Location Decisions in a Natural Resource Model of Cournot Competition

This article focuses on the location decision of firms when competing in a duopoly. Using a spatial Cournot setting, we evaluate what is the optimal location decision of both firms in the linear city. Our original contribution is that firms are dependent on a natural resource input to be able to produce the output sought by the consumers, and that natural resource is controlled by a monopolist, not related with any of the downstream firms. We assume that the natural resource is located in one of the extremes of the market. As an example, we can think of the Port locations, where most important raw materials converge to and an intermediary firm controls the shipping process. Therefore, we solve a three stage location game, where in the first stage downstream firms choose their location, and in the next stages upstream and downstream choose how many quantities they sell in the market, assuming that both firms must sell their product in all points of the linear city - an assumption that is common in the literature. We assume as well that the downstream firms support both input and output transportation costs. We analyze how that location outcome changes with the unit input transportation costs, and what are the consequences on the upstream and downstream firms' profits, input price, and social welfare. We also analyze what would be the optimal decision if a social planner was allowed to decide the location of both downstream firms. We conclude that downstream firms agglomerate independently of the unit input transportation cost. In addition, increases in the unit transportation cost bring the plants closer to the natural resource location, as initially expected. Moreover, the upstream firm loses more profit than the downstream firms when the input transportation conditions deteriorate. When we consider the problem of a social planner, we conclude that the location that firms choose is nearly the same than the location that maximizes total welfare in the economy, which happens due to the two reasons: there is weak competition between the two firms, which is induced by the quantity competition framework; and also because firms when maximizing their profit are also concerned with the minimization of total transportation costs, which is the main objective of a social planner.