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Uniqueness of asset prices in an exchange economy with unbounded utility

Author

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  • 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.

Suggested Citation

  • Takashi Kamihigashi, 1998. "Uniqueness of asset prices in an exchange economy with unbounded utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(1), pages 103-122.
    • 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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    Citations

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    Cited by:

    1. Lise Clain-Chamosset-Yvrard & Takashi Kamihigashi, 2015. "International Transmission of Bubble Crashes in a Two-Country Overlapping Generations," Discussion Paper Series DP2015-43, Research Institute for Economics & Business Administration, Kobe University.
    2. Takashi Kamihigashi, 2015. "A Simple No-Bubble Theorem for Deterministic Sequential Economies," Discussion Paper Series DP2015-38, Research Institute for Economics & Business Administration, Kobe University.
    3. Takashi Kamihigashi, 2006. "Transversality Conditions and Dynamic Economic Behavior," Discussion Paper Series 180, Research Institute for Economics & Business Administration, Kobe University.
    4. Kamihigashi, Takashi, 2003. "Necessity of transversality conditions for stochastic problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 140-149, March.
    5. Takashi Kamihigashi, 2016. "A Simple Optimality-Based No-Bubble Theorem for Deterministic Sequential Economies," Discussion Paper Series DP2016-22, Research Institute for Economics & Business Administration, Kobe University.
    6. Gourieroux, C. & Jasiak, J. & Monfort, A., 2020. "Stationary bubble equilibria in rational expectation models," Journal of Econometrics, Elsevier, vol. 218(2), pages 714-735.
    7. 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.
    8. Montrucchio, Luigi & Privileggi, Fabio, 2001. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," Journal of Economic Theory, Elsevier, vol. 101(1), pages 158-188, November.
    9. Takeo Hori & Ryonghun Im, 2023. "Paper Withdrawn," Discussion Paper Series 262, School of Economics, Kwansei Gakuin University.
    10. Takashi Kamihigashi, 2011. "Recurrent Bubbles," The Japanese Economic Review, Japanese Economic Association, vol. 62(1), pages 27-62, March.
    11. Takashi Kamihigashi & Ryonghun Im, 2022. "Two Types of Asset Bubbles in a Small Open Economy," Discussion Paper Series DP2022-15, Research Institute for Economics & Business Administration, Kobe University.
    12. Hirano, Tomohiro & Toda, Alexis Akira, 2024. "Bubble economics," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    13. Massimiliano Ferrara & Bruno Antonio Pansera & Francesco Strati, 2018. "Classic rational bubbles and representativeness," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(1), pages 19-34, May.
    14. Takashi Kamihigashi, 2008. "The spirit of capitalism, stock market bubbles and output fluctuations," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(1), pages 3-28, March.
    15. Takashi Kamihigashi, 2015. "A Simple No-Bubble Theorem for Deterministic Dynamic Economies," Discussion Paper Series DP2015-24, Research Institute for Economics & Business Administration, Kobe University.
    16. Marco Airaudo, 2017. "Complex stock price dynamics under Max Weber’s spirit of capitalism hypothesis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(1), pages 47-73, June.
    17. Clain-Chamosset-Yvrard, Lise & Kamihigashi, Takashi, 2017. "International transmission of bubble crashes in a two-country overlapping generations model," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 115-126.
    18. João Brogueira & Fabian Schütze, 2017. "Existence and uniqueness of equilibrium in Lucas’ asset pricing model when utility is unbounded," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 179-190, October.
    19. Tomohiro Hirano & Alexis Akira Toda, 2023. "Bubble Necessity Theorem," CIGS Working Paper Series 23-011E, The Canon Institute for Global Studies.
    20. Lise Claini-Chamosset-Yvrard & Takashi Kamihigashi, 2015. "International Transmission of Bubble Crashes: Stationary Sunspot Equilibria in a Two-Country Overlapping Generations Model," Discussion Paper Series DP2015-21, Research Institute for Economics & Business Administration, Kobe University.
    21. Takashi Kamihigashi, 2015. "A Simple No-Bubble Theorem," Discussion Paper Series DP2015-03, Research Institute for Economics & Business Administration, Kobe University.
    22. Kamihigashi, Takashi, 2018. "A Simple optimality-based no-bubble theorem for deterministic sequential economies with strictly monotone preferences," Mathematical Social Sciences, Elsevier, vol. 91(C), pages 36-41.

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