Concentration Measures

There are several metrics used to identify market power. Such as ...

the 'n' concentration ratio (the proportion of overall sales given by the top n firms) and the Herfindhal index.

However, there is also the Price cost margin (Lerner index).

These indicators may not always agree with one another.

Is there some way we can understand which of them is most relevant as an indicator of market power? For example by examining the local characteristics such as what kind of imperfect competition is present, and consumer demand patterns?

• To clarify, which are you more interested in- concentration or market/price setting power? While the two often move together, they aren't the same thing. – AndrewC Jun 5 '18 at 13:58
• Thanks. No indeed, they're not the same thing. One can have high concentration and limit pricing. What I'm interested in knowing is if, say, there are circumstances when these indicators complement (or not) one another in theory terms. For example the H index has a relation to the P-C margin under particular market structure assumptions (e.g., cournot competition). – user17789 Jun 5 '18 at 14:17