Measurement of Market Power Using Trademark Data: models, limitations and applications

This paper analyzes the main models used to measure market power by means of brand data and verifies the advantages of the model developed by Cotterill, Franklin and Ma over the others. This is a very flexible model which can be used to any conjectural assumptions and allows the measurement of both unilateral and collusive market power. Several ways of application are suggested, and very promising perspectives are recognized for this type of study.

KEYWORDS:
Market power; competition; elasticity estimation

Authorship

DANILO R. D. AGUIAR

Professor adjunto da Universidade Federal de Viçosa, Viçosa/MG, Brasil. E-mail: danilo@ufv.br.Universidade Federal de ViçosaBrasilViçosa, MG, BrasilProfessor adjunto da Universidade Federal de Viçosa, Viçosa/MG, Brasil. E-mail: danilo@ufv.br.

** O autor é grato ao CNPq pelo financiamento do programa de pós-doutorado em que este trabalho foi iniciado. É grato, também, ao prof. John Connor, da Purdue University (EUA), pelas discussões mantidas sobre o tema em apreço.

SCIMAGO INSTITUTIONS RANKINGS

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Figures (1)
Formulas (15)

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Figura 1:Relações
Teóricas da Demanda para uma Marca num Oligopólio Diferenciado

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Figura 1:Relações Teóricas da Demanda para uma Marca num Oligopólio Diferenciado

Fonte: adaptado do Cotterill, Franklin & Ma (1996COTTERILL, Ronald W.; FRANKLIN, Andrew & MA, Li Y. (1996) Measuring Market Power Effects in Differentiated Product Industries: An Application to the Soft Drink Industry. Food Marketing Policy Center Research Report, # 32 (April). Department of Agricultural and Resource Economics, University of Connecticut.).

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q_{1} = q_{1} (p_{1}, . . ., p_{n}, D),

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η_{1}^{0} = η_{11} + \sum_{i = 2}^{n} (η_{li}, ε_{il}),

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R = \frac{tgα}{tgβ} = \frac{{(\frac{ΔP}{ΔQ})}^{u}}{{(\frac{ΔP}{ΔQ})}^{c}} = \frac{η_{1}^{c}}{η_{11}}

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C = \frac{tgβ}{tgγ} = \frac{{(\frac{ΔP}{ΔQ})}^{o}}{{(\frac{ΔP}{ΔQ})}^{c}} = \frac{η_{1}^{c}}{η_{1}^{o}}

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CH = \frac{C - R}{C} = 1 - \frac{η_{1}^{o}}{η_{11}}

η_{1}^{c} = - 1; η_{11} = - 2; η_{12} = 0, 5; ε_{21} = 1; e η_{2}^{c} = - 0.6; η_{22} = - 1; η_{21} = 0, 8; ε_{12} = 0, 5 .

η_{1}^{o} = - 2 + (0, 5 \times 1) = - 1, 5; η_{2}^{o} = - 1 + (0, 8 \times 0, 5) = - 0, 6 .

R_{1} = \frac{η_{1}^{c}}{η_{11}} = \frac{- 1}{- 2} = 0, 5 R_{2} = \frac{η_{2}^{c}}{η_{22}} = \frac{- 0, 6}{- 1} = 0, 6 C_{1} = \frac{η_{1}^{c}}{η_{1}^{o}} = \frac{- 1}{- 1, 5} = 0, 66 C_{2} = \frac{η_{2}^{c}}{η_{2}^{o}} = \frac{- 0, 6}{- 0, 6} = 1 {CH}_{1} = 1 - \frac{η_{1}^{o}}{η_{11}} = 1 - \frac{- 1, 5}{- 2} = 0, 25 {CH}_{2} = 1 - \frac{η_{2}^{o}}{η_{22}} = 1 - \frac{- 0, 6}{- 1} = 0, 4

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w_{i} = α_{i} + \sum_{j} γ_{i j} \ln p_{j} + β_{i} \ln (\frac{x}{P})

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\ln p_{1} = θ_{1} + ε_{12} \ln p_{2} + ε_{13} \ln p_{3} + . . . + ε_{1 n} \ln p_{n}, \ln p_{2} = θ_{2} + ε_{21} \ln p_{1} + ε_{23} \ln p_{3} + . . . + ε_{2 n} \ln p_{n}, \ln p_{n} = θ_{n} + ε_{n 1} \ln p_{1} + ε_{n 2} \ln p_{2} + . . . + ε_{n (n - 1)} \ln p_{n - 1} .

π = p_{1} q_{1} + p_{2} q_{2} + p_{3} q_{3} - c (q_{1}, q_{2}, q_{3},),

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\frac{\partial π}{\partial p_{1}} = q_{1} + p_{1} \frac{\partial q_{1}}{\partial p_{1}} + p_{2} \frac{\partial q_{2}}{\partial p_{1}} + p_{3} \frac{\partial q 3}{\partial p_{1}} - \frac{\partial c}{\partial q_{1}} \frac{\partial q_{1}}{\partial p_{1}} - \frac{\partial c}{\partial q 2} \frac{\partial q_{2}}{\partial p_{1}} - \frac{\partial c}{\partial q_{3}} \frac{\partial q_{3}}{\partial p_{1}} = 0 \frac{\partial π}{\partial p_{2}} = q 2 + p_{1} \frac{\partial q_{1}}{\partial p_{2}} + p_{2} \frac{\partial q_{2}}{\partial p_{2}} + p_{3} \frac{\partial q 3}{\partial p_{2}} - \frac{\partial c}{\partial q_{1}} \frac{\partial q_{1}}{\partial p_{2}} - \frac{\partial c}{\partial q 2} \frac{\partial q_{2}}{\partial p_{2}} - \frac{\partial c}{\partial q_{3}} \frac{\partial q_{3}}{\partial p_{2}} = 0 \frac{\partial π}{\partial p_{3}} = q_{2} + p_{1} \frac{\partial q_{1}}{\partial p_{3}} + p_{2} \frac{\partial q_{2}}{\partial p_{3}} + p_{3} \frac{\partial q 3}{\partial p_{3}} - \frac{\partial c}{\partial q_{1}} \frac{\partial q_{1}}{\partial p_{3}} - \frac{\partial c}{\partial q 2} \frac{\partial q_{2}}{\partial p_{3}} - \frac{\partial c}{\partial q_{3}} \frac{\partial q_{3}}{\partial p_{3}} = 0

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w_{1} + w_{1} η_{11} p c m_{1} + w_{2} + η_{21} p c m_{2} + w_{3} + η_{31} p c m_{3} = 0; w_{1} + w_{1} η_{12} p c m_{1} + w_{2} + η_{22} p c m_{2} + w_{3} + η_{32} p c m_{3} = 0; w_{1} + w_{1} η_{13} p c m_{1} + w_{2} + η_{23} p c m_{2} + w_{3} + η_{33} p c m_{3} = 0,

w_{1} = \frac{p_{i} q_{i}}{\sum_{j = 1}^{n} p_{j} q_{j}}, \frac{\partial c}{\partial q_{i}} = m c_{i}, \frac{p_{i} - m c_{i}}{p_{i}} = p c m_{i}, i = 1, 2, 3 .

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- \frac{}{η_{i}^{c}} \frac{p_{i} - m c_{i}}{p_{i}} = p c m_{i}, i = 1, 2, 3 .

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Measurement of Market Power Using Trademark Data: models, limitations and applications

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