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International Journal of Mathematics and Mathematical Sciences
Volume 14, Issue 3, Pages 537-544

An optimal control problem in economics

1Department of Economics, Bradley University, Peoria 61625, Illinois, USA
2Department of Mathematics, Bradley University, Peoria 61625, Illinois, USA

Received 5 February 1990; Revised 2 July 1990

Copyright © 1991 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The first problem in the economics of natural resources is to find the rate at which to extract the resource in order to optimize its value when there are no extraction costs. It is shown that the existence of an optimal extraction path is not guaranteed by a utility function that is merely (strictly) concave, but that the additional requirement of “asymptotic nonlinearity” will assure the existence of the desired optimum.