The recent COVID-19 crisis has revealed the urgent need to study the impact of an infectious disease on market economies and provide adequate policy recommendations. In this regard, we consider here the SIS hypothesis in dynamic general equilibrium models with and without capital accumulation, and we compute the efficient lockdown of altruistic agents. We find that the zero lockdown is efficient if agents are selfish, while a positive lockdown is recommended beyond a critical level of altruism. Moreover, the lockdown intensity increases in the degree of altruism. Our robust analytical results are illustrated by numerical simulations, which show, in particular, that the optimal lockdown never trespasses 60% and that eradication is not always optimal.
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 economy. A common argument shows this solution to be an equilibrium for any unbounded economy with the same fundamentals. Taking the limit of a sequence of truncated economies, we eventually obtain the existence of equilibrium in the Ramsey model.In the second part of the paper, we address the issue of rational bubbles and we prove that they never occur in a productive economy à la Ramsey.
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