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The Cake-eating problem: Non-linear sharing rules

Author

Listed:
  • Eugenio Peluso

    () (Department of Economics (University of Verona))

  • Alain Trannoy

    (EHESS, GREQAM-IDEP, Marseille)

Abstract

Consider the most simple problem in microeconomics, a maximization problem with an additive separable utility function over bundles of two goods which provide equal sat- isfaction to an agent. Although simple, this framework allows for a very wide range of applications, from the Arrow-Debreu contingent claims case to the risk-sharing problem, including standard portfolio choice, intertemporal individual consumption, demand for in- surance and tax evasion. We show that any Engel curve can be generated through such a simple program and the necessary and suffi cient restrictions on the demand system to be the outcome of such a maximisation process. Moreover, we identify three classes of utility function that generate non-linear sharing rules. The gap between the two expen- diture shares increases in absolute, average or marginal terms with the total amount of wealth, depending on whether DARA, DRRA and convex risk tolerance are considered. The extension of the different results to the case of more than two goods is provided.

Suggested Citation

  • Eugenio Peluso & Alain Trannoy, 2012. "The Cake-eating problem: Non-linear sharing rules," Working Papers 26/2012, University of Verona, Department of Economics.
  • Handle: RePEc:ver:wpaper:26/2012
    as

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    File URL: http://dse.univr.it/home/workingpapers/2012WP26PelusoTrannoy.pdf
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    References listed on IDEAS

    as
    1. Christian Gollier, 2001. "Wealth Inequality and Asset Pricing," Review of Economic Studies, Oxford University Press, vol. 68(1), pages 181-203.
    2. Peluso, Eugenio & Trannoy, Alain, 2007. "Does less inequality among households mean less inequality among individuals?," Journal of Economic Theory, Elsevier, vol. 133(1), pages 568-578, March.
    3. David E. Bell, 1988. "One-Switch Utility Functions and a Measure of Risk," Management Science, INFORMS, vol. 34(12), pages 1416-1424, December.
    4. Carroll, Christopher D & Kimball, Miles S, 1996. "On the Concavity of the Consumption Function," Econometrica, Econometric Society, vol. 64(4), pages 981-992, July.
    5. Jehoshua Eliashberg & Robert L. Winkler, 1981. "Risk Sharing and Group Decision Making," Management Science, INFORMS, vol. 27(11), pages 1221-1235, November.
    6. Chevallier, Eric & Müller, Heinz H., 1994. "Risk Allocation in Capital Markets: Portfolio Insurance, Tactical Asset Allocation and Collar Strategies," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 24(01), pages 5-18, May.
    7. Maurizio Mazzocco & Shiv Saini, 2012. "Testing Efficient Risk Sharing with Heterogeneous Risk Preferences," American Economic Review, American Economic Association, vol. 102(1), pages 428-468, February.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Cake-eating problem; sharing rules; concavity; convex risk tolerance;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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