An optimal control problem in economics - Jannett Highfill; Michael McAsey (International Journal of Mathematics and Mathematical Sciences)
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.