The Effects of Third-Degree Price Discrimination in Oligopoly

Retail firms and restaurants commonly offer senior citizen discounts. I suspect this practice is not motivated by altruism. Rather, the behavior can be better explained as profit-maximizing price discrimination; these firms are setting a low price in a market which probably has high elasticity of demand. But why should the demand of senior citizens be more elastic than average? One possibility is that elderly people have below-average income and they would not eat out if restaurant prices were high. Perhaps a more plausible explanation is that retired people simply have more time on their hands to spend commuting across town to take advantage of discounts. The purpose of these discounts may then be to lure senior citizens away from other restaurants rather than to get them out of the house. The analysis of third-degree price discrimination has a long history (A. C. Pigou, 1920; Joan Robinson, 1933), and two articles on the subject have recently appeared in this Review (Richard Schmalensee, 1981; Hal Varian, 1985). The industry structure in these analyses is monopoly. But an explicit model of some form of competition is obviously needed to study discriminatory discounts meant to attract customers from rival firms. And even discounts meant to get people out of the house may have an oligopoly analysis which is qualitatively different from their monopoly anlysis. In this paper I present a simple duopoly model of a differentiated-products industry. I show that a firm's price elasticity of demand in a market can be expressed as the sum of two parts: the industry-demand elasticity and the cross-price elasticity. The first measures the tendency of consumers in a market to stay home when the price goes up; the second the tendency to switch suppliers. In the monopoly case (in which the crossprice elasticity is zero) and the collusive case (in which the cross-price elasticity is irrelevant), discrimination between markets is due to differences in industry-demand elasticity. In the noncooperative oligopoly case, equilibrium price differentials can be accounted for both by differences in cross-price elasticity as well as differences in industry-demand elasticity. Total industry output when the firms can discriminate between two markets is compared to what it would be if discrimination were impossible. Which regime has larger output depends on the sum of the "adjustedconcavity condition" and the "elasticity-ratio condition." The first predominates when the rival products are poor substitutes and the firms have approximate monopoly power, while the second predominates at the other extreme where the products are close substitutes and the firms have almost no market power. The adjusted-concavity condition compares the relative curvature of demands in the two markets and was originally discovered by Robinson (1933) in her analysis of monopoly price discrimination. The elasticity-ratio condition compares the relative difference in industry-demand elasticity between the two markets with the relative difference in cross-price elasticity. According to the elasticity-ratio condition, a discriminatory discount due to high industry elasticity of demand would be "more likely" to increase total output than one due to high cross-price elasticity. The effect of discrimination on profit is also discussed. The distinction made here * Department of Economics, University of Wisconsin-Madison, Madison, WI 53706. This paper is a revision of part of my doctoral dissertation. I am grateful to Steve Matthews, Ken Judd, and John Panzar for guidance in this research. I also thank seminar participants at Wisconsin, the Justice Department, and the 1986 Econometric Society Meetings in New Orleans, and the discussant Martin Perry. The excellent comments of the referees improved the exposition of the paper.