Variety, globalization, and social efficiency.

• Author: Cox, W. Michael

1. Introduction

   Paul Samuelson (1948, p. 484; 1967, p. 426) was fond of pointing out that the "privilege of being able to buy a vast array of goods at low prices cannot be overestimated." Cox and Alto (1998) show that U.S. consumers enjoy 790 different magazines, 285 styles of running shoes, 340 different breakfast cereals, 185 various television channels, 1212 models of vehicles and more--in large part owing to the vast expansion of variety brought by globalization. It is difficult to imagine that these customers would have been only marginally better off had they all just driven a white Chevrolet, eaten Wheaties, read Business Week, and watched the Public Broadcasting System. It is here that the theory of monopolistic competition has become exceedingly useful: to get a handle on the value of variety.

   In a constant elasticity of substitution (CES) utility function, the smaller the elasticity, the higher the value placed on variety. The empirical aspects of estimating elasticities of substitution have been brought out in articles by Feenstra (1994), Bils and Klenow (2001), Broda and Weinstein (2006), and Feenstra and Kee (2008), among others. Broda and Weinstein (2006) estimate that the increase in the number of available varieties due to international trade from 1972-2001 was valued by U.S. consumers at 2.6% of their real income. Other researchers have found larger estimates of the gains from variety.

   We do not try to improve on these estimates. Rather, by a more faithful quantitative representation of the simplest model of monopolistic competition, we try to make more evident how economies of scale and elasticities of substitution fit into the standard model of monopolistic competition.

   The Dixit-Stiglitz-Krugman (DSK) model of monopolistic competition uses the CES utility function to capture the love for variety but adopts the approximation that the number of varieties is sufficiently large so that the elasticity of demand facing each firm is simply equal to the CES between varieties (Dixit and Stiglitz 1977; Krugman 1981). (1) Peculiarly, this solves for the number of firms or varieties while assuming in the calculation an infinite such number. We show that the Bertrand-Nash equilibrium allows a mutual determination of the number of varieties and the elasticity of demand in comparing equilibrium outcomes. The model is almost as simple as the DSK approximation but allows us to focus as well on the role of economies of scale because firms can move down their average cost curves as market size increases.

   Thus, the model provided here connects the informal accounts of monopolistic competition (e.g., Krugman 1979) that stress both the roles of variety and economies of scale with a formal model that actually allows the precise role of each to be exhibited.

   Recent work by Montagna (2001), Melitz (2003), and Feenstra and Kee (2008) emphasizes the importance of firm heterogeneity in determining the impact of globalization on productivity. Their setup is distinguished by a continuum of firms wherein the elasticity of demand facing each firm must equal the elasticity of substitution. In their work, globalization causes the exit of lower productivity firms, resulting in an increase in aggregate productivity. This approach, however, again abstracts from one possible feature whereby globalization can affect welfare--through the exploitation of economies of scale made possible by larger markets.

   Economies of scale are a two-edged sword. The greater are the economies of scale, the fewer are the number of varieties, and the larger is the gain in productivity from globalization; the smaller are the economies of scale, the greater is variety, and the smaller is the gain in productivity. (2) Having a model with variable demand elasticities captures this tension nicely. We will return to this theme in the sequel.

   We look at three theoretical questions: (i) What are the relative roles of variety and per capita output in determining per capita utility? (ii) What are the productivity gains from globalization due to economies of scale? (iii) How great of a departure from social efficiency prevails in a world of free entry and variety? We show that by dropping the approximation DSK and others have used, it is possible to give interesting answers to these questions. For example, to estimate per capita utility it is only necessary to look at per capita incomes in each sector, the relative importance of each sector, and estimates of the substitution parameter in that sector. Broda and Weinstein (2006) use U.S. import shares, but the model itself suggests that the appropriate weights are GDP shares.

   Section 2 presents the analysis of demand, which simply reprises the work of Helpman and Krugman (1985, pp. 117-20), who oddly do not apply the analysis to the model. Section 2 also presents a new graphical analysis of the model of monopolistic competition that parallels Krugman's pioneering treatment. Section 3 then solves for the exact solutions to the relevant variables and shows that the ratio of real income to measured per capita GDP increases with the size of the economy and the preference for variety. The result easily generalizes to an economy with many sectors. Section 3 also shows that per capita consumption of each variety still falls as the population rises and more varieties are introduced. This result followed automatically in Dixit and Stiglitz (1977) and Krugman (1981) because their approximation required a constant output for each firm. Section 4 looks at the issue of globalization and shows how international trade increases real income faster than measured GDP, depending on the relative size of the economy and, once again, the preference for variety. We find that the simple DSK model used here likely gives a gain from trade that is an order of magnitude too large, suggesting that modifications must be made for deeper applications. The DSK approximation that the size of each firm is negligible compromises the question of the socially efficient number of firms. We agree with the spirit of Dixit and Stiglitz (1977) that excessive entry is not a problem, but their claim that the market equilibrium is characterized by insufficient entry is not supported by our analysis. (3) We show that under the assumption of a CES utility function, the socially optimal number of firms falls short of the market equilibrium but only by a fraction that measures the substitutability of the different varieties--so it is essentially a non-issue. This analysis is presented in section 5.

2. The Model

   Consider an economy consisting of a single industry in which there are n varieties of some generic good, such as the automobile or cereal industries, each with the same cost and facing the same demand. Following Dixit and Stiglitz (1977) and Krugman (1979), to capture economies of scale the required labor input for each variety is l = [alpha] + [beta]x, where / and x are labor input and output respectively for fixed ([alpha]) and variable costs ([beta]x). The total labor supply is L and completely mobile between varieties. We let labor be the numeraire, so the wage w = 1. Each worker is a consumer with the same...