##
**Time to build in dynamics of economic models. II: Models of economic growth.**
*(English)*
Zbl 1056.91050

For Part I, cf. ibid. 14, No. 5, 697–703 (2002; Zbl 1008.91078).

The goal of this paper is to show the vitality of Kalecki’s ideas using the example of his proposition of the time for building investment goods as the source of cyclic behaviour in economic systems. For the proof modern methods of analyzing bifurcation in functional equations are used. The main contributions of the author are:

a) showing that the mechanism of inherent cycles which is a result of applying Kalecki’s approach to growth theory is universal and applies to all fundamental theories of ecnomic growth in which the time for building investment goods is introduced;

b) showing that applying dynamical optimization to fundamental models of growth theory also leads to cyclic behaviour representated by a saddle limit cycle in phase space.

The goal of this paper is to show the vitality of Kalecki’s ideas using the example of his proposition of the time for building investment goods as the source of cyclic behaviour in economic systems. For the proof modern methods of analyzing bifurcation in functional equations are used. The main contributions of the author are:

a) showing that the mechanism of inherent cycles which is a result of applying Kalecki’s approach to growth theory is universal and applies to all fundamental theories of ecnomic growth in which the time for building investment goods is introduced;

b) showing that applying dynamical optimization to fundamental models of growth theory also leads to cyclic behaviour representated by a saddle limit cycle in phase space.

Reviewer: Messoud A. Efendiev (Berlin)

### MSC:

91B62 | Economic growth models |

34K60 | Qualitative investigation and simulation of models involving functional-differential equations |

### Citations:

Zbl 1008.91078
PDFBibTeX
XMLCite

\textit{M. Szydłowski}, Chaos Solitons Fractals 18, No. 2, 355--364 (2003; Zbl 1056.91050)

Full Text:
DOI

### References:

[1] | Asea, P. K.; Zak, P. J., Time to build and cycles, Journal of Economic Dynamics and Control, 23, 1155-1175 (1999) · Zbl 1016.91068 |

[2] | Boucekkine, R.; Licandro, O.; Paul, C., Differential-difference equations in economics: on the numerical solution of vintage capital growth models, Journal of Economic Dynamics and Control, 21, 347-362 (1997) · Zbl 0879.90042 |

[3] | Cass, D.; Yaari, M., A re-examination of the pure consumption-loan model, Journal of Political Economy, 74, 200-233 (1966) |

[4] | Frisch, R.; Holme, H., The characteristic solution of a mixed difference and differential equation occurring in economic dynamics, Econometrica, 3, 225-239 (1935) |

[5] | Guckenheimer, J.; Holmes, P., Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Field (1983), Springer-Verlag: Springer-Verlag New York · Zbl 0515.34001 |

[6] | Hale, J. K.; Verduyn Lunel, S. M., Introduction to Functional Differential Equations (1993), Springer-Verlag: Springer-Verlag New York · Zbl 0787.34002 |

[7] | James, R. W.; Beltz, M. H., The significance of characteristic solutions of mixed difference and differential equations, Econometrica, 6, 326-343 (1938) |

[8] | Kalecki, M., A macrodynamic theory of business cycles, Econometrica, 3, 327-344 (1935) |

[9] | Kalecki, M., Capitalism, (Osiatynski, J., Works volume 1 (1973), Oxford University Press) |

[10] | Krawiec, A.; Szydlowski, M., The Kaldor-Kalecki business cycle model, Annals of Operations Research, 89, 89-100 (1999) · Zbl 0939.91094 |

[11] | Larson, A. B., The hog cycle as harmonic motion, Journal of Farm Economics, 46, 375-386 (1964) |

[12] | Pontryagin, L. S., The Mathematical Theory of Optimal Processes (1962), Wiley-Interscience: Wiley-Interscience New York · Zbl 0112.05502 |

[13] | Ramsey, F., A mathematical theory of savings, Economic Journal, 38, 543-559 (1928) |

[14] | Rustichini, A., Hopf bifurcation for functional differential equations of mixed type, Journal of Dynamics and Differential Equations, 1, 145-177 (1989) · Zbl 0684.34070 |

[15] | Szydlowski, M.; Krawiec, A., The Hopf bifurcation in the Kaldor-Kalecki model, (Holly, S., Computation in Economics, Finance and Engineering: Economic Systems (2000), Elsevier), 391-396 |

[16] | Zak, P. J., Kaleckian lags in general equilibrium, Review of political economy, 11, 321-330 (1999) |

[17] | Zak, P. J.; Tampubolon, L.; Young, D., Is time-to-build model empirically viable?, (Seth Greenblatt, Schumpeterian models of economic fluctuations (2000), North-Holland) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.