Conditions for Sustainable Optimal Economic Development

17 Pages Posted: 11 Sep 2006

See all articles by Y. Hossein Farzin

Y. Hossein Farzin

University of California, Davis - Department of Agricultural and Resource Economics; Oxford Centre for the Analysis of Resource Rich Economies (OxCarre)


This paper shows that, for dynamic optimizing economies with different types of natural resource, environmental, and human-made capital stocks, a necessary and sufficient condition for permanently sustaining an optimal utility/consumption level is the stationarity of the current-value Hamiltonian. For economies whose development is not exogenously and directly affected by time (i.e., time-autonomous economies), this stationarity condition generalizes Dixit et al.'s (1980) zero-net-aggregate-investment rule of sustainability, which in turn generalizes Solow-Hartwick's sustainability rule. For non-autonomous economies, the stationarity condition is not generally fulfilled, and the current-value Hamiltonian under (over) estimates the true welfare level by an amount equal to the discounted value of the net pure time effect. For the non-autonomous case of a time-dependent utility discount rate, a general condition on the discount rate function (of which the hyperbolic discount rate function is a special case) upholds the results obtained for autonomous cases. The paper concludes with a discussion of policies that promote both optimality and sustainability objectives.

Keywords: Sustainablity conditions, Optimal path, Hamiltonian value, Stationarity condition, Hyperbolic discounting, Green accounting, Intergenerational equity, Social welfare

JEL Classification: O21, Q32, Q0, C61, D90

Suggested Citation

Farzin, Y. Hossein, Conditions for Sustainable Optimal Economic Development. Review of Development Economics, Vol. 10, No. 3, pp. 518-534, August 2006 , Available at SSRN:

Y. Hossein Farzin (Contact Author)

University of California, Davis - Department of Agricultural and Resource Economics ( email )

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Oxford Centre for the Analysis of Resource Rich Economies (OxCarre) ( email )

University of Oxford, Department of Economics
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