Abstract
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.
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References
Verhulst, P. F., Recherches Mathématiques sur la Loi d'Accroissement de la Population, Memoirs de l'Academie Royale Belgique, Vol. 18, pp. 1–38, 1845 (in French).
Volterra, V.,Calculus of Variations and the Logistic Curve, Human Biology, Vol. 11, pp. 173–178, 1939.
Leitmann, G.,A Minimum Principle for a Population Equation, Journal of Optimization Theory and Applications, Vol. 9, pp. 155–156, 1972.
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Communicated by G. Leitmann
This research was supported by the Centro Teoria dei Sistemi, CNR, and by the Italian Ministry of Public Education.
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Gatto, M., Muratori, S. & Rinaldi, S. On the optimality of the logistic growth. J Optim Theory Appl 57, 513–517 (1988). https://doi.org/10.1007/BF02346168
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DOI: https://doi.org/10.1007/BF02346168