IDEAS home Printed from https://ideas.repec.org/a/spr/snbeco/v1y2021i6d10.1007_s43546-021-00058-5.html
   My bibliography  Save this article

Sustainability over sets and the business cycle

Author

Listed:
  • Lixiao Hao

    (Hebei University of Technology)

  • Vasilios I. Manousiouthakis

    (University of California at Los Angeles (UCLA))

Abstract

Many rigorous works have examined the behavior of Kaldor business cycle models. In this paper, utilizing the sustainability over sets (SOS) concept, a general theorem is proven establishing necessary and sufficient conditions for the existence and identification of rectangular sustainable sets for a general Kaldor model. These conditions can be readily verified, either in the two-dimensional space of lower and upper bounds on income, or in the one-dimensional space of upper bound on income, thus enabling identification of the region of economic sustainability for the considered Kaldor model. The Theorem’s power is illustrated with a case study of a particular Kaldor business cycle model from the literature that can exhibit rich dynamic behavior, and can give rise to economic sustainability regions that encompass multiple stable equilibrium points. Furthermore, a methodology is also presented that identifies non-rectangular sustainable sets, when the imposition of tight lower and upper bounds on one of the economic system variables (e.g., income) prevents the existence of a sustainable rectangular set.

Suggested Citation

  • Lixiao Hao & Vasilios I. Manousiouthakis, 2021. "Sustainability over sets and the business cycle," SN Business & Economics, Springer, vol. 1(6), pages 1-26, June.
    • Handle: RePEc:spr:snbeco:v:1:y:2021:i:6:d:10.1007_s43546-021-00058-5
    DOI: 10.1007/s43546-021-00058-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s43546-021-00058-5
    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/s43546-021-00058-5?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. Varian, Hal R, 1979. "Catastrophe Theory and the Business Cycle," Economic Inquiry, Western Economic Association International, vol. 17(1), pages 14-28, January.
    2. Hiroki Murakami, 2018. "A two†sector Keynesian model of business cycles," Metroeconomica, Wiley Blackwell, vol. 69(2), pages 444-472, May.
    3. Dobrescu, Loretti I. & Opris, Dumitru, 2009. "Neimark–Sacker bifurcation for the discrete-delay Kaldor model," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2462-2468.
    4. Lorenz, Hans-Walter, 1987. "Strange attractors in a multisector business cycle model," Journal of Economic Behavior & Organization, Elsevier, vol. 8(3), pages 397-411, September.
    5. A. Krawiec & M. Szydlowski, 1999. "The Kaldor‐Kalecki business cycle model," Annals of Operations Research, Springer, vol. 89(0), pages 89-100, January.
    6. Eric Neumayer, 2013. "Weak versus Strong Sustainability," Books, Edward Elgar Publishing, number 14993.
    7. John Foster, 2006. "Why Is Economics Not a Complex Systems Science?," Journal of Economic Issues, Taylor & Francis Journals, vol. 40(4), pages 1069-1091, December.
    8. Giorgio Rodano & Gian Italo Bischi & Enrico Saltari & Roberto Dieci, 2001. "Multiple attractors and global bifurcations in a Kaldor-type business cycle model," Journal of Evolutionary Economics, Springer, vol. 11(5), pages 527-554.
    9. W. W. Chang & D. J. Smyth, 1971. "The Existence and Persistence of Cycles in a Non-linear Model: Kaldor's 1940 Model Re-examined," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(1), pages 37-44.
    10. Katriina Soini & Joost Dessein, 2016. "Culture-Sustainability Relation: Towards a Conceptual Framework," Sustainability, MDPI, vol. 8(2), pages 1-12, February.
    11. Andriantiatsaholiniaina, Luc A. & Kouikoglou, Vassilis S. & Phillis, Yannis A., 2004. "Evaluating strategies for sustainable development: fuzzy logic reasoning and sensitivity analysis," Ecological Economics, Elsevier, vol. 48(2), pages 149-172, February.
    12. Nicola Dempsey & Glen Bramley & Sinéad Power & Caroline Brown, 2011. "The social dimension of sustainable development: Defining urban social sustainability," Sustainable Development, John Wiley & Sons, Ltd., vol. 19(5), pages 289-300, September.
    13. Dobrescu, Loretti I. & Opris, Dumitru, 2009. "Neimark–Sacker bifurcation for the discrete-delay Kaldor–Kalecki model," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2405-2413.
    14. Murakami, Hiroki, 2014. "Keynesian systems with rigidity and flexibility of prices and inflation–deflation expectations," Structural Change and Economic Dynamics, Elsevier, vol. 30(C), pages 68-85.
    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. Hiroki Murakami, 2019. "A note on the “unique” business cycle in the Keynesian theory," Metroeconomica, Wiley Blackwell, vol. 70(3), pages 384-404, July.
    2. Agliari, Anna & Dieci, Roberto & Gardini, Laura, 2007. "Homoclinic tangles in a Kaldor-like business cycle model," Journal of Economic Behavior & Organization, Elsevier, vol. 62(3), pages 324-347, March.
    3. Irina Bashkirtseva & Davide Radi & Lev Ryashko & Tatyana Ryazanova, 2018. "On the Stochastic Sensitivity and Noise-Induced Transitions of a Kaldor-Type Business Cycle Model," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 699-718, March.
    4. Hiroki Murakami, 2016. "Alternative monetary policies and economic stability in a medium-term Keynesian model," Evolutionary and Institutional Economics Review, Springer, vol. 13(2), pages 323-362, December.
    5. Murakami, Hiroki, 2020. "Monetary policy in the unique growth cycle of post Keynesian systems," Structural Change and Economic Dynamics, Elsevier, vol. 52(C), pages 39-49.
    6. Wu, Xiaoqin P., 2011. "Codimension-2 bifurcations of the Kaldor model of business cycle," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 28-42.
    7. Murakami, Hiroki, 2018. "Existence and uniqueness of growth cycles in post Keynesian systems," Economic Modelling, Elsevier, vol. 75(C), pages 293-304.
    8. Januário, Cristina & Grácio, Clara & Duarte, Jorge, 2009. "Measuring complexity in a business cycle model of the Kaldor type," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2890-2903.
    9. Murakami, Hiroki, 2015. "Wage flexibility and economic stability in a non-Walrasian model of economic growth," Structural Change and Economic Dynamics, Elsevier, vol. 32(C), pages 25-41.
    10. Irina Bashkirtseva & Alexander Pisarchik & Lev Ryashko & Tatyana Ryazanova, 2016. "Excitability And Complex Mixed-Mode Oscillations In Stochastic Business Cycle Model," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 19(01n02), pages 1-16, February.
    11. Murakami, Hiroki & Zimka, Rudolf, 2020. "On dynamics in a two-sector Keynesian model of business cycles," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    12. Todorov, Vladislav & Marinova, Dora, 2011. "Modelling sustainability," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1397-1408.
    13. Jalan, Jyotsna & Ravallion, Martin, 2001. "Household income dynamics in rural China," Policy Research Working Paper Series 2706, The World Bank.
    14. Wenjie Hu & Hua Zhao & Tao Dong, 2018. "Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect," Complexity, Hindawi, vol. 2018, pages 1-11, January.
    15. Devine, James G., 2011. "The great moderation and "falling off a cliff": Neo-Kaldorian dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 78(3), pages 366-373, May.
    16. Yeva Nersisyan & L. Randall Wray, 2010. "The global financial crisis and the shift to shadow banking," European Journal of Economics and Economic Policies: Intervention, Edward Elgar Publishing, vol. 7(2), pages 377-400.
    17. Chu, Peter C., 2006. "First-passage time for stability analysis of the Kaldor model," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1355-1368.
    18. Murakami, Hiroki, 2014. "Keynesian systems with rigidity and flexibility of prices and inflation–deflation expectations," Structural Change and Economic Dynamics, Elsevier, vol. 30(C), pages 68-85.
    19. Loretti I. Dobrescu & Dumitru Opris, 2008. "Hopf bifurcation for the discrete - delay Kaldor - Kalecki model," "Marco Fanno" Working Papers 0067, Dipartimento di Scienze Economiche "Marco Fanno".
    20. Szydłowski, Marek & Krawiec, Adam, 2005. "The stability problem in the Kaldor–Kalecki business cycle model," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 299-305.

    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:snbeco:v:1:y:2021:i:6:d:10.1007_s43546-021-00058-5. 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.