The indeterminacy of equilibrium city formation under monopolistic competition and increasing returns

We study the indeterminacy of equilibrium in the Fujita-Krugman [When is the economy monocentric?: von Thünen and Chamberlin unified, Reg. Sci. Urban Econ. 25 (1995) 505-528] model of city formation under monopolistic competition and increasing returns. Both the number and the locations of cities are endogenously determined. Assuming smooth transportation costs, we examine equilibria in city-economies where a finite number of cities form endogenously. For any positive integer K, the set of equilibria with K distinct cities has a smooth manifold of dimension K - 1 as its interior for almost all parameter values in a regular parameterization. The disjoint union of these sets over all positive integers K constitutes the entire equilibrium set.