IDEAS home Printed from https://ideas.repec.org/b/spr/mathfi/v18y2024i2d10.1007_s11579-023-00333-z.html
   My bibliography  Save this book

A mean field model for the interactions between firms on the markets of their inputs

Author

Listed:
  • Yves Achdou

    (Université de Paris Cité and Sorbonne Université, CNRS)

  • Guillaume Carlier

    (Université Paris Dauphine, PSL
    INRIA-Paris)

  • Quentin Petit

    (Université Paris Dauphine, PSL
    EDF R &D)

  • Daniela Tonon

    (Università degli Studi di Padova)

Abstract

We consider an economy made of competing firms which are heterogeneous in their capital and use several inputs for producing goods. Their consumption policy is fixed rationally by maximizing a utility and their capital cannot fall below a given threshold (state constraint). We aim at modeling the interactions between firms on the markets of the different inputs on the long term. The stationary equlibria are described by a system of coupled non-linear differential equations: a Hamilton–Jacobi equation describing the optimal control problem of a single atomistic firm; a continuity equation describing the distribution of the individual state variable (the capital) in the population of firms; the equilibria on the markets of the production factors. We prove the existence of equilibria under suitable assumptions.

Suggested Citation

  • Yves Achdou & Guillaume Carlier & Quentin Petit & Daniela Tonon, 2024. "A mean field model for the interactions between firms on the markets of their inputs," Mathematics and Financial Economics, Springer, volume 18, number 2, December.
    • Handle: RePEc:spr:mathfi:v:18:y:2024:i:2:d:10.1007_s11579-023-00333-z
    DOI: 10.1007/s11579-023-00333-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11579-023-00333-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11579-023-00333-z?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. Diogo A. Gomes & João Saúde, 2021. "A Mean-Field Game Approach to Price Formation," Dynamic Games and Applications, Springer, vol. 11(1), pages 29-53, March.
    2. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lionse & Benjamin Moll, 2022. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(1), pages 45-86.
    3. Erzo G. J. Luttmer, 2007. "Selection, Growth, and the Size Distribution of Firms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(3), pages 1103-1144.
    4. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(3), pages 659-684.
    5. Fernando Alvarez & Francesco Lippi & Panagiotis Souganidis, 2023. "Price Setting With Strategic Complementarities as a Mean Field Game," Econometrica, Econometric Society, vol. 91(6), pages 2005-2039, November.
    6. Hopenhayn, Hugo A, 1992. "Entry, Exit, and Firm Dynamics in Long Run Equilibrium," Econometrica, Econometric Society, vol. 60(5), pages 1127-1150, September.
    7. Fernando Alvarez & Hervé Le Bihan & Francesco Lippi, 2016. "The Real Effects of Monetary Shocks in Sticky Price Models: A Sufficient Statistic Approach," American Economic Review, American Economic Association, vol. 106(10), pages 2817-2851, October.
    8. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 953-969.
    Full references (including those not matched with items on IDEAS)

    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. Krueger, Dirk & Uhlig, Harald, 2022. "Neoclassical Growth with Limited Commitment," CEPR Discussion Papers 17757, C.E.P.R. Discussion Papers.
    2. Arellano, Cristina & Bai, Yan & Zhang, Jing, 2012. "Firm dynamics and financial development," Journal of Monetary Economics, Elsevier, vol. 59(6), pages 533-549.
    3. Dirk Krueger & Harald Uhlig, 2024. "Neoclassical Growth with Limited Commitment," PIER Working Paper Archive 24-021, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    4. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lions & Benjamin Moll, 2017. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach," NBER Working Papers 23732, National Bureau of Economic Research, Inc.
    5. Parro, Francisco, 2024. "Unveiling the impact of income taxes on inequality in a HACT model," Journal of Macroeconomics, Elsevier, vol. 79(C).
    6. Thomas J. Sargent & John Stachurski, 2024. "Dynamic Programming: Finite States," Papers 2401.10473, arXiv.org.
    7. Ruitu Xu & Yifei Min & Tianhao Wang & Zhaoran Wang & Michael I. Jordan & Zhuoran Yang, 2023. "Finding Regularized Competitive Equilibria of Heterogeneous Agent Macroeconomic Models with Reinforcement Learning," Papers 2303.04833, arXiv.org.
    8. Light, Bar & Weintraub, Gabriel, 2018. "Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics," Research Papers 3731, Stanford University, Graduate School of Business.
    9. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, April.
    10. Schesch, Constantin, 2024. "Pseudospectral methods for continuous-time heterogeneous-agent models," Journal of Economic Dynamics and Control, Elsevier, vol. 163(C).
    11. Alexandre Gaillard & Christian Hellwig & Philipp Wangner & Nicolas Werquin, 2023. "Consumption, Wealth, and Income Inequality: A Tale of Tails," Working Paper Series WP 2023-43, Federal Reserve Bank of Chicago.
    12. Granda, Catalina & Hamann, Franz & Tamayo, Cesar E., 2019. "Credit and saving constraints in general equilibrium: A quantitative exploration," Journal of Development Economics, Elsevier, vol. 140(C), pages 302-319.
    13. Daron Acemoglu & Martin Kaae Jensen, 2015. "Robust Comparative Statics in Large Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 123(3), pages 587-640.
    14. Andrew Lyasoff, 2023. "Self-Aware Transport of Economic Agents," Papers 2303.12567, arXiv.org, revised Aug 2024.
    15. Frederick Ploeg, 2023. "Fiscal Costs of Climate Policies: Role of Tax, Political, and Behavioural Distortions," De Economist, Springer, vol. 171(2), pages 119-137, June.
    16. Qiusha Peng, 2019. "Financial Frictions, Entry and Growth: A Study of China," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 34, pages 267-282, October.
    17. Kaas, Leo, 2023. "Block-recursive equilibria in heterogeneous-agent models," Journal of Economic Theory, Elsevier, vol. 212(C).
    18. Bar Light, 2021. "Stochastic Comparative Statics in Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 797-810, May.
    19. Galo Nuno & Benjamin Moll, 2018. "Social Optima in Economies with Heterogeneous Agents," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 28, pages 150-180, April.
    20. Zongwu Cai & Hongwei Mei & Rui Wang, 2024. "Model Specification Tests of Heterogenous Agent Models with Aggregate Shocks under Partial Information," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202405, University of Kansas, Department of Economics, revised Feb 2024.

    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:spr:mathfi:v:18:y:2024:i:2:d:10.1007_s11579-023-00333-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.