A comment on mixed oligopoly spatial model: the non-uniform consumer distribution

Market prices, spatial distribution of consumers and firms’ optimal locations in a linear city

“…As Tabuchi (1994) and Shuai (2016) do, we assume that finding the optimal location is equivalent to minimizing consumers' total transportation cost. 12,13 If the entrant firm is to be located between the two incumbent firms, then we need to find the consumer x such that the sum of consumers' transportation costs to the right and to the left of it are equal.…”

“…We deal with this issue in the following section. 12 More broadly speaking, Shuai (2016) explains that, if demand is sufficiently inelastic (which is the case of the gasoline demand), maximizing welfare is always equivalent to minimizing consumers transportation cost. 13 If we think in our empirical application, the goal of the social planner (the General Direction of Highways) is to authorize the construction of a new gas station in such a way that the total probability of vehicles running out of gas is minimized.…”

“…Perhaps the most implausible assumption in the original model by Hotelling (1929) is the uniform distribution of consumers along the straight interval. In fact, since its original formulation, many authors have studied the linearcity model assuming instead that consumers are non-uniformly distributed -for instance, Neven (1986), Tabuchi and Thisse (1995), Anderson et al (1997), Shuai (2016). As these (and many other) authors noticed, consumers usually concentrate on certain sections of a straight interval -for instance, around the center of the interval.…”

“…Some authors have previously analyzed Hotelling's linear-city model assuming a more general class of distribution of consumers. SeeNeven (1986),Tabuchi and Thisse (1995),Anderson et al (1997),Torrisi (2011), Shuai (2016.19 As we have detailed extensively in footnote 8, in our empirical application we cannot assume that individual gas stations' posted prices have an impact on wholesale prices and Brent crude oil prices: no gas station has enough power to determine the evolution of the price of fuel commodities. However, this assumption may not be realistic if there we study dominant-market firms (which may influence wholesale prices).20 These measurement errors could arise due to modeling error, random idiosyncratic facts and/or firm optimization error.…”