Social Welfare in Growth Models with Heterogeneous Agents

Abstract

A problem of aggregation of heterogeneous time preferences naturally arises in economic growth models with consumers who have different discount factors. This problem is typically resolved by constructing a Pareto-efficient (Paretian) social welfare function which evaluates different consumption streams from the perspective of the society as a whole. It turns out, however, that a minimal reasonable and widely accepted Pareto-efficiency requirement leads to very unpleasant consequences: an optimal path (a result of the maximization of a Paretian social welfare function) possesses a number of unsatisfactory features. For instance, socially optimal levels of consumption and their shares in aggregate consumption converge to zero for all consumers except the most patient one. Moreover, an optimal path exhibits time inconsistency: an optimal choice for any future date depends of the decision date. All the discrepancies mentioned above suggest that a social welfare function is not an appropriate normative concept in models with heterogeneous consumers. Moreover, attempts to aggregate heterogeneous time preferences via some voting procedures face another fundamental problem — in dynamic models, voting is multidimensional, so that generically there is no stable outcome of voting. This paper studies the problem of aggregation of heterogeneous time preferences in growth models. In particular, we discuss the main difficulties that arise with the notion of a social optimum under heterogeneous time preferences and review certain possible ways to overcome these difficulties.