Recursive Sustainability: Intertemporal Efficiency and Equity

PV-optimality in a capital-resource economy can imply decreasing utility over some portion of the time horizon. Various criteria have been proposed to maintain intergenerational equity defined as nondeclining utility, but these have some limitations and problems. This paper proposes a new welfare criteria incorporating present value to maintain efficiency, and an equity function with convex costs on declining utility. This criterion is economically efficient, time-consistent and recursive. An extension of dynamic programming to multiple value functions is developed to solve this problem. Increasing the equity weight increasingly eliminates declining portions of utility time paths. Sustainability implies increasing consumption in the early time periods and some intermediate time periods relative to PV-optimality. A surprising result is that sustainability can actually result in increased resource usage in early time periods, followed later by higher levels of resource stocks compared to PV-optimality. The sustainability analysis shows that while conventional benefit-cost and valuation analysis contribute to efficiency, they do not necessarily induce sustainability due to incorrect dynamic GE prices. Similar comments apply to Green NNP analysis. The concepts and extended DP methods developed in this paper extend naturally to uncertainty and can also be applied to generalized consumer and social choice models beyond those typically considered in the literature.