Existence of equilibrium in the Helpman–Krugman model of international trade with imperfect competition

Helpman and Krugman (Market structure and foreign trade. Increasing returns, imperfect competition, and the international economy. MIT Press, Cambridge, 1985) provide a synthesis of the traditional factor proportions theory of international trade and the theory of international trade due to the exploitation of scale economies in imperfectly competitive markets. They derive illuminating results about trade patterns and gains from trade, among other things, leaving unanswered the question of existence of equilibrium, however. The central significance of their characterization of properties of free trade equilibria with inter-industry and intra-industry trade calls for an analysis of existence of equilibrium. This is the object of the present paper. We prove the existence of equilibrium for the integrated multi-sector multi-factor Helpman–Krugman economy without national borders. Well-known conditions ensure that the world economy under free trade reproduces this equilibrium and thus establishes existence of a free trade equilibrium. Since an equilibrium of the integrated economy is not necessarily unique, the same holds true for a free trade equilibrium.