Endogenous ranking and equilibrium Lorenz curve across (ex-ante) identical countries: A generalization

• This paper extends a symmetry-breaking model of trade proposed by Matsuyama (2013) for more general forms of scale economies.
• In any stable equilibrium, ex-ante identical countries sort themselves into specializing in different sets of tradeable goods.
• In any stable equilibrium, a strict ranking of countries in per capita income, TFP and other variables emerges endogenously.
• The equilibrium Lorenz curve is unique and becomes analytically solvable in the limit, as the number of countries grows unbounded.
• Using this limit as an approximation, we study the shape of distribution and perform various comparative statics and welfare analysis.

This paper proposes a symmetry-breaking model of trade with a finite number of identical countries and a continuum of tradeable consumption goods, which differ in their dependence on nontradeable intermediate inputs, “producer services”. Productivity of each country is endogenous due to country-specific external economies of scale in its service sector. It is shown that, in any stable equilibrium, the countries sort themselves into specializing in different sets of tradeable goods and that a strict ranking of countries in per capita income, TFP, the service sector share, and the capital–labor ratio emerge endogenously. Furthermore, the distribution of country shares, the Lorenz curve, is unique and analytically solvable in the limit, as the number of countries grows unbounded. Using this limit as an approximation allows us to study what determines the shape of distribution, perform various comparative statics and to evaluate the welfare effects of trade. In doing so, this paper extends the analysis of Matsuyama (Econometrica, 81:5 (September 2013), 2009–2031) for more general and flexible forms of scale economies. It turns out that the technique introduced in Matsuyama (Econometrica, 81:5 (September 2013), 2009–2031) is useful for the equilibrium characterization in this general case as well. Although some results of comparative statics and on welfare inevitably need to be modified, they change in ways that illuminate the underlying mechanism of symmetry-breaking.