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 developed 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 increases 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 differentiated 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 competitive 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 different network effects. Since some firms may serve both the domestic and foreign markets, we consider 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 country. For example, due to language barriers, users of telephones and televisions may join local networks 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 originate 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 effects 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 literature 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 representative 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 marginal cost is determined by the free entry condition:

∗ Following Melitz and Ottaviano (2008), we assume that is drawn from the following Pareto distribution:

, with

Then, from , we obtain

∗

()()̅ where is a positive constant. A firm with a low marginal cost can be considered as a highly productive firm. Hence, we can measure a firm’s productivity by the inverse of its marginal cost . Those firms with a marginal cost below , or equivalently a productivity above , would stay in the market.

Proposition 1: As network effect increases, the cutoff productivity for a firm to remain in the

∗ market increases, i.e., Proof: See the Appendix.

Proposition 2: As network effect increases, more productive firms raise prices but less productive firms reduce prices. Specifically, ∗ ∗ if ∗ ∗ if

Proof: See the Appendix.

5/15 Proposition 3: As network effect increases, more productive firms make more profits but less productive firms make less profits. Specifically, ∗ ∗ if ∗ ∗ if

Proof: See the Appendix.

The results indicate that more productive firms are better off but less productive firms are worse off as the network effect increases. Intuitively, a larger network effect increases consumers’ willingness to pay and thus the demand for a product. Then, more productive firms will choose to raise prices and earn higher profits, while less productive firms are forced to reduce prices and earn lower profits. Consequently, more firms are driven out of the market and the minimum productivity in the market increases. These results are consistent with the empirical evidence that firm perfor- mance measures (including minimum productivity and average productivity) are higher and selec- tion is tougher in larger markets (Campbell and Hopenhayn 2005; Syverson 2007).

3. The Two-Country Model

We now extend the model to a two-country setting, in which firms face network effect in country and network effect in country , where . We focus on firm behavior in country and refer to country as the “domestic market” and country as the “foreign market”. Trade costs are symmetric between the two countries. Specifically, the cost of delivering a unit of product with cost from one country to the other is , . In order to focus our analysis on network effects, we assume that the two countries are also symmetric in other aspects.1 Although the markets are segmented, a firm can potentially produce in the domestic market and sell in both markets. Since an international firm faces a larger group of consumers, the network effect of its products may be larger than that of domestic products. In this section, we analyze two network structures for consumers of international products: “separate networks” and “integrated network”. In the former structure, the network effect of an international product is in country and in country (e.g., networks are separated due to language barriers). In the latter structure, the network effect of an international product is in both countries (e.g., consumers from different countries join the same network provided by the product).2

1 This means that the two countries have the same number of consumers, variety space, consumer preferences, and distributions of marginal costs. 2 In this case, we assume that .

6/15 3.1 Separate Networks Consider the case in which the networks of the two countries are separated for international products. In this case, since firms face network effect in country and network effect in country , the demand functions and the profit functions for each firm in country are

where the superscript of a variable indicates where the firm is from and the subscript indicates where the firm is selling its products to. Since the markets are segmented and firms produce under constant returns to scale, they independently maximize the profits earned in the domestic market and the foreign market. By , the profit-maximizing prices and outputs satisfy

In equilibrium, and By , the equilibrium outputs are

Then, by and , the equilibrium prices are

When and , the prices are respectively and We denote the cutoff marginal costs by and for firms from country . Similarly, and for firms from country . Obviously, Then, in equilibrium,

In this case, we have the following free entry conditions in country and country :

Given the distribution function in and the conditions in , we obtain ∗ ∗

7/15 ()()̅ where is a positive constant and is an inverse measure of trade costs.

Proposition 4: (i) As network effect increases, both the cutoff productivity of domestic producers and the cutoff productivity of foreign exporters increase. Specifically, ∗ ∗

(ii) As trade cost decreases, the cutoff productivity of domestic producers increases, whereas the cutoff productivity of foreign exporters decreases. Specifically, ∗ ∗

Proof: See the Appendix.

Proposition 4(i) indicates that a larger domestic network effect induces tougher competition in both the domestic and foreign markets. Intuitively, since network effects increase consumers’ willingness to pay, more productive firms can do better than other firms in extracting consumer surplus, which further drives less productive firms out of the market. This then implies tougher competition in the domestic market. As a result, it will be more difficult for foreign exporters to compete with domestic producers and hence the required productivity for exporting increases. Proposition 4(ii) is intuitive. When the trade cost is lower, it is easier for firms to sell their products to the foreign market, which decreases the productivity required for firms to export. On the other hand, the entry of foreign exporters intensifies domestic competition, making it harder for domestic producers to survive. Hence, the productivity required for firms to remain in the domestic market increases.

Proposition 5: The pricing strategies of domestic producers and domestic exporters respond to network effects and in the following way:

∗ ∗ ∗ ∗ if if ∗ ∗ ∗ ∗ if if Proof: See the Appendix.

8/15 Proposition 6: The profits of domestic producers and domestic exporters change with network effects and in the following way:

∗ ∗ ∗ ∗ if if ∗ ∗ ∗ ∗ if if Proof: See the Appendix.

Propositions 5 and 6 indicate that the prices and the profits of domestic firms may be influenced by the network effects in both countries, and the results in the autarky model persist in the

two-country model. It is interesting to see that a domestic firm with ∗ ∗ will raise its price and earn a higher profit in the domestic market when is larger, but will reduce its price and earn a lower profit in the foreign market when is larger.3 In this case, whether the total profit

∗ ∗ is higher or lower given similar changes in and will depend on the relative levels of network effects and and trade cost .

Asymmetric network effects can also influence the number of firms in each country. Let , , ∗ ∗ , and denote respectively the number of sellers, the number of entrants, the number of surviving firms, and the number of exporters in country , where and . Since the number of sellers in country is comprised of surviving firms from country and exporters from country , we have

Given the conditions in , we can solve for the number of entrants in country

∗ ∗ In this case, we have

∗ ∗

which imply

∗ ∗ Substituting into then yields

∗ ∗ ∗ ∗

3 For certain parameter values, we can ensure that such a firm serves in both markets.

9/15 Proposition 7: The number of entrants , the number of surviving firms , and the number of exporters are increasing with network effect and decreasing with network effect , i.e., Proof: See the Appendix.

Proposition 7 indicates that a larger encourages domestic entry and enables more domestic firms to survive and export, while a larger has the opposite effect. Interestingly, although network effect intensifies competition in the domestic market, it benefits domestic firms by making it more difficult for foreign exporters to enter the market. Consequently, more domestic firms are able to enter and capture a portion of market share. More importantly, when network effect is

sufficiently larger than network effect , there will be no entrants in country , i.e., (see equation ).4 This means that firms from the a country with a small network effect face greater challenges than those from a country with a large network effect and, eventually, are no longer able to compete with them when the gap between the effects is sufficiently large. Therefore, asymmetric network effects may lead to a situation where most firms originate from a dominant country (with the largest network effect).

3.2 Integrated Network We now consider the case in which the networks of the two countries are integrated for international products. In this case, international firms face network effect in both countries and domestic producers in each country still face network effect , . Then, the demand functions and the profit functions for each international firm in country become

which imply

Now the free entry conditions in the two countries are given by

4 ∗ ∗ ∗ ∗ ∗ ∗ Note that and together imply and , because would imply . Thus, only a subset of relatively more productive firms in each country choose to export.

10/15 Substituting and into then yields

Proposition 8: If the networks for international products are integrated and , then the cutoff productivities of domestic producers in the two countries are given by

∗ ∗ ()

() where . Proof: See the Appendix.

∗ ∗ Since , we can infer from that , for . Thus in the symmetric () case with , the cutoff productivity in each country is higher under integrated network than under separate networks. The reason is that, since consumers are willing to pay more for international products, more firms with relatively higher productivity would enter the market to enjoy high profits. Such entry increases the level of competition in the domestic market, which makes it harder for domestic firms to survive. Consequently, firms with low productivity are driven out of the market and hence the cutoff productivity increases. For asymmetric network effects, consider the case where . Intuitively, competition will be tougher in country than in country because larger network effects attract the entry of more productive firms and drive less productive firms out of the market, which implies that the cutoff productivity will be higher in country . Moreover, since the networks are integrated for international products, a further increase in will also lead to an increase in , which raises the level of competition in both markets. However, the level of competition will rise more in country because both and increase in country while only increases in country . Then, as the gap between network effects and gets larger, there will be more entry into country and less entry into country , which leads to a similar situation where firms from a country with a small network effect are less able to compete with firms from a country with a large network effect.

11/15

4. Conclusion

This paper introduces network effects into the monopolistically competitive model of trade proposed by Melitz and Ottaviano (2008). We first show that the network effect may intensify firm competition in autarky: facing a larger network effect, more productive firms raise prices and earn higher profits, whereas less productive firms reduce prices and earn lower profits. As a result, low productivity firms are not able to make a profit and thus exit the market. We then extend the autarky model to a two-country setting, where network effects are asymmetric between the two countries. We show that a larger network effect in each country can induce tougher competition among both domestic and foreign firms. More importantly, such an increase in network effect will encourage entry in the domestic market but discourage entry in the foreign market. Based on the results, there are some implications for trade policy and firm strategy in countries with relatively small network effects. Since network effects increase with market size, these countries should be open to trade so that they can cluster together to stand up to the dominance of the country with a much larger network effect. Also, trade liberalization between these countries may further make their firms better off because more firms in each country will be able to export. Moreo- ver, it may be helpful for firms in a country to build strategic partnerships with firms in other countries with small network effects. For example, partner firms could choose to produce and sell the same products in their domestic market: as this strategy increases the network effects of the products, the gap between small and large network effects will become smaller, which then makes it easier for such firms to survive.

Appendix

Proof of Proposition 1:

∗ ∗ ∗ Since , it is clear that for , is decreasing with , i.e., .

Proof of Proposition 2:

∗ ∗ ∗ Since in equilibrium and , we have

∗ ∗ ∗

12/15 Hence, ∗ ∗ ∗ ∗

Proof of Proposition 3:

By , we have ∗ ∗ . Then, Proposition 3 can be directly inferred from Proposition 2.

Proof of Proposition 4:

∗ Since ∗ , it is clear that for , ∗ is decreasing with , i.e., .

∗ By , we have ∗ ∗, which immediately implies .

∗ Given , it is obvious that . From ∗ ∗, we have ∗ ∗

Taking derivative with respect to then yields

∗

Proofs of Propositions 5 and 6:

Since ∗ , ∗ , and ∗ ∗, the proofs of Propositions 5 and 6 are similar to the proofs of Propositions 2 and 3.

Proof of Propositions 7:

()̅ () ∗ ∗ Given , we have () ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗

Since ∗ is decreasing with and is increasing with , for , it is immediate that , , and are increasing with and decreasing with .

13/15 Proof of Propositions 8:

Since implies that the two countries are symmetric, in equilibrium we must have . Then, the free entry condition in country becomes

̂ ̂ ̂ ̂

∗ ∗ Solving equation then yields the expressions for and in .

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