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Exact measures of income in a hyperbolic economy

Published online by Cambridge University Press:  02 August 2004

JOHN C.V. PEZZEY
JOHN C.V. PEZZEY
Affiliation:
Centre for Resource and Environmental Studies, Australian National University, Canberra, ACT 0200, Australia. Tel:Fax: +61 2 6125 4143/0757. E-mail: [email protected] Website http://cres.anu.edu.au/~pezzey
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Abstract

For a closed economy with human-made capital, non-renewable resource depletion and (possibly) exogenous, hyperbolic technical progress as explicit-form inputs to a production function, there is a feasible development path that is ‘as if’ optimal with respect to hyperbolic utility discounting. On this path, typically, welfare-equivalent income > wealth-equivalent income > Sefton-Weale income > net national product, with possibly dramatic differences among these measures; and sustainable income can be greater than, equal to, or less than NNP. For low enough discounting, growing consumption is optimal even when technical progress is zero. A particular discount rate makes all income measures and consumption constant and (except net national product) equal; and zero technical progress then gives the Solow (1974) maximin as a special case. The optimal path is time-consistent because of the way the utility discount rate is chosen to depend on the economy's stocks, and hence on absolute time.

Type
Research Article
Information
Environment and Development Economics , Volume 9 , Issue 4 , August 2004 , pp. 473 - 484
Copyright
© 2004 Cambridge University Press

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Footnotes

I particularly thank Geir Asheim, Pam Mason, Steve Schilizzi and Cees Withagen for detailed and insightful reactions. I also acknowledge very helpful comments from two anonymous referees, and from participants at meetings of the Australian Agricultural and Resource Economics Society and the European Association of Environmental and Resource Economists, and at seminars at the University of York, the Free University of Amsterdam and the University of Bath. The usual disclaimer applies.