Positively Sloping Marginal Revenue, CES Utility and Subsistence Requirements

Abstract

The possibility that marginal revenue may possess a positive slope has long been recognized as important. In her classic The Economics of Imperfect Competition, Joan Robinson [14] accorded considerable significance to the possibility and investigated it at length. Despite Robinson's insights, upward sloping marginal revenue functions remained largely a curiosity, widely regarded as an overly stringent perversity unlikely to occur in reality. Considerable doubt was cast on this view when in 1980 A. A. Walters [20] reported the presence of positively sloping marginal revenue in the pricing policies of the Port of Singapore. The case for upward sloping marginal revenue was furthered by Formby, Layson and Smith's [8] straightforward demonstration that upward sloping marginal revenue schedules are very easily produced and can never be ruled out because simple parallel shifts in strictly convex demand and/ or rotations always transform demand schedules with downward sloping marginal revenue into ones with positively sloping schedules.' This strongly suggests that no theoretically reasonable restrictions can be placed on the behavior of marginal revenue because to do so would rule out such simple transformations as parallel shifts or rotations in demand. Such restrictions would be too stringent to be acceptable. Upward sloping marginal revenue has found important application in such diverse topics as catastrophe theory [3], third-degree price discrimination [13], dual equilibria and monopolistic competition [11], specific taxes and quality [2] and international trade [7].2 The significance of non-monotonic marginal revenue functions is further underscored by the fact that the presence of upward sloping marginal revenue significantly affects the sign of comparative static results (for example, see [18, 260; 15; 16; 2]). A shortcoming of previous analyses lies in the fact that they draw conclusions from consideration of slope, level and curvature of the demand schedule alone. The behavior of marginal revenue derived directly from the more fundamental basis of utility theory has not been examined. This paper takes up this question, employing Wold's theorem to analyze marginal revenue