0; as claimed.

oPðc0 Þ oAðc0 Þ

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" 







P ða ðcj ÞÞ ¼ a ðcj Þ W ð0Þ þ

1 X

# 

W ðiÞZðp; iÞ ðp  cÞ  Uða Þ  f ¼ a ðcj ÞU0 ða ðcj ÞÞ  Uða ðcj ÞÞ  f :

i¼1 

P ða ðcj ÞÞ is strictly increasing in a ðcj Þ by Assumption 1. Because P ða ðcj ÞÞ is the same for all type cj firms, strict monotonicity of P ða ðcj ÞÞ in its argument implies that all firms of type cj must send the same number of ads, regardless of their prices. Therefore, type cj firms’ marginal benefits from sending an extra ad are also the same. Now consider a type cn firm. Its incentives to send an ad is independent of its price. This implies " # 1 X   ðp  cn Þ W ð0Þ þ W ðiÞZðp; iÞ ¼ ðs  cn ÞW ð0Þ 

i¼1

for all p 2 ½s  Dn1 ; s. Since Zðs; iÞ ¼ 0 for all i > 0, the benefit of sending out one more ad for these firms will be ðs  cn ÞW ð0Þ. The right hand side above is exactly the social planner’s incentive to send out one more ad from a type cn firm. Consequently, a type cn firm’s equilibrium incentive for sending ads coincides with the social planner’s, regardless of the price the firm charges. Next, consider type cn1 firms. Firms’ indifference over prices in the interval ½s  Dn1  Dn2 ; s  Dn1  implies " # " # 1 1 X X     ðp  cn1 Þ W ð0Þ þ W ðiÞZðp; iÞ ¼ ðs  Dn1  cn1 Þ W ð0Þ þ W ðiÞZðs  Dn1 ; iÞ i¼1

i¼1

for all p 2 ½s  Dn1  Dn2 ; s  Dn1 . The extra incentive to send one more ad that a type cn1 firm has over a type cn firm is given by " # " # 1 1 X X     ðs  Dn1  cn1 Þ W ð0Þ þ W ðiÞZðs  Dn1 ; iÞ  ðs  Dn1  cn Þ W ð0Þ þ W ðiÞZðs  Dn1 ; iÞ " ¼ ðcn  cn1 Þ W ð0Þ þ

i¼1 1 X

i¼1

#

WðiÞZðs  Dn1 ; iÞ :

i¼1

yielding a social benefit of 

" 

ðs  cn ÞW ð0Þ þ ðcn  cn1 Þ W ð0Þ þ

1 X

# 

W ðiÞZðs  Dn1 ; iÞ

i¼1

which is equivalent to the social planners’ benefit28 " # 1 X    ~ ðs  cn ÞW ð0Þ þ ðcn  cn1 Þ W ð0Þ þ W ðiÞhðcn1 ; iÞ ; i¼1

e ðcn1 ; iÞ is the probability that a consumer with i ads does not have an ad from a firm with marginal where Z cost lower than cn1 . The above correspondence between equilibrium and social incentives can be shown to hold for all remaining cost levels ci < cn1 by repeating the same argument successively. Next, it will be shown that, given the correspondence of the distribution of ads across firms for the social planner’s problem and the competitive equilibrium, entry masses and exit thresholds also coincide. The social planner’s condition for optimal entry is " ( !) # n 1 n X X X M j   ~ aðcj Þ W ð0Þðs  cj Þ þ W ðiÞ  Uðaðcj ÞÞ  f ¼ 0; hðck ; iÞ maxð0; ðck  cj ÞÞ M j¼1 i¼1 k¼2 28 To see this in more detail, one can compare the social planner’s incentives for a type cn firm charging the lowest possible price with that o f a t y p e cn1 P firm charging the highest possible P price. The difference between the two incentives is 1    ~ ðcn  cn1 Þ½W ð0Þ þ 1 i¼1 W ðiÞZðs  Dn1 ; iÞ ¼ ðcn  cn1 Þ½W ð0Þ þ i¼1 W ðiÞZðcn1 ; iÞ.

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189

where the left hand side is the total expected surplus from an additional entering firm and the right hand side is the cost. But it P was established earlier that the term in the curly brackets on the left hand side is just equal to 1 W ð0Þðp  cÞ þ i¼1 W ðiÞZðp; iÞðp  cÞ. Hence, the social planner’s entry condition can be written as n X    M j ~ ðcj Þðp ðcj Þ  cj Þ  Uða ðcj ÞÞ  f ¼ j; m M j¼1 which is exactly the equilibrium free entry condition. Similarly, the threshold cost level for the planner’s problem is given by the lowest possible cj that satisfies " !# 1 n X X ~ a ðcj Þ W ð0Þðs  cj Þ þ W ðiÞ  Uða ðcj ÞÞ  f > 0; hðck ; iÞ maxð0; ðck  cj ÞÞ i¼1

k¼2

which is equivalent to the exit rule in equilibrium, i.e. a firm stays in the industry if ~  ðcÞðp ðcÞ  cÞ  Uða ðcÞÞ  f > 0: m Thus, the equations determining the entry mass and the exit threshold are the same for the competitive equilibrium and the social planner’s problem. It follows that equilibrium is socially optimal for n P 2. The arguments so far are valid for an arbitrarily large number of discrete cost types. To complete the proof, the case of a continuum of cost types must be considered. In that case, the result holds only if different firm types charge different prices in equilibrium, which was shown to be the case in the text. Therefore, equilibrium maximizes social welfare also for the case of a continuum of types. h Proof of Proposition 3. Part (i). The market values in economies 1 and 2 are in the intervals ½0; V 1 ðcÞ and ½0; V 2 ðcÞ, respectively. Suppose that V 2 ðcÞ 6 V 1 ðcÞ. The values of firm type c in the two economies compare as follows a1 ðcÞðp1 ðcÞ  cÞ  U1 ða1 ðcÞÞ P a2 ðcÞðp2 ðcÞ  cÞ  U2 ða2 ðcÞÞ P a1 ðcÞðp1 ðcÞ  cÞ  U2 ða1 ðcÞÞ;  2 ðcÞ

ð25Þ

 1 ðcÞ

where the first inequality follows from V 6V and the last from the fact that the advertising and price choices in economy 1 are not necessarily optimal in economy 2. But then the first and last expressions in (25) imply U2 ða1 ðcÞÞ P U1 ða1 ðcÞÞ, which contradicts U2 ðaÞ < U1 ðaÞ for all a. Therefore, V 2 ðcÞ > V 1 ðcÞ. Part (ii). Fixing the prices at their levels in economy 1, the first order effect of a decline in advertising cost is an increase in the number of ads by all firms. At the new levels of advertising, the markup for the most efficient firm type c at its economy 1 price p1 ðcÞ must satisfy p1 ðcÞ  c ¼

1 1 ¼ ; A q ðp1 ðcÞÞ M 1 a ðcÞ dvðcÞ

ð26Þ

where A is the new total number of ads and q ðp1 ðcÞÞ is the new density of ads at price p1 ðcÞ. The most efficient firm type sends more ads under its economy 1 price, i.e. a ðcÞ > a1 ðcÞ. Thus, the left hand side is greater than the right hand side in (26), if firm type c continues to charge p1 ðcÞ. Consequently, firm type c must lower its price for the equality in (26) to be restored for economy 2. Therefore, p2 ðcÞ < p1 ðcÞ. The range of prices is then higher in economy 2 compared to economy 1, because the maximum price is s in both economies. Part (iii). The result follows directly by an application of the envelope theorem to the social planner’s objective function in (9) with respect to parameter hi in the advertising technology Uð; hÞ. h Proof of Proposition 4. Firm c1 breaks even in economy 1, but cannot sustain non-negative profits in economy 2 for the same price and advertising choices as in economy 1. Therefore, 



a1 ðc1 ÞeA2 ðs  c1 Þ  U2 ða1 ðc1 ÞÞ  f < a1 ðc1 ÞeA1 ðs  c1 Þ  U1 ða1 ðc1 ÞÞ  f ¼ 0: But since U2 ða1 ðc1 ÞÞ < U1 ða1 ðc1 ÞÞ 



a1 ðc1 Þðs  c1 ÞðeA2  eA1 Þ < 0; which yields

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eA2  eA1 < 0;

ð27Þ

because a1 ðc1 Þðs  c1 Þ > 0. It follows from (27) that

A2

>

A1 ,

i.e. more ads are sent in economy 2.

h

Proof of Proposition 5. Part (i) The equilibrium distributions of marginal cost in economies 1 and 2 are given vðcÞ vðcÞ        by vðc  Þ for c 2 ½c; c1 , and by vðc Þ for c 2 ½c; c2 , respectively. Since c1 > c2 , vðc1 Þ > vðc2 Þ for c 2 ½c; c1 , i.e. the 1

2

marginal cost in economy 1 first-order stochastically dominates that in economy 2. Part (ii) Follows from Part (i). Part (iii) The average market value of firms in economy 1 is Z c Z c 1 1 1 j  V 1 ¼ V ðcÞ dvðcÞ ¼ V  ðcÞ dvðcÞ ¼ 1 vðc1 Þ c vðc1 Þ c 1 vðc1 Þ where the second equality follows because V 1 ðcÞ ¼ 0 for c > c1 , and the last from the free entry condition. Similarly, for economy 2, V 2 ¼ vðcj Þ. Since vðc1 Þ > vðc2 Þ by Part (i), it follows that V 2 > V 1 . h 2

Appendix B. The simulation algorithm Consider a discretized version of the uniform distribution for marginal cost with n points given as c ¼ c1 < c2 <    < cn ¼ c with Prðc ¼ ci Þ ¼ 1=n. Step 1. Start with a strictly increasing cumulative distribution of ads across cost levels, Q0 ðcÞ. Step 2. For each ck , k ¼ 1; . . . ; n, solve for the optimal advertising level, aðck Þ, using the social planner’s efficiency condition " # T nk h X X

i1  i 0 0 Wð0Þðs  ck Þ þ WðiÞ i q ðcnj Þ 1  Q ðcnj Þ cnj  ck ¼ U0 ðaÞ; i¼1

j¼0

where q0 ðcÞ is the derivative of Q0 ðcÞ calculated using a discrete approximation, and T is a large positive integer that approximates infinity in the summation over the number of ads received. Step 3. Next, determine the optimal entry mass, M 0 , and the threshold cost level, c0 , given Q0 ðcÞ. This can be done by finding c0 such that c0 ¼ maxfck : aðck ÞLðck Þ  Uðaðck ÞÞ P f g; where Lðck Þ ¼ Wð0Þðs  ck Þ þ

T X

" WðiÞ

i¼1

nk h X

i

i1  q ðcnj Þ 1  Q0 ðcnj Þ cnj  ck

#

0

j¼0

0

and by finding M such that n X max ð0; ðaðck ÞLðck Þ  Uðaðck ÞÞ  f ÞÞ ¼ j: i¼1 n

Step 4. Given fak ðcÞgk¼1 , M 0 , and c0 , compute the updated cumulative distribution function, Q1 ðcÞ, as !, ! X X 1 Q ðcÞ ¼ aðck Þ aðck Þ : ck 6c

ck 6c0

Step 5. If maxci j Q0 ðci Þ  Q1 ðci Þj 6  for some small  > 0, then stop. Otherwise, set Q0 ðcÞ ¼ Q1 ðcÞ and go back to step 1. After solving for the ad distribution, the entry mass, and the exit threshold, optimal prices can be obtained by using the social planner’s allocation of ads in the equilibrium first order condition for price, by virtue of

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Theorem 2. The entire price distribution can then be sequentially solved for by starting with the marginal firm. For the examples in the text, a grid size of 100 was used to discretize the marginal cost range, and the highest number of ads a consumer receives was set to T ¼ 20. References Brown, Jeffrey, Goolsbee, Austan, 2000. Does the Internet make markets more competitive? Evidence from the life insurance industry. Journal of Political Economy 110, 481–507. Burdett, Kenneth, Judd, Kenneth, 1983. Equilibrium price dispersion. Econometrica 51, 955–969. Butters, Gerard, 1977. Equilibrium distributions of sales and advertising prices. Review of Economic Studies 44, 465–492. Chandler, Alfred, Cortada, James, 2000. A Nation Transformed by Information: How Information has Shaped the United States from Colonial Times to the Present. Oxford University Press. Comanor, William, Wilson, Thomas, 1974. Advertising and Market Power. Harvard University Press. Dinlersoz, Emin, and Yorukoglu, Mehmet, 2007. Information and industry dynamics, Manuscript, University of Houston. Granas, Andrzej, Dugundji, James, 2003. Fixed Point Theory. Springer-Verlag, New York. Grossman, Gene M., Shapiro, Carl, 1984. Informative advertising with differentiated products. Review of Economic Studies 51, 63–81. Guth, Robert A., 2006. How Microsoft is learning to love online advertising. The Wall Street Journal, November 16. Hopenhayn, Hugo, 1992. Entry, exit, and firm dynamics in long run equilibrium. Econometrica 60, 1127–1150. Available from: . Ireland, Norman J., 1993. The provision of information in a Bertrand Oligopoly. Journal of Industrial Economics 41, 61–76. Judd, Kenneth L., 1985. The law of large numbers with a continuum of i.i.d. random variables. Journal of Economic Theory 35, 19–25. Reinganum, Jennifer, 1979. A simple model of equilibrium price dispersion. Journal of Political Economy 87, 851–858. Robert, Jacques, Stahl, Dale, 1993. Informative price advertising in a sequential search model. Econometrica 61, 657–686. Salop, Steve, Stiglitz, Joseph, 1977. Bargains and ripoffs: a model of monopolistically competitive prices. Review of Economic Studies 44, 493–510. Stahl, Dale O., 1994. Oligopolistic pricing and advertising. Journal of Economic Theory 64, 162–177. Stegeman, Mark, 1991. Advertising in competitive markets. American Economic Review 81, 210–223. Stigler, George, 1961. The economics of information. Journal of Political Economy 69, 213–225. Sutton, John, 1991. Sunk Cost and Market Structure: Price Competition, Advertising, and the Evolution of Concentration. MIT Press, Cambridge. Wilde, L., Schwartz, A., 1979. Equilibrium comparison shopping. Review of Economic Studies 46, 543–554.