On competitive equitable paths under exhaustible resource constraints: The case of a growing population

The paper examines the nature of competitive paths in an exhaustible resource model, which allows for a growing population. For competitive paths that are equitable in the sense that the per capita consumption level is constant over time, the implicit investment rule is derived. This is seen to be a generalization of Hartwick's rule, obtained in the case of a stationary population. It is also shown that the existence of a competitive equitable path implies that a population can experience at most quasi-arithmetic growth.