Discrete Dynamics in Nature and Society
Volume 7 (2002), Issue 4, Pages 249-259

Intergenerational equity and dynamic duality principles

Hirofumi Uzawa

Research and Development Initiative, 42-8, Motomura-cho, Ichigaya, Shinjuku, Chuo University, Tokyo 162-8473, Japan

Received 14 April 2001

Copyright © 2002 Hirofumi Uzawa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The concept of intergenerational equity concerning intertemporal paths of consumption and capital accumulation is introduced and the analysis of the dynamic processes of capital accumulation and changes in environmental quality that are intergenerationally equitable is developed. The analysis is based upon the dynamic duality principles, as originally developed by Koopmans and Uzawa, and later extended to the case involving environmental quality.

A time-path of consumption and capital accumulation is defined intergenerationally equitable when it is dynamically efficient and, at the same time, the imputed price of each kind of capital, either private capital, or social overhead capital, is identical over time. The existence of an intergenerationally equitable time-path of consumption and capital accumulation is guaranteed when the processes of various kind of capital are subject to the Penrose effect, exhibiting the law of diminishing marginal rates of investment capital accumulation.