Hartwick’s Rule and Economic Conservation Laws

8. Concluding Remarks

In the existing studies on the intergenerational equity problem of optimal capital accumulation and exhaustible resource extraction, an investment rule, Hartwick’s rule, has been proposed. The rule asks to keep the total value of net investment equal to zero. In this paper, we use conservation laws to investigate investment rules for intergenerational equity and Benthamite utility maximization, respectively. From a simple conservation law based on the Max-Min principle for intergenerational equity, we obtain the generalized investment rule indicating the value of net investment equal to a constant, which is sufficient for constant consumption. However, in the Benthamite utility maximization the investment rule as a conservation law is the summation of the discounted difference in value of utility from total wealth and the investment rule from the Max-Min principle. The investment rule in the Benthamite utility maximization is reduced to the rule from the Max-Min principle whenever the discount rate approaches zero. This means that Solow’s Max-Min principle applies to the Benthamite problem if and only if there is no time preference.