Market prices, spatial distribution of consumers and firms' optimal locations in a linear city
We study a game of spatial competition in prices. In particular, we focus on the linear-city duopoly model to see what we can learn about the distribution of consumers, which is not required to be uniform-as in the original Hotelling model. Using variation in firms' prices and costs, we identify points of the distribution of consumers. Based on these points, we estimate the spatial distribution of consumers along the linear city. We apply our methodology to a dataset of prices of two gas stations on a straight highway. By estimating the distribution of consumers, we are able to find the optimal location of an entrant gas station. Using our estimated distribution of consumers and the entrant's optimal point, we simulate welfare gains under counterfactual locations of an entrant.