Abstract
This chapter studies the dynamics of the Kaldor–Kalecki model of national income and capital stock. The investment function is assumed to have not only a Kaldorian characteristics, namely, a S-shaped form but also a Kaleckian characteristics, that is, a gestation delay between “investment decision” and “investment implementation.” We divide the analysis into two parts. In the first part, we assume that the time period under consideration is short enough so that the capital stock is not affected by the flow of investment and then examine the delay effect on dynamics of national income. In the second part, taking the capital accumulation into account, we draw attention to how the delay affects cyclic dynamics observed in the nondelay Kaldor–Kalecki model. It is demonstrated that the investment delay quantitatively affects the dynamic behavior but not qualitatively.
The authors highly appreciate the financial supports from the MEXT-Supported Program for the Strategic Research Foundation at Private Universities 2013–2017 and the Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research (C) 24530202, 25380238 and 26380316). The usual disclaimers apply.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Since “lag” and “delay” do not have distinctive different meanings, we use these words interchangeably. In particular, we mainly use “delay” in this study.
- 2.
There are several extensions of this delay investment function. Kaddar and Talibi Alaoui (2008) introduce time delay also in capital stock in capital accumulation equation (i.e., \(\Phi (Y(t-\theta ),K(t-\theta ))\)). Zhou and Li (2009) assume that the investment function in the capital accumulation depends on the income and the capital stock at different gestation periods (i.e., \(\Phi (Y(t-\theta _{1}),K(t-\theta _{2}))\) with \(\theta _{1}\ne \theta _{2}\)).
- 3.
This is a simplified version of the investment function adopted in Lorenz (1987). It is replaced with the full version in the latter half of this chapter.
- 4.
- 5.
See, for example, Lorenz (1993).
- 6.
The value of \(s_{a}\) is numerically obtained and the value of \(s_{\beta }\) is analytically determined as will be seen.
- 7.
Notice that \(s_{2}\) is identical with \(s_{\beta }.\) See footnote 6.
- 8.
We use the green curve later when the delay model is examined.
- 9.
Solving the second equation yields the same partition curve in a different form.
- 10.
In Fig. 6, \(s_{a}\) and \(s_{A}\) are not labeled to avoid confusion.
References
Beddington J, May R (1975) Time delays are not necessarily destabilizing. Math Biosci 27:109–117
Chang W, Smyth D (1971) The existence and persistence of cycles in a nonlinear model: Kaldor’s 1940 model re-examined. Rev Econ Stud 38:37–44
Grasman J, Wentzel J (1994) Co-existence of a limit cycle and an equilibrium in Kaldor’s business cycle model and its consequences. J Econ Behav Organ 24:369–377
Ichimura S (1955) Toward a general nonlinear macrodynamics theory of economic fluctuations. In: Kurihira K (ed) Post-keynesian economics. George Allen & Unwin, London, pp 192–226
Kaddar A, Talibi Alaoui H (2008) Hopf bifurcation analysis in a delayed Kaldor-Kalecki model of business cycle. Nonlinear Anal Model Control 13:439–449
Kaldor N (1940) A model of the trade cycle. Econ J 50:78–92
Kalecki M (1935) A macrodynamic theory of business cycles. Econometrica 3:327–344
Krawiec A, Szydlowski M (1999) The Kaldor-Kalecki business cycle model. Ann Oper Res 89:89–100
Lorenz H-W (1993) Nonlinear dynamical economics and chaotic motion, second, revised and enlarged. Springer, Berlin
Lorenz H-W (1987) Strange attractors in a multisector business cycle model. J Econ Behav Organ 8:397–411
Manjunath S, Ghosh D, Faina G (2014) A Kaldor-Kalecki model of business cycles: stability and limit cycles, IEEEXplore, pp 2650–2656
Wang L, Wu X (2009) Bifurcation analysis of a Kaldor-Kalecki model of business cycle with time delay. Electron J Quant Theory Differ Equ Spec 27:1–20
Zhang C, Wei J (2004) Stability and bifurcation analysis in a kind of business cycle model with delay. Chaos Solitions Fractals 22:883–896
Zhou L, Li Y (2009) A dynamic IS-LM business cycle model with two time delays in capital accumulation equation. J Comput Appl Math 228:182–187
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Science+Business Media Singapore
About this chapter
Cite this chapter
Matsumoto, A., Szidarovszky, F. (2016). Delay Kaldor–Kalecki Model Revisited. In: Matsumoto, A., Szidarovszky, F., Asada, T. (eds) Essays in Economic Dynamics. Springer, Singapore. https://doi.org/10.1007/978-981-10-1521-2_11
Download citation
DOI: https://doi.org/10.1007/978-981-10-1521-2_11
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-1520-5
Online ISBN: 978-981-10-1521-2
eBook Packages: Economics and FinanceEconomics and Finance (R0)