On the dynamics of capital accumulation across space
Résumé
We solve an optimal growth model in continuous space, continuous and bounded time. The optimizer chooses the opti- mal trajectories of capital and consumption across space and time by maximizing an objective function with both space and time discounting. We extract the corresponding Pontryagin conditions and prove their sufficiency. We end up with a system of two parabolic differential equations with the corresponding boundary conditions. We propose a simple numer- ical set-up to simulate PDE systems which we employ to study the roles of initial capital and technology distributions over space in various scenarios.