The economics of forestry and a set-valued turnpike of the classical type

In recent work, the authors set classical turnpike theory in the context of the economics of forestry, as developed by Mitra and Wan, and presented two far-reaching results. In this paper, we present a conceptual generalization that takes this theory and configures it around a set in the space of forest configurations rather than around the golden-rule forest configuration. Our set-valued analysis hinges on periodicity and yields the earlier results as corollaries under a non-interiority condition on the felicity function that shrinks the set to the point. The question that we pose, and answer, has obvious relevance to more general contexts and, in particular, to turnpike theory as developed by Samuelson, Gale, McKenzie, and their followers.