﻿ Lerner-Index

# Lerner-Index

The Lerner index, also called Lerner'scher degree of monopoly, is named after the economist Abba American P. Lerner measure of the market power or the pricing power of a company.

## Definition

Learner index is defined as follows:

It stands for the price and for the marginal cost.

## Importance

The size of the index expresses how strong a market player can set its price above the marginal cost ( ie how high his so-called markup ), and not in absolute terms, but relative to the price level itself, the Lerner index acts as in many applications as a measure of market power ( the " degree of monopoly " ) appearance of the provider: While in a competitive environment strict equality of price and marginal cost is predominant ( it take as long as a new players in the market, to the profit of each firm is zero ) and the Lerner index is zero accordingly, a monopolist can realize positive profits, which in turn is reflected in a higher Lerner index.

The Lerner index is not easy to calculate in reality. Prices can indeed be easily determined for many products, but the cost structure of these companies almost always unknown to outsiders. The companies evaluate cost information as a competitive sensitive. Nevertheless, certain aspects of the cost structure can be estimated. For example, telephone or power infrastructure are partly regulated by the government, which charges fees for this purpose certain data from which economists draw conclusions in turn. On the other hand, one can also extrapolations do if you know a smaller company and their costs in an industry.

## Use and importance of maximizing profits of a company

When considered in any particular values ​​of the Lerner index. However, this does not apply if the supplier produces profit-maximizing considered in the abstract model.

### Optimality condition of the single-product monopolist

Starting from the general profit maximization problem of a single-product monopolist,

( with the amount of goods, the price-demand function and the cost function ) is the associated optimality condition of first order

They can be brought by dividing both sides by the following form:

The right side of this equation is, however, just the reciprocal of the absolute value of the elasticity of demand. Consequently applies maximum profit:

### Implications for the Lerner index

In the optimum profit of the company of the Lerner index in accordance with the supernatant can assume values ​​between 0 and 1 in principle. Here, a larger value more market power. The two extreme values ​​can be here as extreme poles of market situations perfect competition (L = 0, no market power ) and ( perfect ) monopoly (L = 1, maximum market power ) view. Values ​​in between so indicate lower degrees of monopoly, and consequently forms of oligopolies.

The markup here depends directly on the price elasticity of demand from and behaves to her indirectly proportional, that is, the larger (or smaller) the price elasticity, the smaller (or larger) is the Lerner index. It should be noted that a value of zero can be achieved only when the denominator tends to infinity; this theoretical case is called perfectly elastic demand. A value of one is achieved if just the price elasticity is one (proportional elastic). Now the price elasticity can in principle assume other values ​​(eg, 1 /2), which would not be compatible with the range of values ​​of the Lerner index. This area is called inelastic. It is assumed that the Lerner index value of 1 may not exceed, as a profit -maximizing monopolist would never produce on the inelastic portion of its demand curve.

Overall, it is clear in this formulation of the optimality condition that a profit-maximizing monopolist always has a positive markup - the set, its price is higher than in perfect competition would be the case or could be. One can see that that claim is why the balance in the monopoly is not socially optimal: A continuum of demanders provided the monopolist requires strictly more than he could, just to produce even break even or, in other words, he might lower his price by a marginal unit so still realize a positive gain from the increase in production and at the same time help an additional buyers to gain a benefit (as a result of the price decline all previous buyers would also also experience a benefit increase ). But he is doing so not because he does not discriminate between demanders (ie, they require different pricing) and it is rewarding for him to exclude some buyers through a higher price from consumption to lower than the price for all buyers; the monopoly quantity is analogous behind the Polypolmenge.

## Deficits of the Lerner index as a measure of the degree of monopoly

In practice, the Lerner index is only suitable as a measure of the degree of monopoly. In addition to the already standing problems outlined in its calculation (or the calculation of marginal costs ) are also other deficits. So can the index, for example, ignores the fact that a monopole character can also arise from the existence of entry barriers; are those before, though the markup from various ( demand-induced ) reasons may be rather small, these can be extremely present the monopoly status of the company, because it is " sealed off " from competition because potential competitors elsewhere. In addition, is not recorded that products are usually not perfectly homogeneous; a company can only therefore have the possibility to a higher markup because the product quality offered exceeds that of comparable products from other suppliers. Next, the index cases of incomplete or asymmetric information on markets can be disregarded; Deviations between the marginal cost and the price may be not only due to the pricing power of the company, but rather the degree of imperfection of the market and competitive structure. This is accompanied by the problem that in reality not only marginal cost of pricing are relevant, but also fixed costs differences (and thus the average cost differences ) between companies that can justify price fluctuations without this may arise from a more significant monopoly.

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