SFB 303 Discussion Paper No. A - 435

Author: Araujo, A., P. K. Monteiro, and M. Páscoa
Title: Existence of Equilibria with Infinitely Many Goods, Incomplete Markets and Bankruptcy
Abstract: The existence of equilibria with infinitely many goods and incomplete markets have been studied by many authors. The continuum of states case was studied by Mas-Colell and Monteiro (1990), Hellwig (1991), Mas- Colell and Zame (1991) and Monteiro (1991). Separable utilities and a lower bound on uncovered asset sales are common assumptions. However the strongest assumption is that portfolio returns can be covered by the initial endowments for almost every state and all admissible portfolios. A counter-example in Mas-Colell and Zame (1991) shows that without this assumption (but still with a bound on uncovered sales) an equilibrium may not exist. Our plan in this paper is to eliminate this awkward assumption with the introduction of bankruptcy. The idea of bankruptcy has been considered recently by many authors. Our context is closer to Dubey, Geanakoplos and Shubik (1988), which shows the advantage of the introduction of bankruptcy in many situations. Our model is also close to Araujo-Páscoa (1993) which shows that, with bankruptcy, incomplete market equilibria might be locally determinate. Other papers that work with bankruptcy includes Dubey, Geanakoplos (1989), Zame (1993).In the second section we introduce basic definitions and auxiliary propositions. In the third section we present the model and the fourth section is dedicated to the finite dimensional approximations. In the fifth section the proof of the main theorem is given. Finally in the sixth section the financial return case is considered.
Creation-Date: January 1994
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