From Lerner's Index To Market Segmentation Index (MSI)
Assumption 1: Marginal costs for the monopolist firm are the same for every market segment
Applying Lerner index L=(P-MC)/P to two distinctive market segments we get the degree of monopoly power in market segment Ms as Ls=(Ps-MC)/Ps and Mp as Lp=(Pp-MC)/Pp. Ps is the price charged in Ms while Pp is the price charged in Mp.
This result confirms the validity of the market segmentation index, which is a comparative measure of the degree of monopoly power in two distinctive markets for products that have the same marginal costs. The result says that when the price in the primary market is strictly greater than the price in the secondary market then the Lerner's index is higher in the primary market and therefore the market segmentation index would also be higher for the primary market.
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