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The Cake-eating problem: Non-linear sharing rules

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  • 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.

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Bibliographic Info

Paper provided by University of Verona, Department of Economics in its series Working Papers with number 26/2012.

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Length: 31
Date of creation: Sep 2012
Date of revision:
Handle: RePEc:ver:wpaper:26/2012

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

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  1. Gollier, C., 1997. "Wealth Inequality and Asset Pricing," Papers, Toulouse - GREMAQ 97.486, Toulouse - GREMAQ.
  2. Jehoshua Eliashberg & Robert L. Winkler, 1981. "Risk Sharing and Group Decision Making," Management Science, INFORMS, INFORMS, vol. 27(11), pages 1221-1235, November.
  3. David E. Bell, 1988. "One-Switch Utility Functions and a Measure of Risk," Management Science, INFORMS, INFORMS, vol. 34(12), pages 1416-1424, December.
  4. Eugenio Peluso & Alain Trannoy, 2004. "Does less inequality among households mean less inequality among individuals ?," THEMA Working Papers 2004-11, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  5. Carroll, Christopher D & Kimball, Miles S, 1996. "On the Concavity of the Consumption Function," Econometrica, Econometric Society, Econometric Society, vol. 64(4), pages 981-92, July.
  6. Maurizio Mazzocco & Shiv Saini, 2012. "Testing Efficient Risk Sharing with Heterogeneous Risk Preferences," American Economic Review, American Economic Association, American Economic Association, vol. 102(1), pages 428-68, February.
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