On intertemporal equity and efficiency in a model of global warming

This chapter studies equitable paths in the context of a model in which irreversible global warming is produced by the use of an exhaustible resource. Global warming is assumed to affect both production and instantaneous welfare of society adversely. Our framework is more general than those used in the literature; it encompasses models both with and without global warming. We formalize the law of motion which describes how global warming is generated by the use of the exhaustible resource, by allowing for the possibility that the rate of growth of global warming is proportional to a concave function of the resource use. This global warming function is linear in the model proposed by Stollery (1998). For this framework, we establish three equivalence results connecting the concepts of equity, Hartwick’s Rule of investing the resource rents, and a suitably extended version of Hotelling’s Rule, which takes into account the externalities caused by global warming. Further, we provide in this framework an explicit solution of an equitable path which satisfies Hartwick’s rule of investing resource rents. Consumption and global warming are bounded on this path, and the path is asymptotically similar to the maximin path obtained by Solow (1974) in a model without global warming. When the global warming function is strictly concave, we provide an explicit solution of an equitable path in which consumption and global warming exhibit unbounded quasi-arithmetic growth. This path follows an extended version of Hartwick’s rule of investment, and is seen to attain the maximum sustainable utility among all equitable paths which have a constant savings rate.