A generalized index of market power.

Author:Vallejo, Hernán
Pages:95(14)
 
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Resumen. Este documento analiza dos enfoques para medir poder de mercado --el frecuentemente utilizado índice de Lerner y un conjunto de medidas de explotación--. Se argumenta que el índice de Lerner está diseñado para cuantificar el poder de mercado por el lado de la oferta y que las medidas de explotación están diseñadas para cuantificar el poder de mercado por el lado de la demanda, y que esos dos enfoques no siempre tienen los mismos límites. Para corregir estas propiedades potencialmente no deseables, este documento propone un nuevo índice general para medir poder de mercado, que es simétrico --estando restringido a valores entre cero y uno--, independientemente de si el poder de mercado proviene del lado de la oferta o de la demanda. El índice propuesto permite la presencia de más de una firma y la existencia de variaciones conjeturales.

Palabras clave: poder de mercado, mark up, mark down, índice de Lerner, medidas de explotación, organización industrial, variaciones conjeturales.

Clasificación JEL: D49, L10, L11.

Abstract. This paper analyses two approaches to measuring market power --the commonly used Lerner index and a range of exploitation measures--. It is argued that the Lerner index is designed to quantify market power from the supply side and the exploitation measures are designed to quantify market power from the demand side, and that the two approaches do not always behave in a symmetric way, since they do not always have the same bounds. To sort out these potentially undesirable properties, this paper proposes a new general index to measure market power, which is symmetrical in the sense that it is bounded between zero and one, regardless of whether the market power comes from the supply or the demand side. The index proposed allows for the presence of more than one firm and for the existence of conjectural variations.

Key words: market power, mark up, mark down, Lerner index, exploitation measures, industrial organization, conjectural variations.

JEL classification: D49, L10, L11.

  1. Introduction

    This paper analyses two approaches to measuring market power--the commonly used Lerner index and a range of exploitation measures--, spelling out the central features of the main indexes within each approach. It is argued that the Lerner index is designed to quantify market power from the supply side and the exploitation measures are designed to quantify market power from the demand side, and that the two approaches do not always behave in a symmetric way, since they do not always have the same bounds.

    To sort out these potentially undesirable properties, this paper derives a new general index to measure market power from profit maximization, which is symmetrical in the sense that it is bounded between zero and one, regardless of whether the market power comes from the supply or the demand side. The proposed index allows for the presence of more than one firm and for the existence of conjectural variations.

    The use of the proposed index should increase awareness of the existence and measurement of market power from the supply and the demand side, while making more expedite the use of such measures in empirical estimations, regardless of the side of the market where the market power comes from.

    The paper is organized as follows: the next section presents the theoretical framework in which the Lerner index and three alternative--and related--exploitation measures are derived from profit maximization, describing the main properties of each index. The following section proposes an index that overcomes some of the limitations of the standard measures considered before. The paper ends with the main conclusions.

  2. Theoretical framework

    This section derives measures of market power from profit maximization. In order to make general statements, assume that there are n firms that play Cournot to start with, and keep in mind that this assumption will be relaxed later on through the introduction of a conjectural variations coefficient. Assume also that all firms have identical cost structures.

    2.1. Market power from the supply side

    When market power is generated from the supply side (with prices greater than marginal costs, as in monopoly, monopolistic competition and--often--oligopoly), firms apply a mark up. This case is shown in figure 1.

    Consider the following profit equation for a firm playing Cournot:

    [[PI].sub.i] = [P.sub.G] ([q.sub.i] + [Q.sub.-i]) [q.sub.i] - [TC.sub.i],

    where

    [[PI].sub.i] = profits of firm i,

    [P.sub.G] = per unit price of the good produced by firm i,

    [q.sub.i] = quantity produced by firm i,

    [Q.sub.-i] = quantity produced by all firms in the market, except firm i,

    Q = quantity produced by all firms in the market,

    [TC.sub.i] = total costs of firm i.

    [FIGURE 1 OMITTED]

    Since all firms are assumed to have identical cost structures, the sub-index i can be dropped. Profit maximization with n firms implies that

    [P.sub.G] (Q) + Q[P'.sub.G] (Q) [q/Q] = Mg [C.sub.G].

    Thus the Lerner index--proposed by Abba Lerner (1934) (1)-- with n firms, can be derived as

    [L.sub.H] = [[P.sub.G] - Mg [C.sub.G]/[P.sub.G]] = [s/[eta]],

    where

    [L.sub.H] = Lerner index with more than one firm,

    Mg [C.sub.G] = marginal cost of producing the good,

    H = Herfindahl market concentration index,

    s = market share of a firm,

    [eta] = [[partial derivative]Q [P.sub.F]/[partial derivative][P.sub.F] Q], the negative of the price...

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