Nonlinear pricing in an oligopoly market: the case of specialty coffee.

Firms that use nonlinear pricing may distort product characteristics away from their efficient levels. This paper offers the first empirical study of this issue. Using data from a specialty coffee market, I estimate a structural utility model to compute consumers' benefits from changing products' sizes. I then compare the estimated benefits to cost data. Design distortions are relatively large for products not targeted to the highest-demand consumers. Distortions decrease toward zero with drink size for products with the largest profit margins. These results support some of the central predictions from nonlinear pricing theory, including "no distortion at the top."

1. Introduction

* Nonlinear price schedules are characterized by marginal prices that vary with product size or quality. The most common nonlinear prices are quantity discounts and multipart tariffs. Nonlinear pricing appears in competitive markets when marginal or average costs change with product size, but firms with market power also may use nonlinear prices for second-degree price discrimination. When consumers hold private information about their tastes, a monopolist or oligopolist can use nonlinear pricing as a screening mechanism to induce different types of consumers to buy different products. The pricing strategy is generally coupled with product design decisions that determine how much of a product a consumer will receive. Screening incentives may lead a firm to make a small version of its product "too small" in order to collect more profit from consumers who purchase the larger version.

The modern theoretical second-degree price discrimination literature was initiated by Mussa and Rosen (1978) and Maskin and Riley (1984). (The abbreviation "MR" refers to the contributions of both pairs of authors.) MR consider a monopolist's design of a price-quantity (1) menu when consumers hold private information over a scalar taste parameter. The equilibrium product menu offers the highest-demand consumer an efficiently sized product, and all other buyers self-select into inefficiently small purchasing options. The prices that induce this allocation often include quantity discounts that are unrelated to costs. Competition has been introduced to the MR setting in a variety of ways. (2) For my purposes, the most relevant models of oligopoly nonlinear pricing include a consumer population with private information over vertical and horizontal characteristics. In this case, Rochet and Stole (2002) and Armstrong and Vickers (2001) show that, with sufficient (but not absolute) competition, the equilibrium nonlinear price schedule is "cost plus fee" and product allocations are efficient. When competition is weakened, product menus are typically between the MR allocation and the efficient one.

In this paper, I present a novel empirical study of product design efficiency under nonlinear pricing. I estimate the patterns of allocative distortions that follow from oligopolistic firms offering product menus with quantity discounting. I use the estimates to evaluate whether (and which) distortion patterns predicted in the theoretical literature are realized empirically. I consider the market for specialty coffee (3) near the University of Virginia (UVa), where coffee shops follow the common practice that larger drinks have lower per-ounce prices than smaller drinks. I specify a structural econometric utility model in which consumers vary in their vertical preferences for the shops' products and in their horizontal characteristics regarding their locations relative to the shops. The utility model is estimated using aggregate sales data and information on product and market characteristics. I use the utility estimates and cost data to compare consumers' benefits and the shops' costs for an additional ounce of a drink. This provides an estimate of the average distortion in product size for consumers who self-select into each purchasing option.

The estimated product allocation corresponds to some of the central predictions of second-degree price discrimination theory. Product sizes are close to efficient for the largest, most expensive espresso drinks; this mirrors the "no distortion at the top" result from theory. Distortions exist for the other drinks--these products are generally too small--but inefficiencies decrease toward zero for products of increasing size and with the largest price-cost margins. Although the market studied here is of limited interest to policy makers, my empirical methods are applicable to a variety of markets. Further, the conditions that lead to distorted product designs are not restricted to traditional second-degree price discrimination settings. In many situations, market power and asymmetric information matter for the design and pricing of consumer products or services.

Product design and efficiency have been central to the theoretical nonlinear pricing literature, but empirical research on second-degree price discrimination has primarily focused on other aspects of this pricing strategy. Many studies have asked whether observed price dispersion may be attributed to price discrimination. For examples, see Shepard (1991), Borenstein and Rose (1994) and Busse and Rysman (2005). Recently, other research has used structural econometric methods to analyze the welfare effects of observed and counterfactual market activity. Cohen (forthcoming) and Verboven (2002) estimate markup patterns under equilibrium pricing assumptions and evaluate whether price discrimination occurs in paper towel and European auto markets, respectively. Miravete's (2002) research on telephone service pricing and Clerides' (2001) study of book publishing investigate the importance of unobserved consumer heterogeneity on product selection and welfare in monopoly markets. Ivaldi and Martimort (1994) answer similar questions with data from French farmers who purchased energy from competing firms. Leslie's (2004) study of monopoly pricing of theater tickets and Cohen (forthcoming) compare the distribution of welfare under observed and counterfactual pricing schemes. Crawford and Shum's (2007) analysis of monopoly cable TV firms is most similar to the present paper. They estimate the efficiency properties of cable TV packages under an assumption of optimal pricing and product design by cable firms.

This paper is organized as follows. In the next section, I describe the UVa coffee market. I specify the empirical model of consumer utility in Section 3. Section 4 describes the data and how demand is identified. I also discuss what can be inferred about distortions from the data alone, without the utility model. The estimation strategy is described in the following section. In Section 6, I present the estimated utility parameters and report measures of product design distortions based on these estimates and the cost data. The final section concludes.

2. The market for specialty coffee

* In the late 1960s, an interest in gourmet coffee began to grow in America, culminating in the recent specialty coffee boom. (4) Like many U.S. markets, UVa's main campus ("central grounds") is served by several specialty coffee shops. During the sample period of February and March 2000, five firms operated nine coffee shops on campus or in the surrounding neighborhood. The ARAMARK Corporation had four Greenberry's franchises; Espresso Comer, Starbucks, and Espresso Royale Caffe each operated one coffee shop on the UVa "Corner," a cluster of restaurants and shops adjacent to campus; and Higher Grounds had kiosks in the east and west cafeterias of the UVa Health Sciences complex. (5) The positions of the shops are illustrated in Figure 1.

Although nine shops served the market, it was never the case that all shops were open at once. The off-campus shops (Starbucks, Espresso Royale and Espresso Comer) were open every day of the week from 7 am or 8 am until about midnight, but the other shops' schedules varied. Most variation in operating hours followed the opening and closing of the University facilities in which on-campus shops were located. This variation in schedules affected consumers' choice sets in a way that is useful for identifying the parameters of the empirical model. See Table 1 for information on the shops' operating hours.

[FIGURE 1 OMITTED]

The coffee shops varied in the breadth of their menus, but all offered regular coffee. (6) Each shop employed nonlinear pricing. Firms with multiple coffee shops set one price schedule for all locations, and firms did not adjust their prices as competitors opened and closed. The sample period witnessed almost no price variation. Only Espresso Royale made any price changes, and this was just for one drink size in one product variety. (7) The pricing of two chains (Greenberry's and Higher Grounds) was regulated by the University because these firms operated their shops in UVa facilities. I was told by the owners of Higher Grounds that university oversight did not affect their pricing practices, but ARAMARK representatives reported that the University placed a binding ceiling on the prices charged at the Greenberry's shops. The prices at campus locations could be no higher than at an off-campus (unregulated) Greenberry's.