Savings Growth and the Path of Utility

11 Pages Posted: 19 May 2007

See all articles by Kirk Hamilton

Kirk Hamilton

World Bank

Cees Withagen

Free University of Amsterdam; Tilburg University


We derive an expression relating the change in instantaneous utility to the growth of net (genuine) saving in an economy with multiple stocks and externalities that maximizes welfare in the utilitarian sense. This result is then shown to hold for decentralized competitive efficient economies as well, to yield an extension of the Hartwick rule: instantaneous utility is non-declining along a development path if genuine saving is decreasing. By way of example the rule is applied as a constant genuine saving rate rule in a simple Dasgupta-Heal-Solow-Stiglitz economy. The rule yields a path with unbounded consumption and higher wealth than on the standard Hartwick constant consumption path.

Suggested Citation

Hamilton, Kirk and Withagen, Cees A. M., Savings Growth and the Path of Utility. Canadian Journal of Economics, Vol. 40, No. 2, pp. 703-713, May 2007. Available at SSRN: or

Kirk Hamilton

World Bank ( email )

1818 H Street, N.W.
Washington, DC 20433
United States

Cees A. M. Withagen (Contact Author)

Free University of Amsterdam ( email )

Tinbergen Institute De Boelelaan 1105
1081 HV Amsterdam

Tilburg University ( email )

Postbus 90153
Tilburg, DC Noord-Brabant 5000 LE

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