Asymmetric Input Contracts with Price Leadership and Capacity Constraints

Abstract

This paper considers a vertically related industry where an upstream supplier simultaneously negotiates with two downstream retailers endowed with (possibly) asymmetric bargaining powers, over the purchase of an input. Downstream firms have asymmetric capacities and downstream competition has a price leadership structure. Under linear tariffs, an increase in the upstream supplier's bargaining power towards the large firm induces a positive externality on the small firm's tariff. Under two-part tariff, instead, cross effects vanish. In both regimes, we obtain that, a priori the small firm may end up i) demanding a larger stock of the input and ii) paying less for it. Our model also proves useful to show that the well-known countervailing buyer power hypothesis may not hold because an integrated downstream firm might negotiate a better input price without any pass-through to the final consumers. We mainly relate our analysis to the UK grocery market and to the recent empirical evidence regarding its functioning.