On the Existence and Characterization of Markovian Equilibrium in Models with Simple Non-paternalistic Altruism

This paper presents results on existence and characterization of Markov equilibrium for a broad class of models with intergenerational altruism frequently used in the macroeconomic literature. In these models, parents are assumed to have a simple non-paternalistic utility, as each generation derives utility from its own consumption and the utility of the next generation. Models with simple nonpaternalistic altruism are widely used (Barro [1], Barro and Becker[2], Loury [8]), but results establishing existence and characterizations of equilibrium are surprisingly few and incomplete. Most important is the seminal work of Ray [10] demonstrating the existence of an indirect utility function and a saving policy such that it is optimal for each generation to follow that particular policy, providing its descendants use the same policy, and that the indirect utility function is the same for all generations. In addition, the optimal saving policy is shown to be an increasing function of current endowments. Ray[10] focuses on existence, and there is no characterization of the set of equilibria, no indications on how to compute them, and no conditions under which the equilibrium can be shown to be unique. This paper addresses these concerns.