On discount, temporal justice, sustainability and limited foresight

Abstract

Intertemporal resource allocation with zero rate of time preference is discussed. With time translation invariance, the Hamiltonian, i.e. the total welfare flow, is conserved. This conservation law, the counterpart of the energy principle in analytical mechanics, thus expresses intertemporal justice.

The effect of a limited foresight is taken into account. Planning is done within a limited but diffuse time horizon, and planning beyond the horizon is left to future generations. The heritage handed over to future generations is valued in terms of the welfare flow that it makes possible. The result is a goal function with a non-zero discount rate but also with a complement to the utility term, describing the buildup of long-term productive stocks. This extra term thus counteracts the discount of the future. The resulting goal function is shown to be anestimate of the present value of a total welfare.