Optimal Discounting in Control Problems that Span Multiple Generations

The principal contribution of this paper is the linking together of separate control problems across multiple generations using the bequest motive, intergenerational altruism, rational expectations, and solution boundary conditions. We demonstrate that discounting at the market rate of interest is an endogenous characteristic of a general equilibrium, optimal control problem that spans multiple generations. Within the confines of our model, we prove that it is optimal to discount at the market rate of interest the social benefits to distant generations from immediate clean up at toxic waste sites if the current generation that bears the cleanup cost is perfectly altruistic towards future generations. Also, we show that this result holds for alternative assumptions regarding pure time preference. Moreover, the result holds regardless of whether selfish interim generations attempt to undo the provisions made for distant generations. In our distortion-free deterministic model, the evidence for intergenerational discounting at the market rate of interest is compelling.