Complete monotonicity of the representative consumer’s discount factor
- Resource Type
- Authors
- Chiaki Hara
- Source
- Journal of Mathematical Economics. 44:1321-1331
- Subject
- Economics and Econometrics
Discounting
Monotone polygon
Applied Mathematics
Univariate
Monotonic function
Function (mathematics)
Constant (mathematics)
Power function
Mathematical economics
Expected utility hypothesis
Mathematics
- Language
- ISSN
- 0304-4068
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.