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Complete Monotonicity of the Representative Consumer's Discount Factor

Chiaki Hara ()

No 636, KIER Working Papers from Kyoto University, Institute of Economic Research

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.

Keywords: Complete monotonicity; discount factor; discount rate; representative consumer; expected utility; time additivity; relative risk aversion; Bernstein's theorem. (search for similar items in EconPapers)
JEL-codes: D51 D53 D61 D81 D91 E43 G12 (search for similar items in EconPapers)
Pages: 13pages
Date: 2007-07
New Economics Papers: this item is included in nep-mac and nep-upt
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Journal Article: Complete monotonicity of the representative consumer's discount factor (2008) Downloads
Working Paper: Complete Monotonicity of the Representative Consumer's Discount Factor (2008) Downloads
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