The Cake-eating problem: Non-linear sharing rules
AbstractConsider 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 InfoPaper provided by University of Verona, Department of Economics in its series Working Papers with number 26/2012.
Date of creation: Sep 2012
Date of revision:
Cake-eating problem; sharing rules; concavity; convex risk tolerance;
Find related papers by 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 - - Intertemporal Choice - - - General
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-10-06 (All new papers)
- NEP-IUE-2012-10-06 (Informal & Underground Economics)
- NEP-MIC-2012-10-06 (Microeconomics)
- NEP-PBE-2012-10-06 (Public Economics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gollier, C., 1997.
"Wealth Inequality and Asset Pricing,"
Papers, Toulouse - GREMAQ
97.486, Toulouse - GREMAQ.
- Jehoshua Eliashberg & Robert L. Winkler, 1981. "Risk Sharing and Group Decision Making," Management Science, INFORMS, INFORMS, vol. 27(11), pages 1221-1235, November.
- David E. Bell, 1988. "One-Switch Utility Functions and a Measure of Risk," Management Science, INFORMS, INFORMS, vol. 34(12), pages 1416-1424, December.
- 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.
- Peluso, Eugenio & Trannoy, Alain, 2007. "Does less inequality among households mean less inequality among individuals?," Journal of Economic Theory, Elsevier, Elsevier, vol. 133(1), pages 568-578, March.
- Eugenio Peluso & Alain Trannoy, 2004. "Does Less Inequality among Households Mean Less Inequality among Individuals?," IDEP Working Papers, Institut d'economie publique (IDEP), Marseille, France 0407, Institut d'economie publique (IDEP), Marseille, France, revised Jun 2004.
- Eugenio Peluso & Alain Trannoy, 2004. "Does less inequality among households mean less inequality among individuals?," Department of Economics University of Siena, Department of Economics, University of Siena 432, Department of Economics, University of Siena.
- 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.
- Christopher D. Carroll & Miles S. Kimball, 1995. "On the concavity of the consumption function," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 95-10, Board of Governors of the Federal Reserve System (U.S.).
- Christopher D. Carroll & Miles S. Kimball, 1995. "On the Concavity of the Consumption Function," Macroeconomics, EconWPA 9503003, EconWPA.
- 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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