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Decoupling the CES distribution circle with quality and beyond: equilibrium distributions and the CES-Logit nexus

Author

Listed:
  • Anderson, Simon
  • de Palma, André
Abstract
We show for CES demands with heterogeneous productivities that profit, revenue, and output distributions lie in the same closed power-family as the productivity distribution (e.g., the "Pareto circle"). The price distribution lies in the inverse power-family. Equilib- rium distribution shapes are linked by linear relations between their density elasticities. Introducing product quality decouples the CES circle, and reconciles Pareto price and Pareto sales revenue distributions. We use discrete choice underpinnings to find variable mark-ups for a more flexible demand formulation bridging CES to Logit and beyond. For logit demand, exponential (resp. normal) quality-cost distributions generate Pareto (log-normal) economic size distributions.

Suggested Citation

  • Anderson, Simon & de Palma, André, 2019. "Decoupling the CES distribution circle with quality and beyond: equilibrium distributions and the CES-Logit nexus," CEPR Discussion Papers 14168, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:14168
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    References listed on IDEAS

    as
    1. Christian Kleiber, 2014. "The Generalized Lognormal Distribution and the Stieltjes Moment Problem," Journal of Theoretical Probability, Springer, vol. 27(4), pages 1167-1177, December.
    2. repec:bla:jindec:v:49:y:2001:i:2:p:113-35 is not listed on IDEAS
    3. Richard Baldwin & James Harrigan, 2011. "Zeros, Quality, and Space: Trade Theory and Trade Evidence," American Economic Journal: Microeconomics, American Economic Association, vol. 3(2), pages 60-88, May.
    4. Bruce A. Blonigen & Anson Soderbery, 2019. "Measuring the Benefits of Foreign Product Variety with an Accurate Variety Set," World Scientific Book Chapters, in: Foreign Direct Investment, chapter 15, pages 501-538, World Scientific Publishing Co. Pte. Ltd..
    5. Nigai, Sergey, 2017. "A tale of two tails: Productivity distribution and the gains from trade," Journal of International Economics, Elsevier, vol. 104(C), pages 44-62.
    6. Paolo Bertoletti & Federico Etro, 2017. "Monopolistic Competition when Income Matters," Economic Journal, Royal Economic Society, vol. 127(603), pages 1217-1243, August.
    7. Simon P. Anderson & André de Palma, 2001. "Product Diversity in Asymmetric Oligopoly: Is the Quality of Consumer Goods too Low?," Journal of Industrial Economics, Wiley Blackwell, vol. 49(2), pages 113-135, June.
    8. David Atkin & Azam Chaudhry & Shamyla Chaudhry & Amit K. Khandelwal & Eric Verhoogen, 2015. "Markup and Cost Dispersion across Firms: Direct Evidence from Producer Surveys in Pakistan," American Economic Review, American Economic Association, vol. 105(5), pages 537-544, May.
    9. Marc J. Melitz, 2003. "The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity," Econometrica, Econometric Society, vol. 71(6), pages 1695-1725, November.
    10. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
    11. ANDERSON, Simon P. & de PALMA, André & THISSE, Jacques-François, 1992. "Interpretations of the logit discrete choice models and the theory of product differentiation," LIDAM Reprints CORE 1017, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Anderson, Simon & de Palma, André, 2015. "Economic distributions and primitive distributions in monopolistic competition," CEPR Discussion Papers 10748, C.E.P.R. Discussion Papers.
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    Cited by:

    1. Mohapatra, Debashrita, 2024. "Estimating substitution patterns and demand curvature in Discrete-Choice models of product differentiation," 2024 Annual Meeting, July 28-30, New Orleans, LA 343538, Agricultural and Applied Economics Association.
    2. Anderson, Simon P. & de Palma, André, 2024. "Economic distributions, primitive distributions, and demand recovery in monopolistic competition," Journal of Economic Theory, Elsevier, vol. 217(C).

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    More about this item

    Keywords

    Ces; Monopolistic competition; Quality; Closed power-family distributions; Pareto; Power; Generalised (log-)normal; Logit; Mark-ups; Box-cox;
    All these keywords.

    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • F12 - International Economics - - Trade - - - Models of Trade with Imperfect Competition and Scale Economies; Fragmentation

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