Stability analysis of a delay differential Kaldor's model with government policies

  • Tomás Caraballo
  • Alex Pereira da Silva


This paper is devoted to analysis of the stability of the economy according to an extended version of Kaldor's economic growth model. We consider the role of the government and its simultaneous monetary and fiscal policies and we study whether or not a time delay between the recognition and the implementation of its fiscal policy can affect the economic stability. Numerical simulations provide further conclusions about the long-term behavior of the four variables modeled—namely, national income, capacity of production, bonds value and money supply.


Barro, R. J. and Sala-i Martin, X., Economic growth, second ed., MIT Press, 2004.

Blinder, A. S. and Solow, R. M., Does fiscal policy matter?, J. Public Econ. 2 (1973), no. 4, 319–337.

Chang, W. W. and Smyth, D. J., The existence and persistence of cycles in a non-linear model: Kaldor's 1940 model re-examined, Rev. Econ. Stud. 38 (1971), no. 1, 37–44.

De Cesare, L. and Sportelli, M., A dynamic IS-LM model with delayed taxation revenues, Chaos Solitons Fractals 25 (2005), no. 1, 233–244.

Gabisch, G. and Lorenz, H.-W., Business cycle theory. a survey of methods and concepts, second ed., Springer-Verlag Berlin Heidelberg, 1989.

Gandolfo, G., Economic dynamics, fourth ed., Springer, Heidelberg, 2009.

Goodwin, R. M., A growth cycle, in “Socialism, Capitalism and Economics Growth” (Feinstein, C. H., ed.), Cambridge University Press, 1967, pp. 54–58.

Hale, J. K. and Verduyn Lunel, S. M., Introduction to functional-differential equations, Applied Mathematical Sciences, vol. 99, Springer-Verlag, New York, 1993.

Ichimura, S., Toward a general nonlinear macrodynamic theory of economic fluctuations, in “Post-Keynesian Economics”, Rutgers University Press, 1954, pp. 192–226.

Kaddar, A. and Talibi Alaoui, H., Hopf bifurcation analysis in a delayed Kaldor-Kalecki model of business cycle, Nonlinear Anal. Model. Control 13 (2008), no. 4, 439–449.

Kaldor, N., A model of the trade cycle, Econ. J. 50 (1940), no. 197, 78–92.

Kalecki, M., A macrodynamic theory of business cycles, Econometrica 3 (1935), no. 3, 327–344.

Krawiec, A. and Szydłowski, M., The Kaldor-Kalecki business cycle model, Ann. Oper. Res. 89 (1999), 89–100.

Kuang, Y., Delay differential equations with applications in population dynamics, Mathematics in Science and Engineering, vol. 191, Academic Press, Inc., Boston, MA, 1993.

Mankiw, N. G., Macroeconomics, fifth ed., Worth Publishers, 2003.

Sala-i Martin, X., The world distribution of income: falling poverty and \dots convergence, period, The Quarterly Journal of Economics 121 (2006), no. 2, 351–397.

Matsumoto, A., Destabilizing effects on income adjustment process with fiscal policy lags, Metroeconomica 59 (2008), no. 4, 713–735.

Matsumoto, A., Merlone, U., and Szidarovszky, F., Goodwin accelerator model revisited with fixed time delays, Commun. Nonlinear Sci. Numer. Simul. 58 (2018), 233–248.

Matsumoto, A., Nakayama, K., and Szidarovszky, F., Goodwin accelerator model revisited with piecewise linear delay investment, Advances in Pure Mathematics 08 (2018), 178–217.

Matsumoto, A. and Szidarovszky, F., Delay dynamics in a classical IS-LM model with tax collections., Metroeconomica 67 (2016), no. 4, 667–697.

Matsumoto, A., Szidarovszky, F., and Asada, T., Essays in economic dynamics: theory, simulation analysis, and methodological study, Springer Singapore, 2016.

Mircea, G., Neamţu, M., and Opriş, D., The Kaldor-Kalecki stochastic model of business cycle, Nonlinear Anal. Model. Control 16 (2011), no. 2, 191–205.

Takeuchi, Y. and Yamamura, T., Stability analysis of the Kaldor model with time delays: monetary policy and government budget constraint, Nonlinear Anal. Real World Appl. 5 (2004), no. 2, 277–308.

Wolfstetter, E., Fiscal policy and the classical growth cycle, Zeitschrift für Nationalökonomie 42 (1982), no. 4, 375–393.

Zhou, L. and Li, Y., A dynamic IS-LM business cycle model with two time delays in capital accumulation equation, J. Comput. Appl. Math. 228 (2009), no. 1, 182–187.
How to Cite
Caraballo, T., & Silva, A. (2020). Stability analysis of a delay differential Kaldor’s model with government policies. MATHEMATICA SCANDINAVICA, 126(1), 117-141.