Conditions for Sustainable Optimal Economic Development

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