On Hartwick’s Rule for Constant Utility and Regular Maximin Paths of Capital Accumulation and Resource Depletion

Hartwick’s rule of investigating resource rents in an economy with producible capital and exhaustible resources becomes, in a general model of heterogeneous stocks, a rule whereby the total value of net investment (resource depletion counting negative) is equal to zero. It is shown that holding the discounted present value of net investment constant is necessary and sufficient for a competitive path to give constant utility. Conditions for the general rule to give a maximin path are also discussed.