Geodesic
Optimal stationary regimes in Kaldor's business-cycle controlled model
Matematičeskoe modelirovanie, Tome 31 (2019) no. 2, pp. 33-47.

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The paper studies optimal stationary regimes in a controlled version of N. Kaldor's business cycle model. The parameter characterizing stimulation of demand by a central planner is considered as a control. The value of the stimulating policy is modeled via quadratic function, and the instantaneous utility function is defined as the value of the national income minus the cost of the stimulating policy. In the corresponding optimization problem, the existence of an optimal stationary regime is proved and conditions that guarantee its uniqueness are given. It is shown that optimization of the stationary state always leads to greater values of both the instantaneous utility function and the consumption than in stationary states of initial (uncontrolled) model. The results of numerical simulation are considered as well.
Keywords: dynamic models in economics, N. Kaldor's business cycle model, optimal control, optimal stationary regime. 
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A. S. Aseev. Optimal stationary regimes in Kaldor's business-cycle controlled model. Matematičeskoe modelirovanie, Tome 31 (2019) no. 2, pp. 33-47. http://geodesic.mathdoc.fr/item/MM_2019_31_2_a2/

[1] D. Acemoglu, Introduction to modern economic growth, Princeton Univ. Press, Princeton N.J., 2008

[2] H.-W. Lorenz, Nonlinear dynamical economics and chaotic motion, Springer-Verlag, Berlin–Heidelberg, 1993 | MR | Zbl

[3] L.S. Tarasevich, V.M. Galperin, P.I. Grebnikov, A.I. Leusskii, Makroekonomika, Izd. SPbGUEF, Spb., 1992

[4] N. Kaldor, “A model of trade cycle”, The Economic Journal, 50:197 (1940), 78–92 | DOI

[5] T.V. Riazanova, Stokhasticheskie attraktory i indutsirovannye shumom yavleniia v modeliakh ekonomicheskoi dinamiki, Otchet o nauchno-issledovatelskoi rabote, UrFU, Ekaterinburg, 2013

[6] W.W. Chang, D.J. Smyth, “The existence and persistence of cycles in a nonlinear model: Kaldor's 1940 model re-examined”, Review of Economic Studies, 38:1 (1971), 37–44 | DOI | Zbl

[7] A. Krawiec, M. Szydalowski, “On nonlinear mechanics of business cycle model”, Regular and Chaotic Dynamics, 6:1 (2001), 101–118 | DOI | MR

[8] V. Balan, C.S. Stamin, “Stabilization with feedback control in the Kaldor economic model”, Proceeding of the 4-th International Colloquium “Mathematics in Engineering and Numerical Physics” (October 6–8, 2006, Bucharest, Romania), Geometry Balkan Press, 2007, 19–24 | MR | Zbl

[9] G. Gabisch, H.W. Lorenz, Business cycle theory. A survey of methods and concepts, Springer-Verlag, 1987

[10] J.C.J.M. Van Den Bergh, M.W. Hofkes, Theory and implementation of economic models for sustainable development, Economy Environment, 15, Springer Netherlands, 1998

[11] R.J. Barro, X. Sala-i-Martin, Economic growth, 2nd edition, The MIT Press, 2003

[12] Ph. Hartman, Ordinary differential equations, John Wiley Sons, New York–London–Sydney, 1964 | MR | Zbl

[13] M.J. Weitzman, Income, wealth, and the maximum principle, Harvard University Press, Cambridge, MA, 2003

[14] Iu.N. Kiselev, S.N. Avvakumov, M.V. Orlov, Optimalnoe upravlenie. Lineinaia teoriia i prilozheniia, MAKS Press, M., 2007