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Complete Monotonicity of the Representative Consumer's Discount Factor

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Author Info
Chiaki Hara () (Institute of Economic Research, Kyoto University)
Abstract

A univariate real-valued function is said to be completely monotone if it takes positive values and alternate the signs of its higher order derivatives, starting from everywhere negative first derivatives. We prove that the representative consumer’s discount factor of a continuous-time economy under uncertainty is a power function of some completely monotone function of time satisfying certain boundary conditions if and only if it may be derived from a group of consumers having constant and equal relative risk aversion, and constant and yet possibly unequal discount rates.

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File URL: http://www.kier.kyoto-u.ac.jp/DP/DP636.pdf
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Publisher Info
Paper provided by Kyoto University, Institute of Economic Research in its series KIER Working Papers with number 636.

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Length: 13pages
Date of creation: Jul 2007
Date of revision:
Handle: RePEc:kyo:wpaper:636

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Related research
Keywords: Complete monotonicity; discount factor; discount rate; representative consumer; expected utility; time additivity; relative risk aversion; Bernstein’s theorem.;

Find related papers by JEL classification:
D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
D91 - Microeconomics - - Intertemporal Choice and Growth - - - Intertemporal Consumer Choice; Life Cycle Models and Saving
E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Determination of Interest Rates; Term Structure of Interest Rates
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

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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.:
  1. Christian Gollier & Richard Zeckhauser, 2005. "Aggregation of Heterogeneous Time Preferences," Journal of Political Economy, University of Chicago Press, vol. 113(4), pages 878-896, August.
  2. Chiaki Hara, 2006. "Heterogeneous Risk Attitudes In A Continuous-Time Model," The Japanese Economic Review, Japanese Economic Association, vol. 57(3), pages 377-405. [Downloadable!] (restricted)
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