How Many Firms Should Be Leaders? Beneficial Concentration Revisited

We investigate the relationship between the Herfindahl-Hirschman Index (HHI) and welfare. First, we discuss the model wherein m leaders and N - m followers compete. Daughety (1990) finds that under linear demand and constant marginal cost, the Stackelberg model yields larger welfare and HHI than the Cournot model. Thus, he demonstrates that beneficial concentration occurs. We find that this always occurs under general cost and demand functions when m is sufficiently large, but does not always occur when m is small. Next, we consider the free entry of followers, and find that beneficial concentration always occurs regardless of m. In particular, the more persistent the leadership, the more likely it is to be beneficial.