Bridging the Gap between Growth Theory and the New Economic Geography : The Spatial Ramsey Model

We study a Ramsey problem in infinite and continuous time and space. The problem is discounted both temporally and spatially. Capital flows to locations with higher marginal return. We show that the problem amounts to optimal control of parabolic partial differential equations (PDEs). We rely on the existing related mathematical literature toderive the Pontyagin conditions. Using explicit representations of the solutions to the PDEs, we first show that the resulting dynamic gystem gives rise to an ill-posed problem in the sense of Hadamard (1923). We then turn to the spatial Ramsey problem with linear utility. The botained properties are significantly different from those of the non-spatial linear Ramsey model dute to the spatial dynamics induced by capital mobility.