Ebook Number of Sellers, Average Prices, and Price Dispersion
It has been shown theoretically that price dispersion can result under a variety of different circumstances. Some suggest that dispersion arises as a simple extension of standard monopolistic competition. Others adopt a search-theoretic framework that suggests price dispersion is generated when some consumers do not know the location of a low price. Both approaches are widely accepted, yet their predictions sometimes diverge concerning the correlation between the number of sellers in a market and the moments of the resulting equilibrium distribution of prices.
Intuition might suggest that in markets more densely populated with buyers, the resulting higher number of sellers would be associated with a “more competitive” market, characterized by lower prices and less price dispersion. These associations do appear in modifications of the standard models of monopolistic competition that allow for price variation across sellers. However, this is not necessarily the case for models that adopt the search theoretic approach to price dispersion. For instance, Rosenthal (1980) finds conditions under which “increasing the number of sellers … induces [an increase] in the sellers’ … equilibrium [price] distribution” (p.1579). If markets with fewer sellers have higher search costs, then Samuelson and Zhang (1992) develop a model in which “as search costs increase, prices and price dispersion may decrease” (p.55). Lest one thinks that such models are isolated and special cases, consider the well-known paper by Stiglitz (1987) whose very title “Are Duopolies More Competitive than Atomistic Markets?” highlights the potential for “counter-intuitive” results, namely that markets with a larger number of competitors may have higher prices, with the result depending on assumptions regarding search costs.
Given this theoretical ambiguity, the purpose of this paper is two-fold. First, we highlight the sources of the conflicting theoretical predictions. Section II reviews the approaches to generating an equilibrium price distribution based on monopolistic competition and on search-theoretic models. For the monopolistic competition approach, we develop two alternative modifications of the classic model presented by Perloff and Salop (1985). For the search-theoretic approach, we consider a variant of Carlson and McAfee (1983), a model based on optimal sequential search by consumers with heterogeneous search costs, and Varian’s (1980) model of sales that generates a mixed-strategy pricing equilibrium. In each model, the number of sellers in the market is determined by a zero-profit condition, and a change in the number of sellers occurs if there is a change in market size (in terms of the number of consumers) or a change in the fixed costs of production. For each of the four models considered, we derive the predicted correlation between a change in the number of sellers (seller density) and the first two moments of the equilibrium price distribution, namely the average price in the market and the level of price dispersion.
The second purpose of this paper, presented in Section III, is to use four unique and comprehensive firm-level data sets from the retail gasoline industry to estimate the relationships between seller density and the level and dispersion of gasoline prices. The empirical literature that addresses associations between seller density, average prices, and price dispersion is relatively small when compared to the vast theoretical work on the subject, in part because of problems related to market definition, access to firm-level data that could be used to distinguish differences in product characteristics, and a researcher’s ability to survey all of the relevant prices and market conditions at a single point in time. Fortunately, our empirical work relies on four data sets that contain information on the location and characteristics of the over 3,000 gasoline stations in the San Diego, San Francisco, Phoenix, and Tucson areas. Further, the prices contained in each of the data sets were collected on a single day, so that we have four complete “census” price surveys. Our data provide us with a rare opportunity to examine the relationships between the number of competitors, average product prices, and price dispersion for a frequently-purchased, homogeneous product.
Controlling for station-level differences, we find convincing evidence across all four geographic areas that in markets with a higher number of sellers, there is a statistically significant, albeit modest, decrease in both the mean price and price dispersion for regular unleaded gasoline. This evidence is consistent with variants of the standard models of monopolistic competition, but is at odds with some of the predictions of widely cited search-based price dispersion models. In the conclusion, we suggest some features that could be added to often-used search-theoretic approaches to improve their ability to explain what we observe.
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