Bishop, His Critics, and a Fresh Look at the Role of Cross-Price Elasticities in Market Classification

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The classification of markets according to the nature of competition among firms is one of the fundamental pillars of microeconomics. The use of firm-level cross-price elasticity for this purpose was first proposed by Kaldor in 1934. This was followed by a lively debate with contributions from Weintraub, Fellner, Chamberlain and others during the 1940’s and early 1950’s. The first part of this paper briefly reviews the early literature on this topic, focusing on Bishop’s classic article in 1952. Bishop argues that firm level cross-elasticity should never be used as a stand alone criteria for classifying the nature of competition among firms. He proposes instead, a classification scheme based on the relative size of “own” to “cross” price elasticity. Pfouts and Ferguson’s (1959) point out that Bishop’s scheme implies a perfectly inelastic demand for the product group as a whole; an unacceptable restriction. The second part of this paper presents a generalized analysis of the issue based on the constant elasticity lumped parameter model (CELP) for firm level demand. The approach allows for any given product group demand elasticity and resolves all of the criticisms of Bishops original classification scheme transparently.Firm-level cross-price elasticity is shown to play an important role in classifying the nature of competition among firms. However, it is the factors used in calculating firm-level cross-price elasticity coefficients that should be used as criteria in the classification scheme rather than the actual calculated cross-price elasticity coefficients themselves.