The HHI as a function of the weighted average of the firms’ price-cost margins and the market demand elasticity

HHI = ∑ Si. Si as it equals the sum of the squared market shares of each firm in the industry. (See Friday, March 10, 2006) = -ε. (∑ Si. Si )/(-ε) (multiply and divide with -ε) = -ε.∑Si.L, where L is the Lerner Index of market power in an oligopoly environment (See Friday, March 17, 2006). That is, the HHI equals the absolute value of the market demand elasticity multiply with the weighted average of the firms’ price-cost margins.

Note that in case of monopoly L= -Si/ε=-100/ε (Share equals 100%) So HHI=-ε.100.L=10000 (See Friday, March 10, 2006)