The Ramsey model of economic growth is revisited from the point of view of viability. A viable state is a state from which there exists at least one tra jectory that remains in the set of constraints of minimal consumption and positive wealth. Viability is presented with a constraint of minimal...

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 transition dynamics of endogenous growth models. We illustrate our argument on the Lucas-Uzawa...

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...

In a dynamic general equilibrium setup, this paper highlights the role of vintages and creative destruction in business fluctuations. By stressing the forward-looking characteristic of the optimal scrapping rule, we use a standard rational expectations argument to show the constancy of the...

In this paper, an endogenous growth model is built up incorporating Schumpeterian growth and embodied technological progress. Under embodiment, long run growth is affected by the following effects: (i) obsolescence costs add to the user cost of capital, reducing the research effort; and (ii) the...

This note analyses the adoption and diffusion of innovations in a horizontally differentiated Cournot duopoly in which firms have to choose the dates for adopting a cost-reducing new technology like in Reinganum (1981a). We prove that product differentiation crucially matters in the diffusion...

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. Inthis paper, a methodological set-up allowing to reach...

In this note, we use a technique analogous to Xie's method (1994) to solve analytically the Lucas model with externality in a specific parametric case. In particular, we characterize the shape of imbalance effects in this model. Our results are entirely consistent with the findings of the...

The transition from economic stagnation to sustained growth is often modelled thanks to "population-induced" productivity improvements, which are assumed rather than derived from primary assumptions. In this paper the effect of population on productivity is derived from optimal behavior. More...