Price dispersion and accessibility: a case study of fast food.

• Author: Stewart, Hayden

1. Introduction

   Who pays more for food? This question has been a subject of debate among researchers. Most focus on prices at supermarkets and other grocers and ask whether retail food prices tend to be higher in markets with a greater proportion of lower income consumers, minority consumers, or consumers with some other trait. Recent studies include Kaufman et al. (1997), Hayes (2000), Frankel and Gould (2001), as well as MacDonald and Nelson (1991). A few other studies have examined prices at restaurants, such as Lafontaine (1995), Graddy (1997), Jekanowski (1998), and Thomadsen (2003).

   Being able to explain variation in average retail food prices could be useful for government agencies engaged in price measurement. However, it has also been a goal of researchers who are concerned with social equity. According to Graddy (1997), there is a perception that retailers engage in unfair commercial practices in lower income, minority neighborhoods. She points out that retail establishments have been targeted during some riots in urban centers.

   Empirical evidence does confirm some systematic dispersion of prices. According to Kaufman et al. (1997), who conducted a review of 14 prior studies, grocery prices tend to be higher in urban centers than in suburban markets. Some speculate that greater access to supermarkets in the suburbs is responsible. As compared with central-city stores, supermarkets are argued to offer the lowest prices and the greatest range of brands, package sizes, and quality choices. MacDonald and Nelson (1991) find that a fixed market basket of goods costs about 4% less in suburban locations than in central-city stores. However, they concede that their analysis is not based firmly in economic theory; rather it is only exploratory, due to the lack of a precise model.

   Studies have been less successful at explaining how and why prices might vary with the demographic characteristics of a market. First, recent studies of grocery prices have reached mixed results. For example, Hayes (2000) does not identify a statistically significant relationship between grocery prices and the income level of a market's residents. By contrast, Frankel and Gould (2001) find that prices are highest in markets with more income inequality. In other words, prices are found to be highest where there are more lower income or more higher income households. The lowest prices are found in markets with more consumers in between these two groups. Second, even when they are significant, there is the problem of interpreting estimation results. For example, the model of Frankel and Gould (2001) does not allow those authors to determine whether their findings are due to differences in consumer behavior, costs, or differences in the characteristics of stores and the quality of the services they provide.

   Similar results have been obtained by researchers studying restaurant prices. For example, Graddy (1997) finds that prices are higher in neighborhoods with a higher proportion of black and lower income consumers. However, her model does not identify whether the observed dispersion of prices stems from differences in costs and demand conditions or whether it reflects discriminatory pricing strategies among retailers.

   Utilizing a novel set of data on the price of a fast-food meal and the location of fast-food restaurants in a major urban area, this study tests the structural model of spatial competition developed by Salop (1979). Estimation results based on this model can be easily interpreted. According to this model, cost and demand conditions first determine how many stores choose to locate in a market. Holding all other factors constant, the more firms in a market, the greater access consumers will have to establishments on average. Greater access is defined to mean that consumers will have lower transportation costs and better substitutes for the services of any particular store. Stores will likewise have less market power and price more competitively.

   This study focuses on fast-food prices because the authors believe such an analysis may be more easily undertaken than studies of grocery prices. Arguably, two different outlets affiliated with the same fast-food chain supply relatively homogeneous goods and services. This fact may alleviate the possibility that differences in store formats are confounding the results of studies on grocery prices, such as central city stores being smaller or offering a narrower range of goods and services than suburban supermarkets. (1)

   The results of this study show that cost and demand factors influence prices through their effect on access. For example, consider a community where an increase occurs in demand, such as through an increase in the population or in the income of existing residents. Holding all else constant, this study finds that firms would likely respond by opening more outlets in the community. Consumers would then have more and better substitutes for the services of any particular store. In turn, restaurants would have more competitors, less market power, and charge slightly lower prices. In this way, low population levels and low levels of income might be associated with not only more limited access, but also higher prices. Moreover, we show that the reduced form of our model closely resembles the type of model estimated in past studies, including Graddy (1997), against which we compare our results.

2. Theoretical Framework

   In models of spatial monopolistic competition, consumers are dispersed over a market area that is represented with a line, circle, or other geometric form. Hotelling (1929) proposes a linear market, while Salop (1979) extends Hotelling's model and develops a circular market with an outside, homogeneous good. In that model, the homogeneous good is supplied by a competitive industry. In addition, there are also spatially dispersed firms, which share a common fixed cost, incur a constant marginal cost of production, and sell a second product. The supply of this second good is monopolistically competitive. A number of researchers have further expanded on models of spatial competition, including work by Capozza and Van Order (1978, 1980), MacLeod, Norman, and Thisse (1988), Rath and Zhao (2001), and Puu (2002).

   In Salop's (1979) model, a consumer's costs for purchasing the second good include the retail price (i.e., the mill price) and his or her costs for transportation to a retail store. (2) It is assumed that only if the total cost of obtaining the second item is below the consumer's reservation cost will the consumer purchase a given number of units of this good. (3) The consumer will buy only the homogeneous good otherwise. Significant transportation costs can therefore prevent suppliers of the second good from concentrating all of their production in one location. Customers may incur a prohibitively large cost for travel to this concentrated site.

   Competition among suppliers of the second good is imperfect in the model of Salop (1979). Because they incur a nonzero cost of transportation, consumers prefer to patronize the nearest firm if mill prices are equal. The demand for goods from firm i is then a function of the price of i and the price of all other firms that are sufficiently close to i. Using this model, Salop (1979) derives the demand schedule facing a representative firm and shows that prices for the second good are a function of transportation costs due to their impact on a firm's market power.

   Prices for the second good may decrease with the number of firms in a market under some assumptions about firm behavior. Salop (1979) shows that, as the number of firms in a market increases, each firm will be spatially closer to one of its rivals. Consumers may have more and better substitutes for the goods offered by any single firm. In general, the price charged by firm i will move closer to i's marginal cost. A necessary assumption about firm behavior is that each firm chooses a best price, given the perception that all other firms hold their prices constant. (4) Empirical evidence that prices tend to decrease with the number of firms in a market has been provided by Bresnahan and Reiss (1991).

   The number of firms in a market is determined in advance of prices. In the model of Salop (1979), just enough firms enter a market so that, once prices are later determined, economic profits will be zero. (5) The resulting equilibrium is termed a symmetric zero-profit Nash equilibrium. For instance, given a distribution of firms that are poised to make zero economic profits, a decrease in fixed costs or an increase in demand would allow for positive economic profits. New firms will then enter the market, and, in turn, each firm's market share will decrease. Expected profits then fall with market shares. This process will continue until all firms can once again expect to earn only a zero economic profit.

   In this study, we use the model of Salop (1979) to motivate a system of structural equations that serve as the basis for an empirical analysis. We assume that there are M circular markets and consumers in each market are spatially dispersed. We denote the aggregate demand of consumers in each of these markets, m = 1, ..., M, as [D.sub.m]. We allow [D.sub.m] to vary with the number of consumers in each market. Moreover, we allow the demand for fast food to depend on the social and demographic characteristics of the consumers. However, for prices below the consumer's reservation cost, quantity demanded does not vary with price; rather, consumer demand is inelastic. Consumers pay the retail price and incur a nonzero cost for traveling to restaurants. In market m, let the number of restaurants be [N.sub.m] and all other factors that influence transportation costs be [T.sub.m]. There is free entry, and [N.sub.m] is determined such that economic profits are zero. Also, we assume that the fixed cost associated with operating a restaurant varies across markets...