Abstract
We study a prototypical class of exchange economies with private information and indivisibilities. We establish an equivalence between lottery equilibria and sunspot equilibria and show that the welfare and existence theorems hold. To establish these results, we introduce the concept of the stand-in consumer economy, which is a standard, convex, finite consumer, finite good, pure exchange economy. With decreasing absolute risk aversion and no indivisibilities, we prove that no lotteries are actually used in equilibrium. We provide a simple numerical example with increasing absolute risk aversion in which lotteries are necessarily used in equilibrium. We also show how the equilibrium allocation in this example can be implemented in a sunspot equilibrium. Journal of Economic Literature Classification Numbers: D11, D50, D82.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 39-69 |
| Number of pages | 31 |
| Journal | Journal of Economic Theory |
| Volume | 107 |
| Issue number | 1 |
| DOIs | |
| State | Published - Nov 1 2002 |
Bibliographical note
Funding Information:We study a prototypical class of exchange economies with private information and indivisibilities. We establish an equivalence between lottery equilibria and sunspot equilibria and show that the welfare and existence theorems hold. To establish these results, we introduce the concept of the stand-in consumer economy, which is a standard, convex, finite consumer, finite good, pure exchange economy. With decreasing absolute risk aversion and no indivisibilities, we prove that no lotteries are actually used in equilibrium. We provide a simple numerical example with increasing absolute risk aversion in which lotteries are necessarily used in equilibrium. We also show how the equilibrium allocation in this example can be implemented in a sunspot equilibrium. Journal of Economic Literature Classification Numbers: D11, D50, D82. ν 2002 Elsevier Science (USA) 1We are grateful to the participants at the Cowles Seminar at Yale University, at the Simposio de Analisis Economico, at the NBER Conference on General Equilibrium Theory, and at the Workshop on Information, Financial Markets, and the Business Cycle, especially Pierre-Andre Chiappori. National Science Foundations Grants SBER 9618370, 9617899, and 9515256, and the UCLA Academic Senate provided financial support. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.