Raising Rivals’ Costs When the Downstream Firms Compete in Stackelberg Fashion

The aim of this paper is to investigate the raising rivals’ cost effect when the downstream competition follows Stackelberg pattern. We find that the raising rivals’ cost effect occurs in such a market setup, and the effect is asymmetric. It means that the leader can via the unit R&D investment raise the overall marginal cost of the follower from 1/3 to 1/2, depending on the R&D externalities. The follower can, in turn, via the unit R&D investment raise the overall marginal cost of the leader from 1/6 to 1/2, depending on the R&D spillovers in the industry. We also find that under downstream Stackelberg competition, the larger R&D spillovers lead to the smaller R&D investment as well as the profit of the upstream firm, but the profits of the downstream Stackelberg follower are increasing with the larger R&D externalities. The behavior of output, prices of intermediate and final products as well as the profit of the downstream Stackelberg leader are nonmonotonic with respect to the research externalities. Comparing with the downstream monopoly, we conclude that downstream duopolists jointly invest more in R&D than does a downstream monopolist as long as the R&D spillovers are not very high. The profit of the downstream monopolist is higher than the joint profit of the downstream Stackelberg duopolists for any level of the R&D spillovers. However, the profit of the upstream firm is significantly lower when the downstream market is captured by a monopolist.