Linear Supply Function Competition in A Vertically Related Market

Abstract

Policy making and the practice of competition policy requires an assumption to be made on the type or mode of competition, and it is important to accurately anticipate the outcome from the assumed competition mode. It is well known that outputs under hard competition (Bertrand competition) are larger than under soft competition (Cournot competition) in a conventional setting. The aim of this study is to examine the standard outcome by comparing soft competition to hard competition in a vertically related market. The main analytical contribution of this study is the analysis of policy making and practice by building a supply function model. Supply function competition models a situation where competing firms set their production schedules under given market prices. The degree of competition is judged by the slope. When the slope is zero, the strength of the market competition represents Cournot competition. When the slope is large enough, it represents Bertrand competition. Thus, an intermediate degree of the slope seems to reflect an intermediate degree of competition. The market structure in this paper consists of an upstream monopolist and two downstream firms. I assume that the upstream firm faces a commitment problem due to secret offerings for a trading contract by a linear pricing contract or two-part tariff contract. I model the negotiation for the contract by Nash bargaining considering observability of a breakdown in the negotiation. At equilibrium, I obtained unconventional results under the two-part tariff contract in the supply function model, as well as in comparison to Cournot competition and Bertrand competition. Specifically, wholesale prices under soft competition are lower than under hard competition. Thus, my results show that the total quantity and total surplus under soft competition are larger.