Production Possibilities and Intertemporal Programmes

Exhaustible resources are normally inputs in production, not final consumption goods. It is then important to introduce production possibilities with exhaustible resources directly into our construction. This is the purpose of this chapter.

Begin with the simplest case. There is no uncertainty. The stocks of exhaustible resources are all known at the starting date. In addition, assume away the possibility of discovering substitute products in the future (e.g. harnessing solar energy which is, to all intents and purposes, inexhaustible). Presumably, then, an exhaustible resource would pose a ‘problem’ if it is, in some sense, essential in the production of final consumption goods, and not otherwise. The earth abounds with resources that, with current technology, have little or no use. No one would seem to lose any sleep over the fact that many such resources are exhaustible. So the question is whether one can make this intuitive notion of essentiality precise. It will transpire that one can. Nevertheless, it is not an easy matter to judge under what circumstances a given resource is in fact essential. The matter depends in a complex way on the production possibilities open to the economy.

We concern ourselves with production possibilities facing an economy as a whole. To fix ideas, assume that the economy is closed to trade with the rest of the world. As we are concentrating on the entire economy we need not consider intermediate goods.