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 special functions are intensively used in mathematical physics to solve differential systems. We argue that their use should be most useful in economic dynamics, notably in the assessment of the transtion dynamics of endogenous growth models. We illustrate our argument on the Lucas-Uzawa...

We use two stage optimal control techniques to solve some adoption problems under embodied technical change. We first solve a benchmark problem without learning behavior. At the date of switching, the consumption level is shown to drop, as the relative price of capital goes down (obsolescence)....

A comprehensive study of the linkages between demographic and economic variables should not only account for vintage specificity but also incorporate the relevant economic and demographic decisions in a complete optimal control set-up. In this paper, a methodological set-up allowing to reach the...

A benchmark AK optimal growth model with maintenance expenditures and endogeneous utilization of capital is considered within an explicit vintage capital framework. Scrapping is endogenous, and the model allows for a clean distinction between age and usage dependent capital depreciation and...