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Uniqueness of asset prices in an exchange economy with unbounded utility

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Author Info
Takashi Kamihigashi (Department of Economics, SUNY-Stony Brook, Stony Brook, NY 11794-4384, USA)
Abstract

This paper studies conditions under which the price of an asset is uniquely determined by its fundamental value - i.e., no bubbles can arise - in Lucas-type asset pricing models with unbounded utility. After discussing Gilles and LeRoy's (1992) example, we construct an example of a two-period, representative agent economy to demonstrate that bubbles can arise in a standard model if utility is unbounded below, in which case the stochastic Euler equation may be violated. In an infinite horizon framework, we show that bubbles cannot arise if the optimal sequence of asset holdings can be lowered uniformly without incurring an infinite utility loss. Using this result, we develop conditions for the nonexistence of bubbles. The conditions depend exclusively on the asymptotic behavior of marginal utility at zero and infinity. They are satisfied by many unbounded utility functions, including the entire CRRA (constant relative risk aversion) class. The Appendix provides a complete market version of our two-period example.

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Article provided by Springer in its journal Economic Theory.

Volume (Year): 12 (1998)
Issue (Month): 1 ()
Pages: 103-122
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Handle: RePEc:spr:joecth:v:12:y:1998:i:1:p:103-122

Note: Received: January 22, 1996; revised version: February 18, 1997
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  1. Takashi Kamihigashi, 2007. "The Spirit of Capitalism, Stock Market Bubbles, and Output Fluctuations," Discussion Paper Series 205, Research Institute for Economics & Business Administration, Kobe University, revised Oct 2007. [Downloadable!]
  2. Luigi Montrucchio & Fabio Privileggi, 2001. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," ICER Working Papers - Applied Mathematics Series 05-2001, ICER - International Centre for Economic Research. [Downloadable!]
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  3. Takashi Kamihigashi, 2006. "Transversality Conditions and Dynamic Economic Behavior," Discussion Paper Series 180, Research Institute for Economics & Business Administration, Kobe University. [Downloadable!]
  4. Claudio Mattalia, 2003. "Existence of solutions and asset pricing bubbles in general equilibrium models," ICER Working Papers - Applied Mathematics Series 02-2003, ICER - International Centre for Economic Research. [Downloadable!]
  5. Takashi Kamihigashi, 2001. "Necessity of Transversality Conditions for Stochastic Problems," Department of Economics Working Papers 01-02, Stony Brook University, Department of Economics. [Downloadable!]
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