A spatial price oligopoly model for refined petroleum products: an application to a Brazilian case

The production of petroleum refined products in refineries results in the output of a main product and several byproducts. Conventional oligopoly models cannot be applied to analyze oligopolies in the petroleum industry because they do not consider interaction among products on the supply side. A spatial oligopoly equilibrium model is proposed to analyze the Brazilian market, where the number of companies supplying those products is small. The profit maximizing functions of each firm are formulated by considering the optimization of the operations of refineries, as well as the crude oil production of each company. A given refinery may use crude oil, in the refining process, from the production facilities of the company, or buy other types of crude oil on the world market. An algorithm based on the Gauss/Seidel Method and on a relaxation algorithm for solving variational inequalities is developed to find the equilibrium prices and trading flows of the refined products. At each iteration, a profit maximizing nonlinear problem is solved for each firm, by considering that the strategies (production levels) of the other firms are fixed. It is assumed that each firm uses the last information available. The Brazilian market, where the state monopoly is being opened to competition this year, is analyzed. Policy intervention on prices are also analyzed.