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Network Effects, Trade, and Productivity

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Network Effects, Trade, and Productivity Preprint, forthcoming on Managerial and Decision Economics ∗ Network Effects, Trade, and Productivity Tianle Song† and Susheng Wang‡ April, 2019 Abstract: We consider network effects in the monopolistically competitive model of trade devel- oped by Melitz and Ottaviano (2008). We show that a larger network effect intensifies competition by allowing more productive firms to raise prices and earn higher profits, but forcing less productive firms to reduce prices and earn lower profits. As a result, low productivity firms are driven out of the market. We also show that when network effects are asymmetric, it may be difficult for firms from a country with a small network effect to compete with firms from a country with a large network effect. Keywords: network effects, heterogeneous firms, international trade, productivity JEL classification: F10, F12 ∗ We thank the editor and an anonymous referee for their constructive and insightful feedback. † Corresponding author. Institute for Social and Economic Research, Nanjing Audit University. Email: tsong @connect.ust.hk. ‡ Department of Economics, Hong Kong University of Science and Technology. Email: [email protected]. 1. Introduction A network effect is a positive effect that arises when the value of a product or service to a user in- creases with the total number of users. Many products, especially telecommunication products and consumer electronics, feature network effects. As an example, the consumer utility of using a tele- phone increases directly with the size of the communication network. Consumer benefits can also depend indirectly on the size of the network. For instance, the users of Macintosh computers are better off when there are more users, because the increased demand may lead to a greater variety of Macintosh software (Church et al. 2008). Other similar examples include smartphones, televisions, social media software, and automated teller machines (ATMs). Many products with network effects are sold not only domestically but also internationally. Giv- en this and the fact that more economies are opening up, network effects are becoming increasingly important worldwide. So how do network effects affect the strategies of firms that produce differen- tiated products such as smartphones? If two countries have asymmetric network effects and all products can potentially be traded, how do firms within each country respond? We address these questions by introducing network effects into the monopolistically competi- tive model of trade developed by Melitz and Ottaviano (2008). We first show that, although network effects increase consumers’ willingness to pay, they intensify rather than soften firm competition in autarky. Specifically, facing a larger network effect, more productive firms raise prices and earn higher profits, whereas less productive firms reduce prices and earn lower profits. Consequently, low productivity firms are not able to make a profit and thus are driven out of the market. The intuition is that more productive firms can easily take advantage of the positive network externality and expand. As they expand, less productive firms become even less competitive and this makes it even more difficult for them to survive in the market. We then extend the autarky model to a two-country setting, where the countries may have dif- ferent network effects. Since some firms may serve both the domestic and foreign markets, we con- sider two network structures for their consumers: “separate networks” and “integrated network”. In the former structure, the products are influenced only by the network effect in the destination coun- try. For example, due to language barriers, users of telephones and televisions may join local net- works only. In the latter structure, the products are influenced by a common and larger network effect because of the integrated network of the two markets. For example, smartphone users can also download applications in app stores of other countries. We show that a larger network effect in each country can induce tougher competition among both domestic and foreign firms. If network effects are asymmetric, we find that as the gap between the network effects gets larger, firms from a country with a smaller network effect will be less able to compete with firms from a country with a larger network effect. Hence, asymmetric network effects may lead to a situation where most firms origi- nate from a dominant country (with the largest network effect). 2/15 There is a huge literature on network effects. Yoffie (1997) points out that nowadays network ef- fects have become more significant in many industries, including the computer hardware industry, the consumer electronics industry, and the telecommunications industry. Several studies find strong network effects in many markets (e.g., Blundell et al. 1999; Dranove and Gandal 2003; Ohashi 2003; Nair et al. 2004; Grajek 2010). For instance, Grajek (2010) indicates that ignoring network effects can lead to overestimation of demand elasticity. Blundell et al. (1999) find a robust and positive effect of market share (network effect) on the numbers of innovations and patents and on the impact of innovation on market value. This paper is closely related to the strand of literature on how network effects influence firm strategies. David (1985), Farrell and Saloner (1985), and Arthur (1989) find that industries may lock in an inferior standard by historical events due to network effects. Katz and Shapiro (1985) theoreti- cally show that such a lock-in can occur when multiple equilibria exist in which a single standard dominates. Fershtman and Judd (1987) and Sklivas (1987) indicate that strategic delegation under price competition drives firm owners to choose incentive contracts that encourage managers to use less aggressive pricing in order to reduce the intensity of competition. Hoernig (2012) shows that the opposite is true if network effects are sufficiently strong, which suggests that network effects have a significant impact on firm owners’ equilibrium stance in strategic delegation. Other related litera- ture includes studies on network effects in two-sided markets (Rochet and Tirole 2003, 2008; Arm- strong 2006; Rysman 2009) and those on dynamic price competition with network effects (Xie and Sirbu 1995; Doganoglu 2003; Cabral 2011). Our paper differs from the existing literature in that we consider network effects on pricing strategies and industry dynamics in international trade where firms are heterogeneous in productivity and network effects are asymmetric across countries. The rest of the paper proceeds as follows. Section 2 presents the autarky model and shows how the network effect influences prices, profits, and firm dynamics. Section 3 extends the autarky model to a two-country setting and shows how asymmetric network effects play an important role in the competition between firms from the two countries. Section 4 concludes. The appendix provides the proofs of all results. 2. The Autarky Model We introduce network effects into the monopolistically competitive model of trade developed by Melitz and Ottaviano (2008). Firms operate in the same industry, produce differentiated goods, and are heterogeneous in marginal cost , which is drawn from a common distribution with support , where . Similar to Hoernig (2012), the demand function faced by the firm with marginal cost is 3/15 where is the expectation of equilibrium quantity demanded by consumers, measures the network effect, is the number of consumers, and and are respectively the price and quantity of products sold by the firm. represents the price at which the demand for a variety of products is driven to zero, where is the number of incumbent firms, is the average price, and denote the substitution pattern between the differentiated varieties and the numeraire, and captures the degree of product differentiation between the varieties, with . In equilibrium, we must have . The demand function can be derived from the following quasi-linear utility function of the representative consumer (see Melitz and Ottaviano 2008 for a similar derivation): ∈ ∈ ∈ where and denote the representative consumer and the variety space; and are the repre- sentative consumer’s consumption levels of the numeraire good and each variety ; and repre- sent the expectations of the equilibrium quantity of variety and the equilibrium total quantity of all varieties; and . Then, the “network effects” are shown as follows: ∈ where indicates the marginal effects of network externalities on variety . In particular, captures the marginal effect of the total network variety. This means that the equilibrium consumption level of other goods will also affect the quantity of variety consumed, which is in line with Katz and Shapiro’s (1985) argument of consumption externalities. The firm with marginal cost solves the following profit-maximizing problem: max () where This implies that the profit-maximizing price and output satisfy In equilibrium, . Then, by , we have Substituting into yields 4/15 When the price is We denote by the cutoff marginal cost at which the firm has zero profit and is indifferent between remaining in and exiting from the market. Then, we must have Hence, in equilibrium, ∗ ∗ ∗ Firms make entry decisions before the marginal costs are drawn, and entry incurs a fixed sunk cost . Prior to entry, the expected firm profit is ∗ . Since the unrestricted entry of new firms will drive the expected profit to zero, the cutoff
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