IDEAS home Printed from https://ideas.repec.org/a/bla/metroe/v70y2019i3p384-404.html
   My bibliography  Save this article

A note on the “unique” business cycle in the Keynesian theory

Author

Listed:
  • Hiroki Murakami

Abstract

In this paper, we explore the existence and “uniqueness” of a limit cycle in the Keynesian theory. In a model with the simplest (linear) Keynesian consumption function and the logistic investment function based upon the profit principle, we establish the existence of a periodic orbit (irrespective of the speed of quantity adjustment) and, with the help of the theory on generalized Liénard systems, verify the uniqueness of it for the case in which the speed of quantity adjustment is large enough.

Suggested Citation

  • Hiroki Murakami, 2019. "A note on the “unique” business cycle in the Keynesian theory," Metroeconomica, Wiley Blackwell, vol. 70(3), pages 384-404, July.
    • Handle: RePEc:bla:metroe:v:70:y:2019:i:3:p:384-404
    DOI: 10.1111/meca.12222
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/meca.12222
    Download Restriction: no
    File URL: https://libkey.io/10.1111/meca.12222?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
    ---><---

    References listed on IDEAS

    as
    1. Chiarella,Carl & Flaschel,Peter, 2011. "The Dynamics of Keynesian Monetary Growth," Cambridge Books, Cambridge University Press, number 9780521180184, September.
    2. Olivier Allain, 2015. "Tackling the instability of growth: a Kaleckian-Harrodian model with an autonomous expenditure component," Cambridge Journal of Economics, Cambridge Political Economy Society, vol. 39(5), pages 1351-1371.
    3. Marc Lavoie, 2016. "Convergence Towards the Normal Rate of Capacity Utilization in Neo-Kaleckian Models: The Role of Non-Capacity Creating Autonomous Expenditures," Metroeconomica, Wiley Blackwell, vol. 67(1), pages 172-201, February.
    4. 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.
    5. Varian, Hal R, 1979. "Catastrophe Theory and the Business Cycle," Economic Inquiry, Western Economic Association International, vol. 17(1), pages 14-28, January.
    6. K. Vela Velupillai, 2008. "JAPANESE CONTRIBUTIONS TO NONLINEAR CYCLE THEORY IN THE 1950s," The Japanese Economic Review, Japanese Economic Association, vol. 59(1), pages 54-74, March.
    7. Reiner Franke, 2017. "A simple approach to overcome the problems arising from the Keynesian stability condition," European Journal of Economics and Economic Policies: Intervention, Edward Elgar Publishing, vol. 14(1), pages 48-69, April.
    8. Sasakura, Kazuyuki, 1994. "On the dynamic behavior of Schinasi's business cycle model," Journal of Macroeconomics, Elsevier, vol. 16(3), pages 423-444.
    9. Murakami Hiroki, 2017. "Time elements and oscillatory fluctuations in the Keynesian macroeconomic system," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(2), pages 1-22, April.
    10. Peter Skott, 2012. "Theoretical And Empirical Shortcomings Of The Kaleckian Investment Function," Metroeconomica, Wiley Blackwell, vol. 63(1), pages 109-138, February.
    11. Kind, Christoph, 1999. "Remarks on the economic interpretation of Hopf bifurcations," Economics Letters, Elsevier, vol. 62(2), pages 147-154, February.
    12. Hiroki Murakami, 2018. "A two†sector Keynesian model of business cycles," Metroeconomica, Wiley Blackwell, vol. 69(2), pages 444-472, May.
    13. Sasakura, Kazuyuki, 1996. "The business cycle model with a unique stable limit cycle," Journal of Economic Dynamics and Control, Elsevier, vol. 20(9-10), pages 1763-1773.
    14. Serrano, Franklin, 1995. "Long Period Effective Demand and the Sraffian Supermultiplier," Contributions to Political Economy, Cambridge Political Economy Society, vol. 14(0), pages 67-90.
    15. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    16. Asada, Toichiro & Chen, Pu & Chiarella, Carl & Flaschel, Peter, 2006. "Keynesian dynamics and the wage-price spiral: A baseline disequilibrium model," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 90-130, March.
    17. Benhabib, Jess & Miyao, Takahiro, 1981. "Some New Results on the Dynamics of the Generalized Tobin Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(3), pages 589-596, October.
    18. Akitaka Dohtani & Toshio Inaba & Hiroshi Osaka, 2007. "Corridor Stability of the Neoclassical Steady State," Springer Books, in: Toichiro Asada & Toshiharu Ishikawa (ed.), Time and Space in Economics, chapter 7, pages 129-143, Springer.
    19. Grasman, Johan & Wentzel, Jolanda J., 1994. "Co-existence of a limit cycle and an equilibrium in Kaldor's business cycle model and its consequences," Journal of Economic Behavior & Organization, Elsevier, vol. 24(3), pages 369-377, August.
    20. Peter Flaschel, 2001. "Viability and Corridor Stability in Keynesian Supply-Driven Growth," Metroeconomica, Wiley Blackwell, vol. 52(1), pages 26-48, February.
    21. Murakami, Hiroki & Asada, Toichiro, 2018. "Inflation-deflation expectations and economic stability in a Kaleckian system," Journal of Economic Dynamics and Control, Elsevier, vol. 92(C), pages 183-201.
    22. Franke Reiner, 2012. "Microfounded Animal Spirits in the New Macroeconomic Consensus," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(4), pages 1-41, October.
    23. Kosobud, Richard F & O'Neill, William D, 1972. "Stochastic Implications of Orbital Asymptotic Stability of a Nonlinear Trade Cycle Model," Econometrica, Econometric Society, vol. 40(1), pages 69-86, January.
    24. Dohtani, Akitaka, 2010. "A growth-cycle model of Solow-Swan type, I," Journal of Economic Behavior & Organization, Elsevier, vol. 76(2), pages 428-444, November.
    25. Semmler, Willi & Sieveking, Malte, 1993. "Nonlinear liquidity-growth dynamics with corridor-stability," Journal of Economic Behavior & Organization, Elsevier, vol. 22(2), pages 189-208, October.
    26. 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.
    27. Hiroshi Yoshikawa, 2015. "Stochastic macro-equilibrium: a microfoundation for the Keynesian economics," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 10(1), pages 31-55, April.
    28. William A. Brock & Cars H. Hommes, 2001. "A Rational Route to Randomness," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 16, pages 402-438, Edward Elgar Publishing.
    29. Skott,Peter, 2008. "Conflict and Effective Demand in Economic Growth," Cambridge Books, Cambridge University Press, number 9780521066310, September.
    30. H. Rose, 1967. "On the Non-Linear Theory of the Employment Cycle," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(2), pages 153-173.
    31. Eckhard Hein & Marc Lavoie & Till van Treeck, 2011. "Some instability puzzles in Kaleckian models of growth and distribution: a critical survey," Cambridge Journal of Economics, Cambridge Political Economy Society, vol. 35(3), pages 587-612.
    32. Puu, Tonu, 1986. "Multiplier-accelerator models revisited," Regional Science and Urban Economics, Elsevier, vol. 16(1), pages 81-95, February.
    33. James Tobin, 1993. "Price Flexibility and Output Stability: An Old Keynesian View," Journal of Economic Perspectives, American Economic Association, vol. 7(1), pages 45-65, Winter.
    34. Torre, V, 1977. "Existence of Limit Cycles and Control in Complete Keynesian System by Theory of Bifurcations," Econometrica, Econometric Society, vol. 45(6), pages 1457-1466, September.
    35. Roberto Veneziani & Luca Zamparelli & Reiner Franke & Frank Westerhoff, 2017. "Taking Stock: A Rigorous Modelling Of Animal Spirits In Macroeconomics," Journal of Economic Surveys, Wiley Blackwell, vol. 31(5), pages 1152-1182, December.
    36. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-896, July.
    37. Matsumoto, Akio, 2009. "Note on Goodwin's 1951 nonlinear accelerator model with an investment delay," Journal of Economic Dynamics and Control, Elsevier, vol. 33(4), pages 832-842, April.
    38. Franke, Reiner, 2014. "Aggregate sentiment dynamics: A canonical modelling approach and its pleasant nonlinearities," Structural Change and Economic Dynamics, Elsevier, vol. 31(C), pages 64-72.
    39. Steindl, Josef, 1979. "Stagnation Theory and Stagnation Policy," Cambridge Journal of Economics, Cambridge Political Economy Society, vol. 3(1), pages 1-14, March.
    40. Murakami, Hiroki, 2018. "Existence and uniqueness of growth cycles in post Keynesian systems," Economic Modelling, Elsevier, vol. 75(C), pages 293-304.
    41. 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.
    42. Peter Skott, 2017. "Autonomous Demand and the Harrodian Criticisms of the Kaleckian Model," Metroeconomica, Wiley Blackwell, vol. 68(1), pages 185-193, February.
    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. 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.
    2. Murakami, Hiroki, 2018. "Existence and uniqueness of growth cycles in post Keynesian systems," Economic Modelling, Elsevier, vol. 75(C), pages 293-304.
    3. Murakami, Hiroki & Zimka, Rudolf, 2020. "On dynamics in a two-sector Keynesian model of business cycles," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    4. Murakami, Hiroki, 2022. "The unique limit cycle in post Keynesian theory," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    5. Murakami, Hiroki & Asada, Toichiro, 2018. "Inflation-deflation expectations and economic stability in a Kaleckian system," Journal of Economic Dynamics and Control, Elsevier, vol. 92(C), pages 183-201.
    6. 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.
    7. Di Guilmi, Corrado & Galanis, Giorgos & Proaño, Christian R., 2023. "A Baseline Model of Behavioral Political Cycles and Macroeconomic Fluctuations," Journal of Economic Behavior & Organization, Elsevier, vol. 213(C), pages 50-67.
    8. Stephen Thompson, 2022. "“The total movement of this disorder is its order”: Investment and utilization dynamics in long‐run disequilibrium," Metroeconomica, Wiley Blackwell, vol. 73(2), pages 638-682, May.
    9. Flaschel, Peter & Charpe, Matthieu & Galanis, Giorgos & Proaño, Christian R. & Veneziani, Roberto, 2018. "Macroeconomic and stock market interactions with endogenous aggregate sentiment dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 237-256.
    10. Peter Skott & Júlio Fernando Costa Santos & José Luís da Costa Oreiro, 2022. "Supermultipliers, ‘endogenous autonomous demand’ and functional finance," Metroeconomica, Wiley Blackwell, vol. 73(1), pages 220-244, February.
    11. Eckhard Hein & Ryan Woodgate, 2021. "Stability issues in Kaleckian models driven by autonomous demand growth—Harrodian instability and debt dynamics," Metroeconomica, Wiley Blackwell, vol. 72(2), pages 388-404, May.
    12. Eckhard Hein, 2019. "Harrodian instability in Kaleckian models and Steindlian solutions," FMM Working Paper 46-2019, IMK at the Hans Boeckler Foundation, Macroeconomic Policy Institute.
    13. Dohtani, Akitaka, 2010. "A growth-cycle model of Solow-Swan type, I," Journal of Economic Behavior & Organization, Elsevier, vol. 76(2), pages 428-444, November.
    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.
    15. Gahn, Santiago José, 2021. "On the adjustment of capacity utilisation to aggregate demand: Revisiting an old Sraffian critique to the Neo-Kaleckian model," Structural Change and Economic Dynamics, Elsevier, vol. 58(C), pages 325-360.
    16. Murakami Hiroki, 2017. "Time elements and oscillatory fluctuations in the Keynesian macroeconomic system," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(2), pages 1-22, April.
    17. Guilherme Spinato Morlin & Nikolas Passos & Riccardo Pariboni, 2024. "Growth Theory and the Growth Model Perspective: Insights from the Supermultiplier," Review of Political Economy, Taylor & Francis Journals, vol. 36(3), pages 1130-1155, July.
    18. De Cesare, Luigi & Sportelli, Mario, 2005. "A dynamic IS-LM model with delayed taxation revenues," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 233-244.
    19. Santiago José Gahn & Alejandro González, 2022. "On the empirical content of the convergence debate: Cross‐country evidence on growth and capacity utilisation," Metroeconomica, Wiley Blackwell, vol. 73(3), pages 825-855, July.
    20. Peter Skott, 2019. "Autonomous demand, Harrodian instability and the supply side," Metroeconomica, Wiley Blackwell, vol. 70(2), pages 233-246, May.

    More about this item

    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:bla:metroe:v:70:y:2019:i:3:p:384-404. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0026-1386 .

    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.