Infinite-horizon choice functions

Abstract

We analyze infinite-horizon choice functions within the setting of a simple technology. Efficiency and time consistency are characterized by stationary consumption and inheritance functions, as well as a transversality condition. In addition, we consider the equity axioms Suppes-Sen, Pigou-Dalton, and resource monotonicity. We show that Suppes-Sen and Pigou-Dalton imply that the consumption and inheritance functions are monotone with respect to time-thus justifying sustainabilitywhile resource monotonicity implies that the consumption and inheritance functions are monotone with respect to the resource. Examples illustrate the characterization results.Journal of Economic Literature Classification Numbers: D63, D71.

Intergenerational egalitarianism

“…Proving how difficult it is to assign consumption bundles such that generations are treated equally, the paper emphasizes that equality of well-beings (indepen-7 Further advances of the utility streams literature are surveyed in Asheim (2010). 5 dently of how these are measured) cannot correspond to a very egalitarian distribution of resources.…”

“…8 In such a setting, Epstein (1986) redistribution of resources via production and investment with a multidimensional commodity framework. As in Asheim et al (2010), the incompatibility between equity and efficiency in the infinite horizon framework is avoided by imposing specific domain restriction.…”

“…The results of the finite horizon model do not depend on this restriction. In the infinite horizon version, a lower bound on productivity is necessary to combine equity and efficiency even in a one-dimensional framework (see Asheim et al, 2010). As an example, assume a unit of good has to be shared among infinite many agents -corresponding to the case of one commodity with unitary net return on capital: equality, requiring all agents to be assigned the same quantity, is not compatible with efficiency, requiring the good to be distributed to the agents.…”

“…2 Well-known difficulties characterize the infinite horizon framework (see the seminal contribution of Diamond, 1965, and the recent review by Asheim, 2010). To distinguish the sources of tension between equity and efficiency, I first analyze the finite time horizon, and then extend the framework to the infinite time horizon.…”

On the Nature of Suppes-Sen Choice Functions in an Aggregative Growth Model

“…More generally, this paper investigates the nature of paths (in the standard aggregative model of growth) that are maximal according to the Suppes-Sen grading principle. 1 The Suppes-Sen grading principle 2 is a subrelation to every social welfare quasi-ordering which respects two widely accepted guiding principles of intertemporal social choice: finite anonymity (the equal treatment of all generations) and efficiency (the positive sensitivity of the social preference structure to the well-being of each generation). Thus, a characterization of paths which are maximal according to the grading principle would be useful in making intertemporal social choices.…”