Abstract
This paper studies the effect of station density on prices in the retail gasoline market in the Czech Republic. We estimate the impact of the number of competing stations in various drivingdistance ranges around each station on prices. We find that station density has a negative effect on prices; the effect decreases with distance and is statistically significant up to six kilometers. This suggests that the retail gasoline market is local rather than national.
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The application is available both for Android and iOS. Google claims that it has been downloaded more than 100,000 times (the published range is from 100,000 to 500,000) on February 2015. The application’s official web page is http://www.pumpdroid.com/.
For most stations, the price data is almost complete or complete. E.g. in October 2014, 81 % of stations (with at least one price observation in this month) had more than 20 price observations. Most of these prices are reported by the stations or chains. In the remaining cases, the data comes from Pumpdroid users who are motivated to submit new information about prices only after the price changes. This means that there are gaps in time series of these stations. However, these gaps have no economic consequences because the price stays the same when the data are missing. For this reason, we fill in the missing data with the last available price information when computing the price averages.
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We thank Mr. Marcel Matula of Pumpdroid for kindly providing us with the data.
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Appendix A: Modeling the effects of station density
Appendix A: Modeling the effects of station density
The model has a structure of M spokes. Each spoke has a length d _{ i }. There are N+1 firms, where N≤M. Firms have a constant marginal cost c. Firm 0 is located at the center; N firms are located at the extremes of N spokes. Firms are indexed such that firm i is located at the extreme of spoke i. There is a continuum of consumers with mass 1. The mass of consumers which are uniformly distributed along each spoke is 1/M. So, the distribution function of consumers along spoke i is 1/(M d _{ i }).
The consumers behave in the same way as in the Hotelling model. Each consumer buys one unit of goods; the preferences can be described by the utility function U = R−p−T x, where R is the reservation price; p is the price to be paid; T are the transportation costs; and x is the distance to the firm. The demand for the production of firm 0 along the spoke is given as follows

\(D_{0}=\frac {Rp_{0}}{T}\) if there is no competitor.

\(D_{0}=\frac {1}{2}+\frac {p_{i}p_{0}}{2d_{i}T}\) if there is a competitor.
The profit of firm 0 is
The profit of firm \(i \in \{1,\dots ,N \}\) is
We derive bestresponse functions and solve for the equilibrium price \(p_{0}^{*}\). The equilibrium price \(p_{0}^{*}\) is implicitly given by the following equation.
Suppose without loss of generality that there are N _{1} firms at a distance d _{1} from the center, N _{2} firms in distance d _{2} from the center, and so on. Of course, it holds that \(N_{1}+N_{2}+\dots +N_{k}=N\). The distances are indexed such that \(d_{1}<d_{2}<\dots <d_{k}\).
By differentiating the Eq. 2 according to N _{ i } we can express how the equilibrium price depends on the number of firms at a distance d _{ i }:
It follows from the condition (2) that the lefthand side of the equation is negative. The second term on the righthand side is positive. Hence, we may conclude that if you increase the number of firms at any distance level d _{ i }, the price of firm 0 falls:
Suppose that d _{ i }<d _{ j }. We want to compare \(\frac {\partial p_{0}^{*}}{\partial N_{i}}\) and \(\frac {\partial p_{0}^{*}}{\partial N_{j}}\), i.e. what happens with the price if we add a competitor at a distance d _{ i } or at a distance d _{ j }. The comparison of these two effects depends only on the lefthand side of Eq. 3 because the second term on the righthand side is the same for both. Obviously, the absolute value of the lefthand side is decreasing in d _{ i }. Therefore it follows that if we increase the number of firms at a lower distance d _{ i }<d _{ j }, the price of firm 0 falls more:
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Kvasnička, M., Staněk, R. & Krčál, O. Is the Retail Gasoline Market Local or National?. J Ind Compet Trade 18, 47–58 (2018). https://doi.org/10.1007/s1084201702490
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DOI: https://doi.org/10.1007/s1084201702490