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 investigate the effects of collaterals and monetary policy on growth rate dynamics in a Ramsey economy where agents have heterogeneous discount factors. We focus on the existence of business-cycle fluctuations based on self-fulfilling prophecies and on the occurrence of deterministic cycles...

We study the existence of equilibrium and rational bubbles in a Ramsey model with heterogeneous agents, borrowing constraints and endogenous labor. Applying a nonstandard fixed-point theorem by Gale and Mas-Colell's (1975), we prove the existence of equilibrium in a time-truncated bounded...

We revisit the seminal paper on endogenous fertility by Barro and Becker (1989) taking into account households' heterogeneity in terms of capital endowments, mortality differential and cost per surviving child. Focusing on an endogenous growth version, we show at first that there exists a unique...

We consider a two-sector economy with money-in-the-utility-function and sector-specific externalities. We provide conditions on technologies leading to the existence of local indeterminacy for any value of the interest rate elasticity of money demand, provided the elasticity of intertemporal...

Several contributions have already pointed out that initial wealth in- equalities do persist in the long run in the Ramsey model with heteroge- nous agents. We show that this result is not robust to the introduction of endogenous fertility. Our argument builds on the Barro-Becker (1989) seminal...

In this paper, we study the occurrence of local indeterminacy in two-sector monetary economies. In order to capture the credit market imperfections and the liquidity services of money, we consider a general MIUF model with two alternative timings in monetary payments: the Cash-In-Advance timing,...

Cet article propose de présenter dans un cadre simple, mais unifié, un certain nombre de résultats liés à l'existence et aux fluctuations d'une bulle rationnelle. Nous développons une économie d'échange à générations imbriquées dans laquelle chaque ménage fait un choix de...