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How do you interpret the Lerner Index?

I ask because at Uni. we have been told that, for monopoly, when the producer max. his profit, he sets the price such as the demand is elastic and the lerner index is between (0,1). BUT that if elasticity increases, then the index decreases and the market cap is higher. We have been told this at two different classes, but yesterday, talking in general, we have been told that when LI increases, then market cap is higher.

Thus, I don't understand how to analyse LI anymore.

Could you explain it to me, please?

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