Quantity-setting oligopolies in complementary input markets: The case of iron ore and coking coal

This paper investigates the benefits of a merger when goods are complements and firms behave in a Cournot manner both in a theoretical model as well as in a real-world application. In a setting of two complementary duopolies a merger between two firms each producing one of the goods always increases the firms' total profit, whereas the remaining firms are worse o↵. However, allowing for a restriction on one of the merging firms' output, we proof that there exists a critical capacity constraint (i) below which the merging firms are indi↵erent to the merger, (ii) above which the merger is always beneficial and (iii) the lower the demand elasticity is the smaller this critical capacity constraint becomes. Using a spatial multi-input equilibrium model of the iron ore and coking coal markets, we investigate whether our theoretical findings may hold true in a real market as well. The chosen industry example is particularly well suited since (a) goods are complements in pig iron production, (b) each of the inputs is of little use in alternative applications, (c) international trade of both commodities is highly concentrated and (d) a few (large) firms are active in both input markets. We find that due to limited capacity, these firms gain no substantial extra benefit from optimising their divisions simultaneously.