Review of Industrial Organization
13: 401–407, 1998.
1998 Kluwer Academic Publishers. Printed in the Netherlands.
Herﬁndahl Concentration with an Import Fringe and
with Supply Constraints
JOHN E. KWOKA, JR.
Department of Economics, George Washington University, Washington, DC 20052, U.S.A.
Abstract. The widely used Herﬁndahl index of concentration measures market power incorrectly in
cases where a core of sellers faces a competitive fringe or where some subset of sellers is supply-
constrained. These cases arise, for example, where domestic sellers face a small fringe of imports, or
where import supply of any magnitude is limited by natural or artiﬁcial constraints. Returning to the
theoretical roots of the Herindahl, this paper demonstrates how the index should be modiﬁed to deal
with such circumstances.
Key words: Concentration, Herﬁndahl index, imports, quotas.
Economic research as well as antitrust policy have adopted the Herﬁndahl index as
a measure of market concentration. Relative to the traditional concentration ratio,
the Herﬁndahl index – deﬁned as the sum of squared shares of all ﬁrms – is widely
believed to represent the size distribution of ﬁrms in a market more completely
(Department of Justice, 1992).
Whatever its other merits, however, the conventionally-calculated Herﬁndahl
index does not measure market concentration correctly in certain settings.
important and related cases involve markets with a fringe of “outside” sellers and
markets where outside sellers of any size are supply-constrained. The former case
is illustrated by local markets with a fringe of more distant sellers or by national
markets with modest amounts of foreign imports. For example, local electricity
markets may be highly concentrated but subject to some competition from more
distant, fringe sellers. Markets for steel and other products may face competition
from foreign sellers that constitute a fringe.
The second case arises when natural or artiﬁcial constraints limit or even sever
competition from such “outside” sources. Supply constraints are also illustrated by
these same cases, speciﬁcally, by transmission constraints on electric power and
by quotas on foreign imports of steel.
Here we examine the nature of the problem with the Herﬁndahl measure of
concentration under these circumstances. Further, by re-examining its theoreti-
These other “merits” are not universally believed compelling. See Kwoka (1985); also, Shepherd
(1997, pp. 74–75).