The widely used Herfindahl index of concentration measures market powe
r incorrectly in cases where a core of sellers faces a competitive fri
nge or where some subset of sellers is supply-constrained. These cases
arise, for example, where domestic sellers face a small fringe of imp
orts, or where import supply of any magnitude is limited by natural or
artificial constraints. Returning to the theoretical roots of the Her
indahl, this paper demonstrates how the index should be modified to de
al with such circumstances.