IDEAS home Printed from
   My bibliography  Save this paper

Heterogeneous Beliefs in a Continuous-Time Model


  • Chiaki Hara

    (Institute of Economic Research, Kyoto University)


In an exchange economy under uncertainty populated by consumers having constant and equal relative risk aversion but heterogeneous probabilistic beliefs, we analyze the nature of the representative consumer's probabilistic belief and discount rates. We prove a formula that implies that the representative consumer's discount rates are raised or lowered by belief heterogeneity depending on whether the constant relative risk aversion is greater or smaller than one. We also show that the representative consumer's discount rates may be a hyperbolic function of time even when the individual consumers' discount rates are equal to one another, as long as their beliefs are heterogeneous.

Suggested Citation

  • Chiaki Hara, 2010. "Heterogeneous Beliefs in a Continuous-Time Model," KIER Working Papers 701, Kyoto University, Institute of Economic Research.
  • Handle: RePEc:kyo:wpaper:701

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Chang, Fwu-Ranq, 1996. "Uncertainty and investment in health," Journal of Health Economics, Elsevier, vol. 15(3), pages 369-376, June.
    2. Peter P. Wakker, 2000. "Uncertainty aversion: a discussion of critical issues in health economics," Health Economics, John Wiley & Sons, Ltd., vol. 9(3), pages 261-263.
    3. Nishimura, Kiyohiko G. & Ozaki, Hiroyuki, 2007. "Irreversible investment and Knightian uncertainty," Journal of Economic Theory, Elsevier, vol. 136(1), pages 668-694, September.
    4. Selden, Thomas M., 1993. "Uncertainty and health care spending by the poor: The health capital model revisited," Journal of Health Economics, Elsevier, vol. 12(1), pages 109-115, April.
    5. Faruk Gul & Wolfgang Pesendorfer, 2001. "Temptation and Self-Control," Econometrica, Econometric Society, vol. 69(6), pages 1403-1435, November.
    6. Picone, Gabriel & Uribe, Martin & Mark Wilson, R., 1998. "The effect of uncertainty on the demand for medical care, health capital and wealth," Journal of Health Economics, Elsevier, vol. 17(2), pages 171-185, April.
    7. Marcus Berliant & Hideo Konishi, 2005. "Salience: Agenda choices by competing candidates," Public Choice, Springer, vol. 125(1), pages 129-149, July.
    8. Grossman, Michael, 1972. "On the Concept of Health Capital and the Demand for Health," Journal of Political Economy, University of Chicago Press, vol. 80(2), pages 223-255, March-Apr.
    9. Dardanoni, Valentino & Wagstaff, Adam, 1987. "Uncertainty, inequalities in health and the demand for health," Journal of Health Economics, Elsevier, vol. 6(4), pages 283-290, December.
    10. Adam Oliver, 2000. "Uncertainty aversion: a reply to the paper by Andersson and Lyttkens," Health Economics, John Wiley & Sons, Ltd., vol. 9(3), pages 253-255.
    11. Dow, James & Werlang, Sergio Ribeiro da Costa, 1992. "Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio," Econometrica, Econometric Society, vol. 60(1), pages 197-204, January.
    12. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    13. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 443-478.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Representative consumer; expected utility; hyperbolic discounting; constant relative risk aversion; Ito's Lemma; Girsanov's Theorem;

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • Q51 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Valuation of Environmental Effects
    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kyo:wpaper:701. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ryo Okui). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.