The Lerner index, formalized in 1934 by British economist of Russian origin Abba Lerner, is a measure of a firm's market power.
The Lerner index is defined by:
| L= | P-MC |
| P |
where P is the market price set by the firm and MC is the firm's marginal cost. The index ranges from 0 to 1. A perfectly competitive firm charges P = MC, L = 0; such a firm has no market power. 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. The index rises to 1 if the firm has MC = 0.
The following factors affect the value of the Lerner index:
The Lerner Rule or Lerner Condition is that if it is to maximize its profits, the firm must choose its price so that the Lerner Index equals -1 over the elasticity of demand facing the firm (note that this is not necessarily the same as the market elasticity of demand):
| P-MC | |
| P |
=
| -1 | |
| Ed |
A drawback of the Lerner Index is that while it is relatively easy to observe a firm's prices, it is quite difficult to measure its marginal costs. In practice, the average cost is often used as an approximation.
The Lerner index can never be greater than one. As a result, if the firm is maximizing profit, the elasticity of demand facing it can never be less than one in magnitude (|E|<1). If it were, the firm could increase its profits by raising its price, because inelastic demand means that a price increase of 1% would reduce quantity by less than 1%, so revenue would rise, and since lower quantity means lower costs, profits would rise. Put another way, a monopolist never operates along the inelastic part of its demand curve.
Market power alone does not guarantee high profits, since profits depend on the ratio of average costs to price. A firm may have more market power than another firm, but still make less profit. As an example, let's compare an average supermarket and a convenience store operating in the same area. In supermarkets, the margin is usually 15-20%, and in convenience stores 25-30 %. This is due to the fact that supermarkets operate in a more competitive environment — during their operation, other outlets are also working at the same time to ensure a significant number of customers, it is necessary to offer attractive prices. 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. The number of visitors to such stores is generally less dependent on prices than in supermarkets (less elastic demand). According to the Lerner coefficient, small stores have more monopoly power because they charge higher margins on the same product. But at the same time, such stores usually receive a much smaller amount of profit than a supermarket, since they have a much smaller sales amount, and the average unit cost is higher.
The Lerner Rule comes from the firm's profit maximization problem. 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:
Profit=P(Q)Q-C(Q)
| dProfit | |
| dQ |
=(
| dP | |
| dQ |
Q+P)-
| dC | |
| dQ |
=0
P-MC=-
| dP | |
| dQ |
Q
| \begin{align} | P-MC |
| P |
&=-
| dP | |
| dQ |
| Q | |
| P |
\\ &\\ &=-1/\left(
| dQ | |
| dP |
| P | |
| Q |
\right)\\ &\\ &=-
| 1 | |
| Ed |
,\end{align}
Let's suppose we need to fill in the gaps in the following table:
| Industry | Price,P | Marginal cost,MC | Elasticity of demand,Ed | Lerner index,L | |
|---|---|---|---|---|---|
| A | 10 | 0.4 | |||
| B | 30 | -2 | |||
| C | 40 | 30 |
| Industry | Price,P | Marginal cost,MC | Elasticity of demand,Ed | Lerner index,L | |
|---|---|---|---|---|---|
| A | 10 | 6 | -2.5 | 0.4 | |
| B | 30 | 15 | -2 | 0.5 | |
| C | 40 | 30 | -4 | 0.25 |
| Year | Mean | Median | |
|---|---|---|---|
| 2000 | 0.4438 | 0.5486 | |
| 2001 | 0.5598 | 0.5455 | |
| 2002 | 0.5723 | 0.5530 | |
| 2003 | 0.6165 | 0.6089 | |
| 2004 | 0.5430 | 0.5371 | |
| 2005 | 0.5980 | 0.6163 | |
| 2006 | 0.5673 | 0.5457 | |
| 2007 | 0.5650 | 0.5739 | |
| 2008 | 0.5109 | 0.5029 | |
| 2009 | 0.3921 | 0.3289 | |
| 2010 | 0.6742 | 0.6582 |
| Year | Mean | Median | |
|---|---|---|---|
| 2000 | 0.5905 | 0.6898 | |
| 2001 | 0.6864 | 0.6959 | |
| 2002 | 0.6930 | 0.6692 | |
| 2003 | 0.7170 | 0.7204 | |
| 2004 | 0.6595 | 0.6482 | |
| 2005 | 0.6955 | 0.7100 | |
| 2006 | 0.6718 | 0.6806 | |
| 2007 | 0.6696 | 0.6776 | |
| 2008 | 0.6255 | 0.6328 | |
| 2009 | 0.5266 | 0.4880 | |
| 2010 | 0.7642 | 0.7355 |
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.They analyzed the period from 2010 to 2013. 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. As a research method, the Lerner index was chosen to determine which of the groups of banks (small, medium and large; partners and non-partners of various development banks) have higher market power and how it changes over time. This work made a significant contribution to the study of banking competition, adapting the indicator for assessing the competition of the entire banking services market to the assessment of the degree of competition in the market of a single product - lending to small and medium-sized businesses, as well as showing the presence of competition.
| Year | Value | Standard deviation | |
|---|---|---|---|
| 2010 | 0,3159 | 0,1274 | |
| 2011 | 0,2137 | 0,1337 | |
| 2012 | 0,2285 | 0,1341 | |
| 2013 | 0,3027 | 0,1405 |