Learner Index

The Lerner Index, also known as the Lerner monopoly degree , is a measure of the market power or the pricing power of a company named after the US economist Abba P. Lerner .

definition

The learner index is defined as follows:

{\ displaystyle L = {p-GK \ over p}}

Here stands for the price and for the marginal costs . ${\ displaystyle p}$ ${\ displaystyle GK}$

meaning

The index size expresses how strongly a market player can set his price above the marginal costs (that is, how high his so-called markup is), and not in absolute terms, but relative to the price level itself. The Lerner Index functions in many applications as a measure of the market power (the "degree of monopoly") of the provider under consideration: While in a competitive environment there is strict equality of price and marginal costs (new players enter the market until the profit of each company is zero) and the Learner index is accordingly zero, a monopoly can realize positive profits, which in turn is reflected in a higher learner index.

In reality, the learner index is not easy to calculate. Although prices can be easily determined for many products, the cost structures of companies are practically always unknown to outsiders. Companies rate cost information as sensitive to competition. Nevertheless, certain aspects of the cost structure can be assessed. For example, telephone or energy infrastructures are partially regulated by the government, which collects certain data for this purpose, from which economists in turn draw conclusions. On the other hand, you can also make extrapolations if you know a smaller company in an industry and its costs.

Use and importance in maximizing profits in a company

Viewed in isolation, the learner index can assume any value. However, this does not apply if the provider in question produces in the abstract model in a profit-maximizing manner.

Optimality condition of the one-product monopoly

Based on the general profit maximization problem of a one-product monopoly,

{\ displaystyle \ max _ {q} p (q) \ cdot qc (q)}

(with the quantity of goods, the price-sales function and the cost function ), is the associated first-order optimality condition ${\ displaystyle q}$ ${\ displaystyle p (q)}$ ${\ displaystyle c (q)}$

{\ displaystyle p '(q ^ {*}) \ cdot q ^ {*} + p (q ^ {*}) - c' (q ^ {*}) = 0 \ Leftrightarrow p (q ^ {*}) -c '(q ^ {*}) = - p' (q ^ {*}) \ cdot q ^ {*}}

.

It can be reduced to the following form by dividing both sides with : ${\ displaystyle p (q ^ {*})}$

{\ displaystyle {\ frac {p (q ^ {*}) - c '(q ^ {*})} {p (q ^ {*})}} = - {\ frac {p' (q ^ {* }) \ cdot q ^ {*}} {p (q ^ {*})}} = - \ left ({\ frac {\ mathrm {d} p} {\ mathrm {d} q}} {\ frac { q ^ {*}} {p ^ {*}}} \ right)}

The right side of this equation is the reciprocal of the absolute value of the elasticity of demand . Hence the following applies in the profit maximum: ${\ displaystyle \ epsilon _ {p} \ equiv \ left (\ mathrm {d} q / \ mathrm {d} p \ right) \ cdot (p / q)}$

{\ displaystyle {L = {\ frac {1} {| \ epsilon _ {p} |}}}}

.

Implications for the Learner Index

In the company's profit optimum, the learner index can in principle assume values between 0 and 1 according to the above. A higher value means more market power. The two extreme values can be seen as extreme poles of the market situations of perfect competition (L = 0, no market power at all) and (perfect) monopoly (L = 1, maximum market power). Values in between indicate lower degrees of monopoly, hence forms of oligopolies.

The markup here depends directly on the price elasticity of demand and is indirectly proportional to it, i.e. H. the larger (or smaller) the price elasticity, the smaller (or larger) the learner index becomes. It should be noted here that a value of zero can only be achieved (approximately) if the denominator tends towards infinity; this theoretical case is called completely elastic demand. A value of one is reached when the price elasticity is one (proportionally elastic). In principle, the price elasticity can also assume other values (e.g. 1/2) that would not be compatible with the value range of the Lerner index. This area is called inelastic. It is assumed that the Lerner Index cannot exceed 1 because a profit-maximizing monopolist would never produce on the inelastic section of its demand curve . ${\ displaystyle 0 <| \ epsilon | <1}$

Overall, this formulation of the optimality condition makes it clear that a profit-maximizing monopolist always has positive markup - the price he sets is higher than would or could be the case in perfect competition. This also shows why the equilibrium in a monopoly is not socially optimal: given a continuum of demand, the monopoly strictly demands more than he actually could in order to just cover costs or, in other words, he could lower his price by a marginal unit , so that you can still realize a positive profit from the additional production and at the same time help an additional customer to gain benefit (as a result of the price decrease, all previous customers would also experience an increase in benefit). But he does not do this precisely because he cannot discriminate between buyers (i.e. charge different prices from them) and it is more worthwhile for him to exclude some buyers from consumption by paying a higher price than to lower the price for all buyers; the monopoly set remains analogously behind the polypole set.

Deficits in the Lerner Index as a measure of the degree of monopoly

In practice, the Lerner Index is only partially suitable as a measure of the degree of monopoly. In addition to the problems already outlined above with its calculation (or the calculation of marginal costs), there are also other deficits. For example, the index disregards the fact that a monopoly character can also arise from the existence of market entry barriers; If there are, the markup may be rather low for various (demand-induced) reasons, but the monopoly status of the company can nevertheless be extraordinarily strong because it is otherwise “sealed off” from the competition by potential competitors. In addition, it does not record that products are usually not completely homogeneous; A company can also have the option of higher markup simply because the product quality offered exceeds that of comparable products from other providers. Furthermore, the index does not take into account cases of incomplete or asymmetrical information on markets; Deviations between the marginal costs and the price can be due not only to the company's pricing power, but rather to the degree of imperfection in the market or competitive structure. This is accompanied by the problem that in reality not only marginal costs are relevant for price setting, but also fixed cost differences (and thus average cost differences) between companies, which can give rise to price fluctuations without this being the result of a more significant monopoly position.

Web links

Lerner index derivation (PDF file; 20 kB) - mathematical transformations, TU Dresden

literature

Kenneth G. Elzinga and David E. Mills: The Lerner Index of Monopoly Power: Origins and Uses. In: American Economic Review. 101, No. 3, 2011, pp. 558–564, doi : 10.1257 / aer.101.3.558 (draft published as a working paper, University of Virginia, 2011, Internet http://economics.virginia.edu/sites/economics. virginia.edu/files/Lerner%20Index%20of%20Monopoly%20Power.pdf , accessed June 18, 2013).
Nicola Giocoli: Who Invented the Lerner Index? Luigi Amoroso, the Dominant Firm Model, and the Measurement of Market Power. In: Review of Industrial Organization. 41, No. 3, 2012, pp. 181-191, doi : 10.1007 / s11151-012-9355-7 .
Abba P. Lerner: The Concept of Monopoly and the Measurement of Monopoly Power. In: The Review of Economic Studies. 1, No. 3, 1934, pp. 157-175 ( JSTOR 2967480 ).
Nolan H. Miller: Notes on Microeconomic Theory. Lecture notes, Harvard University, 2006, online ( Memento from December 15, 2011 in the Internet Archive ) (PDF; 1 MB), p. 236, accessed on January 2, 2015.

Individual evidence

↑ Walter Nicholson, Christopher Snyder: Microeconomic Theory . Cengage Learning Emea; Edition: International ed of 11th revised ed (September 20, 2011). ISBN 978-1111525514 , page 412.

↑ Of course, this is simply a generalization of the polypolist's profit maximization problem, for whom the price level p is given (and is not a function of the quantity). In special cases, the following also applies in the case of perfect competition, cf. the section “Implications for the Learner Index”.

↑ This is because according to the law of demand . ${\ displaystyle \ left (\ mathrm {d} p / \ mathrm {d} q \ right) <0}$

↑ The representation follows partly Elzinga / Mills 2011.

[1] Walter Nicholson, Christopher Snyder: Microeconomic Theory . Cengage Learning Emea; Edition: International ed of 11th revised ed (September 20, 2011). ISBN 978-1111525514 , page 412.

[2] Of course, this is simply a generalization of the polypolist's profit maximization problem, for whom the price level p is given (and is not a function of the quantity). In special cases, the following also applies in the case of perfect competition, cf. the section “Implications for the Learner Index”.