Herfindahl index

From Schweser: example: Industry has four firms with market shares of 40%, 30%, 20% and 10%. “An alternative way to interpret the Herfindahl index is to view its reciprocal, 1/0.3=3.33 for the above example, as the equivalent number of equal sized firms in the industry.” I don’t understand this. “the equivalent number of equal sized firms in the industry”? What do they mean?

I read that passage yesterday and had the exact same question. Do not know what they mean either…

I think it means that its equivalent to having 3 firms each with the same market share (i.e. equal size). So the Herfindahl index of 0.3 is equivalent to having 3.33 firms each with 30% market share.

I’ll second yickwong’s post. We know the Herfindahl index will be somewhere between zero and one, but the interpretation of this value’s reciprocal may be more intuitive: Given the relative market shares of the firms in the above example, the competitive equivalent would be to have about three firms in this industry, each with equal market share. The industry appears to be an oligopoly.