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.

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...

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...

This paper analyzes and compares the macroeconomic performance of defined-benefit and defined-contribution pay-as-you-go pension systems when population ages. When the fertility rate decreases or longevity rises, it is shown that a shift from defined benefit (defined total benefit or defined...

We explore the optimal fertility age-pattern in a four-period OLG economy with physical capital accumulation. For that purpose, we firstly compare the dynamics of two closed economies, Early and Late Islands, which differ only in the timing of births. On Early Island, children are born from...

Introduced by Samuelson (1975), the Serendipity Theorem states that the competitive economy will converge towards the optimum steady-state provided the optimum population growth rate is imposed. This paper aims at exploring whether the Serendipity Theorem still holds in an economy with risky...

This paper aims at investigating whether or not a utilitarian social planner should subsidize longevity-enhancing expenditures in an economy with a PAYG pension system. For that purpose, a simple two-period OLG model is developed, in which the length of the second period of life can be raised by...

We study how mortality reductins and income growth interact, looking at their relationship prior to the Industrial Revolution, when income per capita was stagnant. We first present a model of individual medical spending giving a rationale for individual health expenditures even when medicine...