OPTIMAL UTILIZATION OF EXHAUSTIBLE RESOURCES

Abstract

The problem of optimal utilization of exhaustible resources is taken up in this thesis. A simple economy with an exhaustible, finite resource and capital input has been considered. Provision has been made for using part of the output of the economy in research towards developing alternative technology/technologies free from present resource constraints. The satisfaction to the society has been maximized without intertemporal discounting of future satis faction. Since the time horizon cannot be fixed before hand a terminal criterion has been proposed to determine the final time. Amodel of this economy has been developed resulting in a Bolza problem of control. Pontryagin's maximum principle has been used to obtain the necessary conditions for optimality. Gradient methods have been used to obtain the optimal solutions. A methodology has been proposed to determine the functional relationships for various functions to be used in the simulation of the model. Results have been obtained for a number of parameter values and sensitivity of the solutions to parameter changes have been discussed. Amodel of economy with multiple research projects has been developed for optimal utilization of the output in consumption and alter native technologies. Model with independent research projects has been studied in some detail and a special class of interdependent projects has also been investigated. Some

useful results have been obtained. Finally,a methodology has been given for developing empirical relationships for terminal values and control variables as functions of most important parameters and their usefulness is out lined.