We study the optimal dynamics of an AK economy where population is uniformly distributed along the unit circle. Locations only differ in initial capital endowments. Spatio-temporal capital dynamics are described by a parabolic partial differential equation. The application of the maximum...

We review an emerging application field to parabolic partial differential equations (PDEs), that's economic growth theory. After a short presentation of concrete applications, we highlight the peculiarities of optimal control problems of parabolic PDEs with infinite time horizons. In particular,...

We study the optimal dynamics of an AK economy where population is uniformly distributed along the unit circle. Locations only differ in initial capital endowments. Spatio-temporal capital dynamics are described by a parabolic partial differential equation. The application of the maximum...

We consider a small-open, collateral-constrained AK economy. We show that the combination of CARA preferences and uncertainty on capital inflows in such an economy generates long-term (expected) growth while the deterministic counterpart does not. In this framework, long-term growth is entirely...

This paper aims at clarifying the conditions under which financial globalization originates welfare gains in a simple endogenous growth setting. We focus on the capital-deepening effect of financial globalization in an open-economy AK model and we show that constrained borrowing triggers...

We study the compatibility of the optimal population size concepts produced by different social welfare functions and egalitarism meant as "equal consumption for all individuals of all generations". Social welfare functions are parameterized by an altruism parameter generating the Benthamite and...

In this paper, we devise a social criterion in the spirit of the critical utility level of Blackorby-Donaldson (1984) to study an optimal population size problem in an endogenously growing economy populated by workers living a fixed amount of time and without capital accumulation. Population...

We show that leapfrogging and growth reversals entail sizeable welfare gains and losses, respectively, in an AK economy that cannot credibly commit to investment when borrowing from international financial markets. Small no-commitment delays originate a trade-off that has an ambiguous effect on...

In this paper, we apply two optimization methods to solve an optimal control problem of a linear neutral differential equation (NDE) arising in economics. The first one is a variational method, the second follows a dynamic programming approach. Due to the infinite dimensionality of the NDE, the...

We reconsider the optimal population size problem in a continuous time economy populated by homogenous cohorts with a fixed life span. This assumption is combined with a linear production function in the labor input and standard rearing costs. A general social welfare function is specified,...