PRICE DISCRIMINATION AT THE LINKS

I. INTRODUCTION The theoretical analysis of price discrimination and nonlinear pricing generally has been ahead of its empirical application. This is not surprising because theoretical treatments invariably involve restricted, mathematically pure settings in order to prove or illustrate a specific theorem (Goldman et al., 1984; Katz, 1984; Oren et al., 1982; Shmanske, 1991a; 1991c; Spence, 1980; Spulber, 1992). Thus, even though it is perfectly obvious that sellers do not use uniform pricing, it is far from obvious how to measure empirically or test propositions about price discrimination with real world data. Therefore, the applied analysis of price discrimination either takes the form of descriptive case studies of various industries including medicine (Kessel, 1958), theme parks (Oi, 1971), telecommunications, and even gambling (Shmanske, 1991b), or it takes the form of a simulation experiment (Shmanske, 1993). There is a noticeable lack of statistical analysis of either the extent of price discrimination or the effect of price discrimination on other variables. The primary goal of this paper is to develop an empirical measure that captures in a significant manner the effect of price discrimination. At stake is a categoric improvement on the typical demand study that regresses quantity (or revenue) on a vector of demand shift variables and the price. One is usually interested in obtaining estimates, in either single or multiple equation settings, of the price elasticity or slope of a demand function, as well as estimates of the coefficients of the demand shift variables. This is all straightforward enough if, as in simple theory, sellers use uniform pricing. Unfortunately, sellers never do. In light of this fact, what is the proper measure of price in such an equation? There is no established answer to this question. Empiricists use whatever measure is available, including median price, average revenue (i.e., total revenue divided by quantity), "regular" or modal price, advertised price, suggested retail price, and so on, as long as the appropriate negative coefficient is achieved. If the theory of price discrimination suggests anything at all for practical estimation, it is that the pricing function cannot be captured with one variable. This paper examines several candidates for the variable to be added. As the basis for empirical measurement, this paper uses the public access golf course industry in the San Francisco area. The golf course industry provides an attractive opportunity to study price discrimination because of the wide variety of pricing policies used, including two-part pricing, quantity discount pricing, time-of-day pricing, seasonal pricing, day-of-week pricing, and further market segmentation by age or residency. II. THE DEMAND FOR GOLF A. Golf Course Operations Two conceptually different types of golf courses are surveyed in this study: municipal courses and private, daily fee courses. Daily fee courses are run for profit, while municipal courses are owned by a city, county, or other governmental jurisdiction. Municipal courses can be run by city employees, or their operations can be contracted out to a golf course management company. When contracted out, there are often restrictions on some of the policies used - for example, the mandatory provision of reduced rates for senior citizens or residents. Thus, policies employed by municipal courses often are hammered out in city council meetings with an eye toward political ramifications, and not necessarily to maximize a pecuniary value. Additionally, there is a wide variety in the type of contracts that cities will enter into with golf course management companies. Some contracts call for lump sum payments, essentially making the management company the residual claimant. Others call for profit or revenue sharing of different amounts on different items. For example, the city may get x% of the green fee revenues and y% of the cart rentals. …