High price and penetration can coexist
A recent analysis covering panel data from 14 European countries, Russia and the US compares the price ratio between brands and private labels across 79 categories. Whether brands are priced below or more than double the price of private label (PL) does not impact their chances of reaching more than 10% penetration (about 44% of all brands do).
However, this result varies across baskets: Being relatively expensive in food categories reduces the likelihood of such penetration levels whereas being relatively cheap hurts in personal and household care. But setting high prices has its limits: Out of the 1000 most expensive brands (relative to their category PL peers), only 30% reach a penetration higher than 10%.