Money in Consumption-Loan Type Models: An Addendum

Abstract

In the Cass, Okuno, and Zilcha (1979), we presented several examples of consumption-loan type models exhibiting the nonexistence of any competitive equilibrium which is Pareto optimal. One sort of example—involving nonmonotonicity in tastes—seemed very special. Evidently, it depended on having just the right combination of some consumption satiation together with some boundary endowments. We conjectured that such speciality wasn't essential to the intuitive proposition being advanced, that somewhat less than total satiation might unfavorably restrict potential intertemporal market transfers—even given the institution of money, in its role as a store of value, as a common means for facilitating trade between the present and the future. Rather, we proposed as a more likely reason for such speciality the particular analytic methodology being utilized, the limitation to considering only models for which competitive equilibria could be essentially characterized as the nonnegative solutions to a first order difference equation (and thus completely represented in terms of a two-dimensional diagram). It turns out that while our intuition was correct, our reasoning wasn't. In fact, it is now apparent that the only operative constraint was simply our lack of sufficient ingenuity.