Possibility Theorems for Equitably Aggregating Infinite Utility Streams

Abstract

The need to aggregate and evaluate infinite streams of returns or utility arises in several areas of economics, ranging from intergenerational welfare theory to environmental economics. The subject of intergenerational equity in the context of aggregating infinite utility streams has been of enduring interest to economists, starting with the work of Ramsey (1928), who had maintained that discounting one generation’s utility or income vis-à-vis another’s to be ‘ethically indefensible’, and something that ‘arises merely from the weakness of the imagination.’ His conjecture about the difficulty of aggregating infinite streams, while respecting intergenerational equity, turned out to be compelling, as a large number of impossibility theorems were proved subsequently by a number of authors, starting with the seminal works of Koopmans (1960) and Diamond (1965).

This paper benefited greatly from a presentation and discussion at the IEA Roundtable Meeting in Hakone, Japan, 10–12 March 2005, and from a detailed comment by Yongsheng Xu. This is an area where, over the years, we have had conversations with and comments from a large number of economists and would like to thank, in particular, Geir Asheim, Claude d’Aspremont, Kuntal Banerjee, Marc Fleurbaey, Nick Kiefer, Wlodek Rabinowicz, Tomoichi Shinotsuka, Kotaro Suzumura and Jorgen Weibull.