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An optimal equilibrium for a reformulated Samuelson economic discrete time system

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  • Maria Filomena Barros

    (Universitat Autonoma de Barcelona
    Advanced Research Centre for Applied Mathematics (ARCAM))

  • Fernando Ortega

    (Universitat Autonoma de Barcelona
    Advanced Research Centre for Applied Mathematics (ARCAM))

Abstract

This paper studies the equilibrium of an extended case of the classical Samuelson’s multiplier–accelerator model for national economy. This case has incorporated some kind of memory into the system. We assume that total consumption and private investment depend upon the national income values. Then, delayed difference equations of third order are employed to describe the model, while the respective solutions of third-order polynomial correspond to the typical observed business cycles of real economy. We focus on the case that the equilibrium is not unique and provide a method to obtain the optimal equilibrium.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jecstr:v:8:y:2019:i:1:d:10.1186_s40008-019-0162-2
    DOI: 10.1186/s40008-019-0162-2
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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. Chari, V V & Christiano, Lawrence J & Kehoe, Patrick J, 1994. "Optimal Fiscal Policy in a Business Cycle Model," Journal of Political Economy, University of Chicago Press, vol. 102(4), pages 617-652, August.
    3. 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.
    4. Dassios, Ioannis K. & Szajowski, Krzysztof J., 2016. "Bayesian optimal control for a non-autonomous stochastic discrete time system," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 556-564.
    5. Frank Westerhoff, 2006. "Samuelson's multiplier-accelerator model revisited," Applied Economics Letters, Taylor & Francis Journals, vol. 13(2), pages 89-92.
    6. Chow, Gregory C, 1985. "A Model of Chinese National Income Determination," Journal of Political Economy, University of Chicago Press, vol. 93(4), pages 782-792, August.
    7. Arie P. Schinnar, 1978. "The Leontief Dynamic Generalized Inverse," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 92(4), pages 641-652.
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    Cited by:

    1. 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.
    2. 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.
    3. Muñoz-Guillermo, María, 2021. "Revisiting the business cycle model with cubic nonlinear investment function," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. Sorin Lugojan & Loredana Ciurdariu & Eugenia Grecu, 2022. "Another Case of Degenerated Discrete Chenciner Dynamic System and Economics," Mathematics, MDPI, vol. 10(20), pages 1-19, October.

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