Intergenerational competitive equilibria under technological uncertainty and an exhaustible resource constraint

Abstract

This paper presents a model of competitive intertemporal equilibrium in a finite-horizon, overlapping generations economy facing technological uncertainty and an exhaustible resource constraint. Individuals form rational expectations regarding future prices and economic conditions, and income is redistributed from one generation to the next through government-mandated lump-sum transfers. Under uncertainty, the relationship between resource price appreciation and the interest rate is mediated by consumers' risk aversion with respect to consumption in alternative states of nature. The intuitively appealing proposition that the expected resource price rises at the expected rate of interest holds only as a special case. If future generations are taken to be state-contingent in the sense that their composition depends on the states of nature prevailing when they are born, then equilibria are generally Pareto efficient. But if future generations are state-independent so that the set of individuals born at a given date is independent of the prevailing state of nature, then equilibria may be inefficient because markets do not exist where successive generations may equilibrate their marginal rates of substitution across consumption in alternative contingent states. Such inefficiencies may be remedied through the implementation of appropriate intergenerational transfers. An optimal intergenerational welfare distribution may be supported as a competitive equilibrium if the income transfer regime is properly selected and enforced. The social optima that result for a simple version of the model under the maximin welfare criterion indicate that greater sacrifices are required on the part of the present generation when future generations are taken to be state-contingent than when they are regarded as state-independent. This finding provides a possible explanation for the extreme risk aversion of conservationists with respect to the welfare of future generations.