When Different Market Concentration Indices Agree

Abstract

Market concentration ratios are popular statistics for characterizing the extent of market dominance in an imperfectly competitive market, but these ratios may not agree when comparing two markets. Neither do they necessarily agree with the Herfindahl-Hirschman or entropy indices. This letter compares two Cournot oligopoly markets in which firms have constant unit costs. It is shown that the majorization pre-ordering on normalized marketing margin vectors is both necessary and sufficient for all aforementioned indices to agree on which is the more concentrated market.