IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v203y2022ics0022053122000618.html
   My bibliography  Save this article

Generalized separability and integrability: Consumer demand with a price aggregator

Author

Listed:
  • Fally, Thibault

Abstract

This paper examines demand systems where the demand for a good depends on other prices only through a common price aggregator (a scalar function of all prices). We refer to this property as “generalized separability” and provide the functional forms of demand that this property implies when demand is rational, i.e., derived from utility maximization. Generalized separability imposes restrictions on either income or price effects, and greater flexibility is obtained by adding indirect utility as an additional aggregator. We provide examples and applications which encompass a large variety of examples from the literature. In particular, generalized separability can be used in simple general-equilibrium models to obtain a more tractable framework and yet generate a wider range of effects of market size and productivity on firm size, entry, and prices.

Suggested Citation

  • Fally, Thibault, 2022. "Generalized separability and integrability: Consumer demand with a price aggregator," Journal of Economic Theory, Elsevier, vol. 203(C).
    • Handle: RePEc:eee:jetheo:v:203:y:2022:i:c:s0022053122000618
    DOI: 10.1016/j.jet.2022.105471
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053122000618
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2022.105471?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Michael Spence, 1976. "Product Selection, Fixed Costs, and Monopolistic Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(2), pages 217-235.
    2. Kiminori Matsuyama, 2019. "Engel's Law in the Global Economy: Demand‐Induced Patterns of Structural Change, Innovation, and Trade," Econometrica, Econometric Society, vol. 87(2), pages 497-528, March.
    3. David Atkin & Benjamin Faber & Thibault Fally & Marco Gonzalez-Navarro, 2020. "Measuring Welfare and Inequality with Incomplete Price Information," NBER Working Papers 26890, National Bureau of Economic Research, Inc.
    4. Novy, Dennis, 2013. "International trade without CES: Estimating translog gravity," Journal of International Economics, Elsevier, vol. 89(2), pages 271-282.
    5. Feenstra, Robert C., 2018. "Restoring the product variety and pro-competitive gains from trade with heterogeneous firms and bounded productivity," Journal of International Economics, Elsevier, vol. 110(C), pages 16-27.
    6. Marc J. Melitz & Giancarlo I. P. Ottaviano, 2021. "Market Size, Trade, and Productivity," World Scientific Book Chapters, in: Firms and Workers in a Globalized World Larger Markets, Tougher Competition, chapter 4, pages 87-108, World Scientific Publishing Co. Pte. Ltd..
    7. LaFrance, Jeffrey T. & Pope, Rulon D., 2006. "Full Rank Rational Demand Systems," CUDARE Working Papers 7152, University of California, Berkeley, Department of Agricultural and Resource Economics.
    8. Evgeny Zhelobodko & Sergey Kokovin & Mathieu Parenti & Jacques‐François Thisse, 2012. "Monopolistic Competition: Beyond the Constant Elasticity of Substitution," Econometrica, Econometric Society, vol. 80(6), pages 2765-2784, November.
    9. Feenstra, Robert C., 2003. "A homothetic utility function for monopolistic competition models, without constant price elasticity," Economics Letters, Elsevier, vol. 78(1), pages 79-86, January.
    10. Dixit, Avinash K & Stiglitz, Joseph E, 1977. "Monopolistic Competition and Optimum Product Diversity," American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.
    11. Pollak, Robert A, 1972. "Generalized Separability," Econometrica, Econometric Society, vol. 40(3), pages 431-453, May.
    12. Gene M. Grossman & Elhanan Helpman, 1991. "Quality Ladders in the Theory of Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(1), pages 43-61.
    13. Diego Comin & Danial Lashkari & Martí Mestieri, 2021. "Structural Change With Long‐Run Income and Price Effects," Econometrica, Econometric Society, vol. 89(1), pages 311-374, January.
    14. Parenti, Mathieu & Ushchev, Philip & Thisse, Jacques-François, 2017. "Toward a theory of monopolistic competition," Journal of Economic Theory, Elsevier, vol. 167(C), pages 86-115.
    15. Blackorby, Charles & Davidson, Russell & Schworm, William, 1991. "Implicit separability: Characterisation and implications for consumer demands," Journal of Economic Theory, Elsevier, vol. 55(2), pages 364-399, December.
    16. Fally, Thibault, 2019. "Generalized separability and the gains from trade," Economics Letters, Elsevier, vol. 178(C), pages 8-12.
    17. Paolo Bertoletti & Federico Etro, 2022. "Monopolistic competition, as you like it," Economic Inquiry, Western Economic Association International, vol. 60(1), pages 293-319, January.
    18. Krugman, Paul R., 1979. "Increasing returns, monopolistic competition, and international trade," Journal of International Economics, Elsevier, vol. 9(4), pages 469-479, November.
    19. Ligon, Ethan, 2016. "All λ-separable demands and rationalizing utility functions," Economics Letters, Elsevier, vol. 147(C), pages 16-18.
    20. Kimball, Miles S, 1995. "The Quantitative Analytics of the Basic Neomonetarist Model," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 27(4), pages 1241-1277, November.
    21. Paolo Bertoletti & Federico Etro, 2016. "Preferences, entry, and market structure," RAND Journal of Economics, RAND Corporation, vol. 47(4), pages 792-821, November.
    22. Marc J. Melitz & Gianmarco I. P. Ottaviano, 2008. "Market Size, Trade, and Productivity (DOI:10.111/j.1467-937x.2007.00463.x)," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 985-985.
    23. Paolo Bertoletti & Federico Etro & Ina Simonovska, 2018. "International Trade with Indirect Additivity," American Economic Journal: Microeconomics, American Economic Association, vol. 10(2), pages 1-57, May.
    24. Paolo Bertoletti & Federico Etro, 2017. "Monopolistic Competition when Income Matters," Economic Journal, Royal Economic Society, vol. 127(603), pages 1217-1243, August.
    25. Costas Arkolakis & Arnaud Costinot & Dave Donaldson & Andrés Rodríguez-Clare, 2019. "The Elusive Pro-Competitive Effects of Trade," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(1), pages 46-80.
    26. Nocke, Volker & Schutz, Nicolas, 2017. "Quasi-linear integrability," Journal of Economic Theory, Elsevier, vol. 169(C), pages 603-628.
    27. Peter Neary & Monika Mrazova, 2013. "Not so demanding: Preference structure, firm behavior, and welfare," Economics Series Working Papers 691, University of Oxford, Department of Economics.
    28. Matsuyama, Kiminori, 2017. "Beyond CES: Three Alternative Classes of Flexible Homothetic Demand Systems," CEPR Discussion Papers 12210, C.E.P.R. Discussion Papers.
    29. Arthur Lewbel & Krishna Pendakur, 2009. "Tricks with Hicks: The EASI Demand System," American Economic Review, American Economic Association, vol. 99(3), pages 827-863, June.
    30. E. Glen Weyl & Michal Fabinger, 2013. "Pass-Through as an Economic Tool: Principles of Incidence under Imperfect Competition," Journal of Political Economy, University of Chicago Press, vol. 121(3), pages 528-583.
    31. Jessie Handbury, 2021. "Are Poor Cities Cheap for Everyone? Non‐Homotheticity and the Cost of Living Across U.S. Cities," Econometrica, Econometric Society, vol. 89(6), pages 2679-2715, November.
    32. Xavier Vives, 1987. "Small Income Effects: A Marshallian Theory of Consumer Surplus and Downward Sloping Demand," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(1), pages 87-103.
    33. 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.
    34. Matsuyama, Kiminori, 2020. "When Does Procompetitive Entry Imply Excessive Entry?," CEPR Discussion Papers 14991, C.E.P.R. Discussion Papers.
    35. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
    36. David Hummels & Peter J. Klenow, 2005. "The Variety and Quality of a Nation's Exports," American Economic Review, American Economic Association, vol. 95(3), pages 704-723, June.
    37. Paolo Bertoletti & Federico Etro, 2021. "Monopolistic competition with generalized additively separable preferences [New trade models, same old gains?]," Oxford Economic Papers, Oxford University Press, vol. 73(2), pages 927-952.
    38. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-730, May.
    39. Jacques-Francois Thisse & Philip Ushchev, 2016. "When Can A Demand System Be Described By A Multinomial Logit With Income Effect?," HSE Working papers WP BRP 139/EC/2016, National Research University Higher School of Economics.
    40. Xavier Vives, 1990. "Trade Association Disclosure Rules, Incentives to Share Information, and Welfare," RAND Journal of Economics, The RAND Corporation, vol. 21(3), pages 409-430, Autumn.
    41. Deaton, Angus, 1974. "A Reconsideration of the Empirical Implications of Additive Preferences," Economic Journal, Royal Economic Society, vol. 84(334), pages 338-348, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Federico Etro, 2023. "Hybrid Marketplaces with Free Entry of Sellers," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 62(2), pages 119-148, March.
    2. Bhat, Chandra R., 2022. "A closed-form multiple discrete-count extreme value (MDCNTEV) model," Transportation Research Part B: Methodological, Elsevier, vol. 164(C), pages 65-86.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Monika Mrázová & J. Peter Neary, 2017. "Not So Demanding: Demand Structure and Firm Behavior," American Economic Review, American Economic Association, vol. 107(12), pages 3835-3874, December.
    2. Fally, Thibault, 2018. "Integrability and Generalized Separability," CEPR Discussion Papers 12667, C.E.P.R. Discussion Papers.
    3. Paolo Bertoletti & Federico Etro, 2022. "Monopolistic competition, as you like it," Economic Inquiry, Western Economic Association International, vol. 60(1), pages 293-319, January.
    4. Parenti, Mathieu & Ushchev, Philip & Thisse, Jacques-François, 2017. "Toward a theory of monopolistic competition," Journal of Economic Theory, Elsevier, vol. 167(C), pages 86-115.
    5. Etro, Federico, 2017. "Research in economics and monopolistic competition," Research in Economics, Elsevier, vol. 71(4), pages 645-649.
    6. Federico Etro, 2018. "Macroeconomics with Endogenous Markups and Optimal Taxation," Southern Economic Journal, John Wiley & Sons, vol. 85(2), pages 378-406, October.
    7. Mrázová, Monika & Neary, J. Peter, 2020. "IO for exports(s)," International Journal of Industrial Organization, Elsevier, vol. 70(C).
    8. Monika Mrázová & J. Peter Neary & Mathieu Parenti, 2021. "Sales and Markup Dispersion: Theory and Empirics," Econometrica, Econometric Society, vol. 89(4), pages 1753-1788, July.
    9. Etro, Federico, 2017. "The Heckscher–Ohlin model with monopolistic competition and general preferences," Economics Letters, Elsevier, vol. 158(C), pages 26-29.
    10. Fally, Thibault, 2019. "Generalized separability and the gains from trade," Economics Letters, Elsevier, vol. 178(C), pages 8-12.
    11. Dhingra, Swati & Morrow, John, 2017. "Efficiency in large markets with firm heterogeneity," Research in Economics, Elsevier, vol. 71(4), pages 718-728.
    12. Jacques-François Thisse & Philip Ushchev, 2018. "Monopolistic competition without apology," Chapters, in: Luis C. Corchón & Marco A. Marini (ed.), Handbook of Game Theory and Industrial Organization, Volume I, chapter 5, pages 93-136, Edward Elgar Publishing.
    13. Bykadorov, Igor & Kokovin, Sergey, 2017. "Can a larger market foster R&D under monopolistic competition with variable mark-ups?," Research in Economics, Elsevier, vol. 71(4), pages 663-674.
    14. Martin Alfaro, 2022. "The microeconomics of new trade models," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 55(3), pages 1539-1565, August.
    15. Etro, Federico, 2023. "Technologies for endogenous growth," Journal of Mathematical Economics, Elsevier, vol. 105(C).
    16. Nocco, Antonella & Ottaviano, Gianmarco I.P. & Salto, Matteo, 2019. "Geography, competition, and optimal multilateral trade policy," Journal of International Economics, Elsevier, vol. 120(C), pages 145-161.
    17. Badis Tabarki, 2020. "International Trade under Monopolistic Competition beyond the CES," Documents de travail du Centre d'Economie de la Sorbonne 20018, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    18. Badis Tabarki, 2020. "International Trade under Monopolistic Competition beyond the CES," Post-Print halshs-02966937, HAL.
    19. Feenstra, Robert C., 2018. "Restoring the product variety and pro-competitive gains from trade with heterogeneous firms and bounded productivity," Journal of International Economics, Elsevier, vol. 110(C), pages 16-27.
    20. Ziran Ding, 2022. "Firm heterogeneity, variable markups, and multinational production: A review from trade policy perspective," Journal of Economic Surveys, Wiley Blackwell, vol. 36(5), pages 1311-1357, December.

    More about this item

    Keywords

    Consumer demand; Separability; Price aggregator; Integrability; Rationalization; Non-homothetic preferences;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D40 - Microeconomics - - Market Structure, Pricing, and Design - - - General
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:203:y:2022:i:c:s0022053122000618. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.