Bridging the gap between growth theory and the new economic geography: The spatial Ramsey model∗

In this paper, we solve a Ramsey model in continuous time and space, with both time and space discounting. We extract the corresponding Pontryagin conditions and prove their sufficiency. Then, we consider a finite time sub-problem and study the existence of solutions and the behaviour of these solutions when the time horizon increases. We end up by proving at the same time, the existence of a solution to the original infinite time optimization problem and the convergence to a stationary solution of this problem. However, both results are only obtained for a non-zero measure set of initial conditions, but not for any initial condition. ∗We acknowledge the financial support of the Belgian French speaking community (Grant ARC 99/04235 “Growth and incentive design”) and of the Belgian Federal Government (Grant PAI P5/10, “Equilibrium theory and optimization for public policy and industry regulation”). Address for correspondance: Raouf Boucekkine, Université catholique de Louvain, place Montesquieu 3, B-1348 Louvain-la-Neuve, Belgium. [email protected]