An oligopolist or monopolist charges P > MC, so its index is L > 0, but the extent of its markup depends on the elasticity (the price-sensitivity) of demand and strategic interaction with competing firms.
Convenience stores charge a higher price than supermarkets because some of their customers fall at a time when there is not a large selection of outlets or for the sake of a minor purchase, it makes no sense to look for other options.
According to the Lerner coefficient, small stores have more monopoly power because they charge higher margins on the same product.
A firm choosing quantity Q facing inverse demand curve P(Q) and incurring costs C(Q) has profit equalling revenue (where R = PQ) minus costs: Under suitable conditions (that this is a convex maximization problem, e.g. P(Q) and C(Q) are linear functions), we can find the maximum by taking the derivative of profit with respect to Q and getting the first-order-condition: which gives the standard rule of MR = MC.
To get the Lerner Rule, switch to the notation dC/dQ = MC and rewrite as Divide by P to get using the derivative definition of elasticity.
The mean of the Lerner index computed for the full sample is 53.58 %, which do not confirm either monopoly or perfect competition in the credit market of Czech Republic.
In 2015, the article "Application of the Lerner index to the assessment of competition in small and medium-sized business in lending market of Russia" was published.
The objectives of this work were to assess the degree of competition in the segment of lending to small and medium-sized businesses, as well as to analyze the market power of various groups of commercial banks.
The results of the study showed that the segment of lending to small and medium-sized businesses by structure is a monopolistic competition, the dominant position in which is occupied by state-owned banks.
The monopoly power of this group is due to their use of economies of scale, the low cost of funding, and the lower risks of loans issued.