The core-periphery model: A note on the existence and uniqueness of short-run equilibrium

We consider the core-periphery model [P. Krugman, Increasing returns and economic geography, Journal of Political Economy 199 (1) (1991) 483–499]. The nature and stability of the possible steady states of the model have been made progressively precise; [M. Fujita, P. Krugman, A. Venables, The Spatial Economy. Cities, Regions and International Trade, MIT Press, Cambridge, 1999; R. Baldwin, R. Forslid, Ph. Martin, G. Ottaviano, F. Robert-Nicoud, Economic Geography and Public Policy, Princeton Univ. Press, 2003]. In that model as well as in all the new economic geography models that have been derived from it, the short-run (instantaneous) equilibrium is implicitly determined by the current labor distribution across regions. The numerical computations used so far to determine the short-run equilibrium, tend to suggest its existence. In this paper, an existence and uniqueness proof of short-run equilibrium is provided.