We model an intergenerational society, with a representative agent at each date, who must deplete a renewable resource, from which he derives utility, to produce consumption goods. We adopt the intergenerational lexicographic minimum as the social welfare function. Initially, technological progress is assumed to exist exogenously. We study the technological requirements for the leximin solution to support non-decreasing welfare over time, and a non-decreasing level of the natural resource. Three utility functions are studied. With a CES utility function, possessing less substitutability than the Cobb-Douglas, the leximin solution involves increasing utilities over time and an increasing size of the natural resource, if the rate of transformation of the resource into the consumption good is greater than a computed bound. Finally we study a model with endogenous technical progress.
Roemer, John E., "Intergenerational Justice and Sustainability under the Leximin Ethic" (2005). Cowles Foundation Discussion Papers. 1796.