On the optimality of the logistic growth

The rate at which a population should grow is determined by finding the best trade-off between the loss due to the deviation from a target population size and the loss associated to the growing effort. It is also shown that, in the case of infinite-time horizon and quadratic loss functions, the optimal growth is logistic. This research was supported by the Centro Teoria dei Sistemi, CNR, and by the Italian Ministry of Public Education.