International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), 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 Jannett Highfill and Michael McAsey. 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.