International Journal of Mathematics and Mathematical Sciences 
Volume 14 (1991), Issue 3, Pages 537-544
doi:10.1155/S016117129100073X

An optimal control problem in economics

Jannett Highfill1 and Michael McAsey2

 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

Abstract

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.