This paper proposes a symmetry‐breaking model of trade with a (large but) finite number of (ex ante) identical countries and a continuum of tradeable goods, which differ in their dependence on local differentiated producer services. Productivity differences across countries arise endogenously through free entry to the local service sector in each country. In any stable equilibrium, the countries sort themselves into specializing in different sets of tradeable goods, and a strict ranking of countries in per capita income, TFP, and the capital‐labor ratio emerges 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, to perform various comparative statics, and to evaluate the welfare effects of trade.