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...

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...

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...

We study an optimal growth model with one-hoss-shay vintage capital, where labor resources can be allocated freely either to production, technology adoption or capital maintenance. Technological progress is partly embodied. Adoption labor increases the level of embodied technical progress....

We construct a vintage capital model à la Whelan (2002) with both exogenous embodied and disembodied technical progress, and variable utilization of each vintage. The lifetime of capital goods is endogenous and it relies on the associated maintenance costs. We study the properties of 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...

The special functions are intensively used in mathematical physics to solve differential systems. We argue that they 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 model,...

We explore the hypothesis that demographic changes which began in the seventeenth and eighteenth centuries are at the root of the acceleration in growth rates at the dawn of the modern age. During this period, life tables for Geneva and Venice show a decline in adult mortality; French marriage...

This paper provides theoretical foundations to the contemporaneous increase in computer usage, human capital and multi-tasking observed in many OECD countries during the 1990s. The links between work organization, technology and human capital is modelled by establishing theconditions under which...