THE STRUCTURE OF THE PSEUDO-EQUILIBRIUM MANIFOLD IN ECONOMIES WITH INCOMPLETE MARKETS

This paper addresses the classical question: Is financial innovation b eneficial to a society when markets are incomplete? The general answer given here is, 'on average, yes'. The approach we employ is global an alysis. To be precise, we consider the standard two-period exchange ec onomy with uncertainty over S states of nature in the second period. T here are I agents and J real assets, where J < S. It is shown that the set of Pareto pseudo-equilibria Phi(p) forms a submanifold (a subvect or bundle) of the pseudo-equilibrium manifold Phi (vector bundle), who se codimension in Phi is (S-J)(I-1). A simple economic intuition captu red by this result is that, from a global point of view, more assets a re beneficial to a society in the sense that more assets reduce the co dimension of the set of Pareto equilibria and therefore enlarge its re lative size in Phi. Therefore,'on average', there is a greater chance of efficiency if we open new markets. Furthermore, the presence of the term (I-1) indicates that the inefficiency cost of market incompleten ess increases as the number of agents increases.