PARETO IMPROVING FINANCIAL INNOVATION IN INCOMPLETE MARKETS

In this paper we develop a differential technique for investigating th e welfare effects of financial innovation in incomplete markets. Utili zing this technique, and after parametrizing the standard competitive, pure-exchange economy by both endowments and utility functions, we es tablish the following (weakly) generic property: Let S be the number o f states, I be the number of assets and H be the number of households, and consider a particular financial equilibrium. Then, provided that the degree of market incompleteness is sufficiently larger than the ex tent of household heterogeneity, S - I greater than or equal to 2H -1 [resp. S - I greater than or equal to H + 1], there is an open set of single assets [resp. pairs of assets] whose introduction can make ever y household better off land, symmetrically, an open set of single asse ts [resp. pairs of assets] whose introduction can make them all worse off). We also devise a very simple nonparametric procedure for reducin g extensive household heterogeneity to manageable size, a procedure wh ich not only makes our restrictions on market incompleteness more pala table, but could also prove to be quite useful in other applications i nvolving smooth analysis.