Strategic saving decisions in the infinite-horizon model

We study a mechanism that prevents the long-run distribution of wealth from becoming degenerate in the Ramsey–Cass–Koopmans model when households have different time-preference rates. This mechanism is based on the observation that price-taking behavior is no longer justified when all wealth is owned by a single household. Formalizing this observation, we obtain a model with a unique stationary equilibrium in which, depending on the parameter constellation, any number of households can own positive stocks of capital. We characterize this equilibrium and show for example that an increase in the dispersion of the time-preference rates across households unambiguously increases aggregate output. Whereas the main results are derived for a rather general class of production functions, we devote a separate section to the special case of the Cobb–Douglas technology for which the equilibrium conditions are particularly simple. The research reported in this paper forms part of the project “Economic Growth with Strategic Saving Decisions” supported by the Austrian Science Fund (FWF) under project number P17886. Comments from Robert Becker, Edward Green, Takashi Kamihigashi, David Levine, Fabrizio Zilibotti, anonymous referees, and participants at various conferences and seminars are gratefully acknowledged.