A MATHEMATICAL MODEL OF A MONOPOLISTIC WORLD OIL MARKET

The recently demonstrated power of the Organization of Oil Producing Countries (OPEC) to act as a monopolist has brought much attention to the issue of the utilization of energy resources. The development of energy alternatives by the oil consuming nations provides them with a means of augmenting their capacity to adjust oil purchases to price, and this appears as the most likely recourse in countering the OPEC's power. This thesis explores the development of energy alternatives by the oil consuming nations and the pricing of oil by the OPEC, and presents a methodology for forecasting oil prices and purchases. This methodology also selects the optimal plan of development of energy alternatives by the oil consuming nations.;In this thesis we analyse the decisions of the consuming nations in detail, and, unlike the existing studies, we consider their full impact on the producers' decisions. Another consideration that is original to this thesis is the impact of the oil pricing policy on the prices of other goods, which affects the buying power of the producers and, consequently, their net benefits. This factor is expected to enter into the decisions of the oil producers as they seek pricing policies that will maximize their benefits.;Our analysis of the oil market is based on the simultaneous optimization of the benefits of the oil producers and the consuming nations. The variables of our decision space consist of the producers' decisions--the oil prices--and the consuming nations' decisions--the oil purchases and the decisions to undertake the development of energy alternatives. We employ a "simulation" approach in which the energy development plan of the consuming nations is specified, and its value is assessed from the evaluation of the remaining decision variables. This evaluation is performed by a mathematical model that solves the producers' optimization problem by employing Dynamic Programming. The specified energy plan enters into the mathematical model through the demand curves used to describe the consuming nations' oil purchases in terms of price. These demand curves reflect the consumers' capacity to reduce oil purchases at increased prices, to the extent made possible by the energy alternatives that the specified energy plan provides. Since a plan may include some entirely new and perhaps hypothetical alternatives, the estimation of these demand curves cannot rely on traditional econometric techniques. Instead, we developed a method for the derivation of the demand curves that employs the technological and cost characteristics of the energy alternatives in the specified plan. Our method uses a parametric price equilibrium model, for the solution of which we developed a finite algorithm. This algorithm solves the parametric linear complementarity problem, to which the demand curve derivation problem is reduced.;Although the analysis of the world oil market has been addressed by other investigators, their work has not fully accounted for the potential of the oil consuming nations to influence oil pricing policy. While analyzing the decisions of the oil producers in some detail, the existing studies have taken as fixed certain key decision variables of the oil consuming nations, thus reducing the number of options open to these nations in selecting an optimal energy policy. These decision variables dealt with the development of energy alternatives; these were implicitly postulated when the demand curve for oil imports by the consuming nations was specified.