Is sustainable growth optimal?

This paper analyzes sustainable growth in a stochastic environment, with human extinction as a possible outcome. The basic constraint of sustainability is that consumption never decreases over an infinite horizon, which requires that the probability of extinction be maintained at zero. We show that this problem can be examined in a standard optimal-growth model. Under certain conditions, the solution of this problem is a corner solution with probability of survival equal to one, at the cost of economic growth. These conditions depend on the initial development level and on the elasticity of utility with respect to consumption. In some circumstances, which depend on the social discount rate, optimal-growth paths do not exist. In these situations, the sustainable-growth concept has a clear autonomy with respect to the usual optimality criterion.