Sustainable development, the Hartwick rule and optimal growth

Defining sustainable development as non-declining utility, the consistency of this concept with the Hartwick rule and optimal growth is explored when resources are exhaustible. A simple proof that a generalized Hartwick rule is necessary and sufficient for constant consumption is derived. The existence of a maximal constant consumption path is shown to depend critically on the elasticity of substitution; if this is less than 1, consumption declines; if it is greater than 1 then consumption is not maximal; if it is equal to 1 (the Cobb-Douglas case) then existence is proved. Consumption can increase along an optimal path if the pure rate of time preference is 0; if it is non-zero then consumption declines. Copyright Kluwer Academic Publishers 1995