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Continuity of a model with a nested CES utility function and Bertrand competition

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  • Kucheryavyy, Konstantin

Abstract

In recent years models with a nested constant elasticity of substitution utility function and heterogeneous firms involved in some form of competition have become popular in the international trade literature. This paper considers one particular model of this class — with firms competing in prices — and shows continuity of the model as the elasticity of substitution between goods goes to infinity. This result contrasts with the conjecture of prior literature. Continuity of the model ensures consistency of its outcomes when the elasticity of substitution approaches infinity. Therefore, researchers who were reluctant to use this model because of the lack of proof of continuity can now rely on this paper’s result to employ the model in their research.

Suggested Citation

  • Kucheryavyy, Konstantin, 2012. "Continuity of a model with a nested CES utility function and Bertrand competition," Economics Letters, Elsevier, vol. 117(2), pages 473-476.
  • Handle: RePEc:eee:ecolet:v:117:y:2012:i:2:p:473-476
    DOI: 10.1016/j.econlet.2012.06.036
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    References listed on IDEAS

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    1. Andrew Atkeson & Ariel Burstein, 2008. "Pricing-to-Market, Trade Costs, and International Relative Prices," American Economic Review, American Economic Association, vol. 98(5), pages 1998-2031, December.
    2. Andrew B. Bernard & Jonathan Eaton & J. Bradford Jensen & Samuel Kortum, 2003. "Plants and Productivity in International Trade," American Economic Review, American Economic Association, vol. 93(4), pages 1268-1290, September.
    3. Jonathan Eaton & Gene M. Grossman, 1986. "Optimal Trade and Industrial Policy Under Oligopoly," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(2), pages 383-406.
    4. Andrew Atkeson & Ariel Burstein, 2007. "Pricing-to-Market in a Ricardian Model of International Trade," American Economic Review, American Economic Association, vol. 97(2), pages 362-367, May.
    5. Beatriz de Blas & Katheryn Russ, 2010. "Understanding Markups in the Open Economy under Bertrand Competition," NBER Working Papers 16587, National Bureau of Economic Research, Inc.
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    Cited by:

    1. Mary Amiti & Oleg Itskhoki & Jozef Konings, 2016. "International Shocks and Domestic Prices: How Large Are Strategic Complementarities?," NBER Working Papers 22119, National Bureau of Economic Research, Inc.
    2. Miren Azkarate-Askasua & Miguel Zerecero, 2023. "Union and Firm Labor Market Power," CRC TR 224 Discussion Paper Series crctr224_2023_475, University of Bonn and University of Mannheim, Germany.
    3. Balázs Murakozy & Katheryn Niles Russ, 2015. "Competition with Multinational Firms: Theory and Evidence," CERS-IE WORKING PAPERS 1534, Institute of Economics, Centre for Economic and Regional Studies.
    4. Kazuyoshi Ohki, 2016. "Welfare analysis and policy implications in Melitz-type model where markup differs across industries," ISER Discussion Paper 0984, Institute of Social and Economic Research, Osaka University.
    5. Pham, Hoang, 2023. "Trade reform, oligopsony, and labor market distortion: Theory and evidence," Journal of International Economics, Elsevier, vol. 144(C).
    6. Beatriz de Blas & Katheryn N. Russ, 2015. "Understanding Markups in the Open Economy," American Economic Journal: Macroeconomics, American Economic Association, vol. 7(2), pages 157-180, April.

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    More about this item

    Keywords

    CES utility; Bertrand competition; Heterogeneous firms; General equilibrium; Firm pricing; Continuity;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models
    • F12 - International Economics - - Trade - - - Models of Trade with Imperfect Competition and Scale Economies; Fragmentation

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