Chapter 5 - Incomplete financial markets and indeterminacy of competitive equilibrium

Summary

INTRODUCTION

The general conception of this line of inquiry is to broaden the canonical Walrasian or competitive equilibrium paradigm - a la Arrow-Debreu - to encompass (with regard to the economy's financial sector) richer institutional structure and various market failures. I believe that this is a very important undertaking for (somewhat) generalist-type theorists like myself: the Walrasian tradition is simply much too fundamental to be left to (purely) mathematical-type theorists with their excessive concern about existence in ever more abstract settings, or to (impurely?) macro- or finance-type theorists with their excessive reliance on non-robust or overly parametric examples. Be that as it may, the range of specific developments thus far has been quite modest, concentrating on inside (i.e., private) financial transactions within incomplete financial markets (using Arrow's famous reformulation of complete contingent goods markets as the benchmark), while maintaining the simplifications of perfect information, price-taking behavior, etc.

As one might have predicted, this research has focused on the three classical issues in general equilibrium theory: existence, optimality, and uniqueness or, better, determinacy. I will not have much to say about either existence or optimality - the first because I view it as primarily a technical issue (and, unsurprisingly, one which has received an inordinate amount of attention), the second because I cannot claim to be an expert on its intricacies. Fortunately, an excellent discussion of recent results on both problems can be found in John Geanakoplos' introduction to the special issue of the JME devoted to “Incomplete Markets” (Geanakoplos, 1990).