Maximin, Discounting, and Separating Hyperplanes

Is Hartwick’s rule a necessary condition for maximin in Solow’s [1974] model? Until recently this has been an open question; this is surprising given the prominence of the model. Cairns and Yang [2000] as well as Withagen, Asheim and Buchholz (this issue) claim that the answer is in the affirmative and claim to provide a formal proof. The latter team argues that the proof by the former is not correct and provides an alternative proof, based on Withagen and Asheim [1998]. Although Cairns and Yang [2000] assert that the methodology of Withagen and Asheim [1998] is “contrived”, our proof in this issue is not in dispute. This settles the question: Hartwick’s rule is necessary in Solow’s model. Nevertheless there is continued controversy. The main point in Cairns’ reply in this issue refers to discounting. In Withagen and Asheim it is assumed (in a very general setting) that an efficient constant utility path is supported by positive utility discount factors