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Inheritance

Published online by Cambridge University Press:  01 July 2016

David Stirzaker
David Stirzaker*
Affiliation:
University of Oxford
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Abstract

We consider a population of reproducing individuals who inherit, earn, consume, and bequeath wealth. A model is constructed to describe the wealth of an individual selected from the nth generation by following a random line of descent from the initial individual. It is shown that bequests are commonly a convex function of wealth. Considering a linear approximation to the bequest function enables us to obtain estimates of the limiting distribution of wealth as the number of generations increases, when earnings of parent and offspring are independent. More generally when earnings of parent and offspring are not independent we obtain upper bounds for the tail of the wealth distribution using a martingale inequality.

Keywords

WEALTHINHERITANCEQUEUESUTILITY
Type
Research Article
Information
Advances in Applied Probability , Volume 12 , Issue 3 , September 1980 , pp. 574 - 590
Copyright
Copyright © Applied Probability Trust 1980 

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References

Abramowttz, M. and Stegun, I. (1964) Handbook of Mathematical Functions. Dover, New York.Google Scholar
Bevan, D. (1974) Savings and inheritance. Unpublished.Google Scholar
Bevan, D. (1979) Inheritance and the distribution of wealth. Economica 46, 381–402.Google Scholar
Kendall, D. (1975) Some problems in mathematical genealogy. In Perspectives in Probability and Statistics, ed. Gani, J., distributed by Academic Press, London for the Applied Probability Trust, Sheffield, 325–345.Google Scholar
Kingman, J. F. C. (1964) A martingale inequality. Proc. Camb. Phil. Soc. 59, 359–361.Google Scholar
Lindley, D. (1952) Theory of queues. Proc. Camb. Phil. Soc. 48, 272–289.Google Scholar
Stirzaker, D. (1980) Bequest functions and wealth distribution in a stratified society. To appear.Google Scholar