Chapter 8 - Infinite-dimensional equilibrium theory: discussion of Jones

Summary

There is little I can possibly add to the thorough account of the current state of equilibrium theory with infinitely many commodities that has been given in the chapter of L. Jones. But since the duty of the commentator is to offer comments I will oblige by touching on two points. The first concerns a contrast between the analytical treatment of exchange and of production economies, the second refers to the difficulties to extend the theory to environments where the first fundamental theorem fails and, in particular, to incomplete markets economies.

But before plunging into my specific comments perhaps I will be allowed a word on the purposes of the theory. The following observation is evident enough but it nonetheless bears repeating. While from a purely formal point of view an equilibrium model with infinitely many commodities includes, and therefore generalizes, the standard model with finitely many commodities, the justification of the theory is not generality but, on the contrary, concreteness. If all we wanted to know is, say, that an equilibrium exists we would do as well with the finite number of commodities model. After all the number of commodities can be arbitrarily large and since large can be very large indeed there can be no loss of substance in doing so.