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On the microeconomic foundations of linear demand for differentiated products

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  • Amir, Rabah
  • Erickson, Philip
  • Jin, Jim

Abstract

This paper provides a thorough exploration of the microeconomic foundations for the multi-variate linear demand function for differentiated products, which is widely used in industrial organization. The setting is the standard representative consumer with a quasi-linear utility function. A key finding is that strict concavity of the quadratic utility function is critical for the demand system to be well defined. Otherwise, the true demand function may be quite complex: Multi-valued, non-linear and income-dependent. We uncover failures of duality relationships between substitute products and complementary products, as well as the incompatibility between high levels of complementarity and concavity. The two-good case emerges as a special case with strong but non-robust properties. A key implication is that all conclusions derived in applied economic models via the use of linear demand that does not satisfy the Law of Demand ought to be regarded with some suspicion.

Suggested Citation

  • Amir, Rabah & Erickson, Philip & Jin, Jim, 2017. "On the microeconomic foundations of linear demand for differentiated products," Journal of Economic Theory, Elsevier, vol. 169(C), pages 641-665.
  • Handle: RePEc:eee:jetheo:v:169:y:2017:i:c:p:641-665
    DOI: 10.1016/j.jet.2017.03.005
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    3. Camille Cornand & Rodolphe Dos Santos Ferreira, 2020. "The social value of information and the competition motive: price versus quantity games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1101-1137, November.
    4. Friberg, Richard & Steen, Frode & Ulsaker, Simen A., 2018. "Hump-shaped cross-price effects and the extensive margin in cross-border shopping," Discussion Paper Series in Economics 29/2018, Norwegian School of Economics, Department of Economics.
    5. Thomas Grebel & Lionel Nesta, 2020. "Competition and private R&D investment," PLOS ONE, Public Library of Science, vol. 15(5), pages 1-26, May.
    6. Choné, Philippe & Linnemer, Laurent, 2020. "Linear demand systems for differentiated goods: Overview and user’s guide," International Journal of Industrial Organization, Elsevier, vol. 73(C).
    7. Sugaya, Takuo & Wolitzky, Alexander, 2018. "Bounding payoffs in repeated games with private monitoring: n-player games," Journal of Economic Theory, Elsevier, vol. 175(C), pages 58-87.
    8. Michail Anthropelos & Constantinos Kardaras & Georgios Vichos, 2020. "Effective risk aversion in thin risk‐sharing markets," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1565-1590, October.
    9. Pinho, Joana & Resende, Joana & Soares, Isabel, 2018. "Capacity investment in electricity markets under supply and demand uncertainty," Energy, Elsevier, vol. 150(C), pages 1006-1017.
    10. Anne-Christine Barthel & Eric Hoffmann, 2020. "On the existence and stability of equilibria in N-firm Cournot–Bertrand oligopolies," Theory and Decision, Springer, vol. 88(4), pages 471-491, May.
    11. Tsuyoshi Toshimitsu & Tetsuya Nakajima, 2021. "On the “merger paradox” in price competition with asymmetric product differentiation," Australian Economic Papers, Wiley Blackwell, vol. 60(1), pages 153-162, March.
    12. Bos, Iwan & Vermeulen, Dries, 2019. "On the Microfoundation of Linear Oligopoly Demand," Research Memorandum 004, Maastricht University, Graduate School of Business and Economics (GSBE).
    13. Samuli Leppälä, 2020. "Innovation, R&D Spillovers, and the Variety and Concentration of the Local Industry Structure," Scandinavian Journal of Economics, Wiley Blackwell, vol. 122(3), pages 1231-1255, July.
    14. Klophaus, Richard & Grosche, Tobias, 2020. "Consumer surplus analysis of selected long-haul air transport routes connecting Germany with California and China," Research in Transportation Economics, Elsevier, vol. 80(C).
    15. Camille Cornand & Rodolphe dos Santos Ferreira, 2017. "The social value of information and the competition motive: Price vs. quantity games," Working Papers halshs-01614815, HAL.
    16. Philippe Choné & Laurent Linnemer, 2019. "The quasilinear quadratic utility model: an overview," CESifo Working Paper Series 7640, CESifo.
    17. Nocke, Volker & Schutz, Nicolas, 2017. "Quasi-linear integrability," Journal of Economic Theory, Elsevier, vol. 169(C), pages 603-628.
    18. Mariana Cunha & Filipa Mota, 2020. "Coordinated Effects of Corporate Social Responsibility," Journal of Industry, Competition and Trade, Springer, vol. 20(4), pages 617-641, December.
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    More about this item

    Keywords

    Linear demand; Gross substitutes; Gross complements; Edgeworth complements; Representative consumer; Law of Demand;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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