Toru Kikuchi / Journal of Economic Research 8 (2003) 69{76 69 On the Interconnection of Networks and Gains from Trade in Business Services Toru Kikuchi 1 Kobe University Received 1 April 2003; accepted 1 November 2003 Abstract Using a two-country model of monopolistic competition with country-speci c communications networks, this note establishes a link between gains from trade in intermediate business services and gains from the interconnection of networks. Keywords: Monopolistic competition; Interconnection of communications networks; Trade in intermediate business services JEL classi cation: D43; F12 1 Introduction Ever since the seminal work of Ethier (1979), intra-industry trade in intermediate business services (e.g., business software development, accounting, data processing) has been one of the major aspects of trade theory. Harris (1998) explores an important relationship between trade in business services and advancement in communications networks (e.g., the Internet, mobile telecommunications networks). 2 1 Graduate School of Economics, Kobe University 2-1, Rokkodai Nada,Kobe,Japan, (e-mail) kikuchi@econ.kobe-u.ac.jp. The author is grateful to James Atsu Amegashie, David Anderson and two anonymous referees for helpful comments. The author is also grateful to the Department of Economics at Simon Fraser University for generous support and hospitality over the period in which this paper was written. 2 Along this line, Kikuchi(2002) develops a two-country trade model that emphasizes theroleofcommunicationsnetworksin determining comparative advantages. See, also, Kikuchi(2003).
70 On the Interconnection of Networks and Gains from Trade in Business Services He emphasizes that advanced networks will facilitate the enhancement of international trade in intermediate business services.evidence of this includes, for example, the fact that sophisticated software engineers from India can deliver their services to the United States and Europe via the Internet. In the trade theory literature, however, relatively little is known about the welfare consequences of trade in intermediate business services via communications networks. The main contribution of this note is to establish a link between gains from trade in intermediate business services and gains through network e ects. These links are obtained by introducing the concept of `interconnected networks' into the workhorse two-country model of monopolistic competition (i.e., Krugman, 1980). In this model, a country is treated as a collection of regions which produce di erentiated business services and exchange them via a country-speci c communications network. The welfare e ects of the international exchange of services are examined on the basis of this model. Trade liberalization in the service sector can be interpreted as the interconnection of countryspeci c networks. It will be shown that the distribution of gains from the interconnection of networks will be varied according to the degree of substitution between business services. The next section develops a model of monopolistic competition in which business services are traded via country-speci c networks. Section 3 deals with the question of the distribution of gains from the interconnection of networks. 2 The Model Suppose that there are two countries in the world, Home and Foreign, and that they are similar in regard to consumers' preferences and production technologies but not necessarily in regard to size. There is only one primary factor of production: labor. There are two sectors: the competitive sector which uses only business services as inputs, and the monopolistically competitive sector which produces a large variety of business services. A country might be thought of as a collection of regions among which business services are exchanged via a countryspeci c communications network. Each region is endowed with L units
Toru Kikuchi / Journal of Economic Research 8 (2003) 69{76 71 of labor, and labor is assumed to be physically immobile across regions. Home (Foreign) consists of m(m )regions. Without loss of generality, Home is assumed to be larger than Foreign (m >m ). Each region's production function of the nal good is as follows: 3 Ã 1 nx µ X = x µ! i ; 0 <µ<1; (1) i where n is the number of available intermediate business services, x i is the quantity of service i, and1=(1 µ) > 1 is the elasticity of substitution between every pair of services. Business services are supplied by monopolistically competitive rms. The central assumption is that both the production and the distribution of services require communications through the country-speci c network, which is provided by the natural monopolist. To get on the network, each service rm has to pay a xed fee, w, where w is the wage rate. 4 Once each rm gets on the network, it has a constant marginal cost, w. With the number of service rms being very large, the elasticity of demand for each service becomes 1=(1 µ). Thus each service is priced at a markup over marginal cost: p = w=µ. Withn rms, the pro t of each rm, ¼, is given as: ¼ = px w( + x). Thus the level of output thatgenerateszeropro tsisgivenby¹x = µ= (1 µ). If a region does not exchange business services with other regions, the output level of that region becomes X = n (1 µ)=µ (n¹x): (2) The number of services produced within a region is given by n =(1 µ)l=. In what follows, units are chosen such that n = 1: each region is assumed to produce one type of service, and without exchange, that is the only service available to the region. At monopolistically competitive equilibrium, each region specializes in a di erent service. 3 One may think of this as the utility of households that are consuming di erentiated consumption goods. 4 This assumption implies (a) that there are aggregate constant returns in providing communications services, and (b) that the pricing of communications services is done on an average-cost basis. See Harris (1998).
72 On the Interconnection of Networks and Gains from Trade in Business Services Consider the Home autarky equilibrium in which m regions' services are exchanged via a Home-speci c communications network. In this case, service rms in each region send their own services to other regions via the network. At the same time, the volume of services importsineachregionisgivenby¹x(m 1)=m. This implies that, in each region, nal good producers assemble m types of services provided via the network. Each region produces the following amount of output: X = m (1 µ)=µ ¹x. Thus, one can think of Home (Foreign) itself as representing a network of size m(m ). The total amount of the Home output becomes: V A mx A = m (m (1 µ)=µ ¹x) =m 1=µ ¹x; where superscript A represents the autarky value. This shows that the productivity per region (V=m) rises as the total number of regions increases. The productivity bene ts of communications are the gains from trade that accrue from increased specialization in the provision of business services. 5 3 Gains from the Interconnection of Networks This section investigates the welfare consequences of trade in business services. Before turning to the analysis, some terminology needs to be clari ed. First, `trade in services' is synonymous with the `interconnection of country-speci c networks': through the interconnected networks, every service rm sends its service to the other country. Second, gains from the interconnection of networks are measured in terms of changes in the level of total output. Suppose that two countries of size m and m are connected through the internationally interconnected networks: Home-speci c network and Foreign-speci c network are interconnected. 6 In this case, both coun- 5 In the literature of network economics, network e ects denote positive externality, which is di erent from the simple proportional increase of output with the increased service diversity discussed here (e.g., Katz and Shapiro, 1985). However, in this model, to keep matters simple, it is assumed that there is no positive externality, although it is important to include the positive externality e ect. 6 It is natural to assume that there is an additional cost of interconnection for each network. However, to keep matters simple, assume that there are no additional costs.
Toru Kikuchi / Journal of Economic Research 8 (2003) 69{76 73 tries will gain through an increase in the range of available business services. In each region, nal good producers assemble m + m types of services provided via the interconnected networks. Thus the total amount of the Home output becomes: 7 V T mx T = m (m + m ) (1 µ)=µ ¹x; where superscript T represents the trading equilibrium. Increases in the level of output in each country are calculated as: V V T V A =[m (m + m ) (1 µ)=µ m 1=µ ]¹x; (3) V V T V A =[m (m + m ) (1 µ)=µ m 1=µ ]¹x: (4) Subtracting (4) from (3) yields the relationship V V =[(m m ) (m + m ) (1 µ)=µ m 1=µ + m 1=µ ]¹x: (5) 7 Since the zero-pro t output ¹x remainsconstantinthismodel,thereareneither gains nor loss from changes in each rm's average cost. Thus, the gains from trade come solely through increased service diversity. Krugman (1979) develops a di erent model in which trade leads to an increase in scale of production as well as an increase in diversity.
74 On the Interconnection of Networks and Gains from Trade in Business Services Figure 1. Figure 1 plots the relationship between V V and µ. This shows that gains from the interconnection of networks might be asymmetrical between the two countries. This surprising feature can be summarized as follows: Proposition: If the elasticity of substitution is below (above) the cuto level, the larger country will gain more (less) than the smaller one from the interconnection of networks. Two special cases warrant further attention. First, given that µ < 0:5 holds, the di erence in gains grows as µ decreases, i.e., the value placed on variety increases. The reason is as follows. From (2),
Toru Kikuchi / Journal of Economic Research 8 (2003) 69{76 75 it follows that X is convex (concave) in the number of available services when µ<(>)0:5. 8 Thus, given that µ<(>)0:5 holds, the larger (smaller) a country is, the more it gains from interconnection. This result is quite contrary to the one from the competitive analysis (i.e., the smaller country gains more than the larger country). 9 It also implies that there might be asymmetric incentives for interconnection. Thus, when network e ects are incorporated into trade models, the argument for trade gains might require modi cation. Next, consider the case in which µ =0:5. Here the value of the Home network before interconnection takes place is m 2, in accordance with `Metacalfe's Law' which says that the usefulness of a network is proportional to the m 2 of the number of people it connects. In this case, from (5), one can conclude that each country gets equal value from interconnection (i.e., V V = 0). The intuition behind this is fairly simple. On one hand, each region in the larger country gets a bit of extra value from connecting to the smaller country, but there are many regions. On the other hand, each region in the smaller country gains more through an increase in the number of available services, but there are fewer regions in the smaller country. 10 This implies that, given the particular value of the elasticity of substitution, gains from interconnection are split more or less equally, even among countries of di erent size. As Varian (2000) suggests, this gives some rationale for why settlement-free interconnection is common among large backbone providers of the Internet. Though the model presented here is extremely simple and crucially dependent on several restrictive assumptions, it establishes a link between the workhorse trade model of monopolistic competition and network e ects. Furthermore, the analysis presented here provides at least some grounds for the widespread concern over gains from the interconnection of networks. 8 By using (2), it is easy to calculate that partialx=partialnj n¹x=const: = [(1 µ)=µ]n (1 2µ)=µ (n¹x), and @ 2 X=@n 2 j n¹x=const: =[(1 µ)(1 2µ)=µ 2 ]n (1 3µ)=µ (n¹x). 9 This is known as Mill's Paradox. See Chipman (1965). 10 One can also interpret this result as follows: V canbeexpressedas V = m v; where v measures gains from trade per region. For the larger country m is greater than m, but v is smaller than v. Thus, whether V is greater than V or not depends on the value of variety.
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