We derive an R&D-based semi-endogenous growth model where technological progress depends on the available amount of technological opportunity. Incremental innovations provide direct increases in the knowledge stock but they reduce technological opportunity and thus the potential for further...

We endogenize the discount rate via a broad measure of wealth and provide empirical evidence that wealth affects the discount rate negatively. We demonstrate that the Pontryagin conditions require positive felicity for intuitive results, whereasthe concavity of the Hamiltonian requires negative...

We analyze a Ramsey economy when net investment is constrained to be non negative. We prove existence of a competitive equilibrium when utility need not be bounded from below and the Inada-type conditions need not hold. The analysis is carried out by means of a direct and technically standard...

We analyse a Ramsey economy when net investment is constrained to be non negative. We prove existence of a competitive equilibrium when utility need not hold. The analysis is carried out by means of direct and technically standard strategy.

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 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 famous Mincer equation regressing log earnings on years of schooling is derived from a linear human capital accumulation equation at the individual level. Even if the cross-sectional Mincer equation holds at the level of individuals, it does not hold at the macro level of countries because...