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...

In this paper we use a new analytical approach to the Lucas-Uzawa model (Boucekkine and Ruiz Tamarit, 2007) to extend the existing results on the dynamics, and notably on the imbalance effects arising in the model. The approach does not only allow to extend the traditional analysis to any...

This paper develops a theory of optimal fertility behavior under mortality shocks. In a 3- periods OLG model, young adults determine their optimal fertility, labor supply and life-cycle consumption with both exogenous child and adult mortality risks. For fixed prices (real wages and interest...