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Revisiting Samuelson’s models, linear and nonlinear, stability conditions and oscillating dynamics

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  • Fabio Tramontana

    (Department DiMSEFA Università Cattolica del Sacro Cuore)

  • Laura Gardini

    (University of Urbino)

Abstract

In this work, we reconsider the dynamics of a few versions of the classical Samuelson’s multiplier–accelerator model for national economy. First we recall that the classical one with constant governmental expenditure, represented by a linear second-order difference equation, is able to generate oscillations converging to the equilibrium for a wide range of values of the parameters, and give its analytic solution for all the possible cases. A delayed version proposed in the recent literature, represented by a linear third-order difference equation, is also considered. We show that also this model is able to produce converging oscillations, and give a complete analysis of the stability region of the equilibrium. A new simple nonlinear model is proposed, showing that it keeps oscillatory behavior, although coupled with other dynamics related to global effects. Our analysis confirms that the seminal work of Samuelson and simple modifications of it, may give powerful tools in the study of the business cycles.

Suggested Citation

  • Fabio Tramontana & Laura Gardini, 2021. "Revisiting Samuelson’s models, linear and nonlinear, stability conditions and oscillating dynamics," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 10(1), pages 1-15, December.
    • Handle: RePEc:spr:jecstr:v:10:y:2021:i:1:d:10.1186_s40008-021-00239-3
    DOI: 10.1186/s40008-021-00239-3
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    References listed on IDEAS

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    1. Ioannis K. Dassios & Mel T. Devine, 2016. "A macroeconomic mathematical model for the national income of a union of countries with interaction and trade," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 5(1), pages 1-15, December.
    2. Dassios, Ioannis K. & Baleanu, Dumitru I., 2018. "Caputo and related fractional derivatives in singular systems," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 591-606.
    3. Frank Westerhoff, 2006. "Samuelson's multiplier-accelerator model revisited," Applied Economics Letters, Taylor & Francis Journals, vol. 13(2), pages 89-92.
    4. Fernando Ortega & Maria Filomena Barros, 2020. "The Samuelson macroeconomic model as a singular linear matrix difference equation," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 9(1), pages 1-10, December.
    5. Ioannis Dassios & Alexandros Zimbidis & Charalambos Kontzalis, 2014. "The Delay Effect in a Stochastic Multiplier–Accelerator Model," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 3(1), pages 1-24, December.
    6. Gemmell, Norman, 1990. "Wagner's Law, Relative Prices and the Size of the Public Sector," The Manchester School of Economic & Social Studies, University of Manchester, vol. 58(4), pages 361-377, December.
    7. Maria Filomena Barros & Fernando Ortega, 2019. "An optimal equilibrium for a reformulated Samuelson economic discrete time system," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 8(1), pages 1-10, December.
    8. Ilias Kostarakos & Stelios Kotsios, 2017. "Feedback policy rules for government spending: an algorithmic approach," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 6(1), pages 1-10, December.
    9. Puu, Tonu & Gardini, Laura & Sushko, Irina, 2005. "A Hicksian multiplier-accelerator model with floor determined by capital stock," Journal of Economic Behavior & Organization, Elsevier, vol. 56(3), pages 331-348, March.
    10. Dollery, Brian & Singh, Sukhvinder, 1998. "A Note on the Empirical Analysis of Wagner's Law," Economic Analysis and Policy, Elsevier, vol. 28(2), pages 245-257, September.
    11. Dalla, Eleni & Varelas, Erotokritos, 2016. "An economic model for the interpretation of business cycles and the efficiency of monetary policy," The Journal of Economic Asymmetries, Elsevier, vol. 14(PA), pages 29-38.
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