Efficiency and concentration

Baumol, Panzar, and Willig 1982] introduced the idea that there may be efficiency gain from merger of two or more firms. This paper shows that the Debreu 1951]-Farrell 1957] type index suggested by Färe 1986] to calculate the gain in efficiency from merger of firms can be related to a concentration formula. We then introduce a dominance relation consistent with the ordering generated by the Färe gain function. Next, it is shown that a normalized form of the gain function satisfying a homogeneity condition becomes a subclass of the Hannah-Kay 1977] concentration indices. A limiting case of this subclass becomes the entropy-based index of concentration.The editor of this paper was Rolf Färe.I wish to express sincere gratitude to Shmuel Nitzan for bringing my attention to this problem. Comments and suggestions from Rolf Färe, Alexis Jacquemin, and two anonymous referees are acknowledged with thanks.