On Certain Implications of Non-linearity in Keynesianizm

On Certain Implications of Non-linearity in Keynesianizm

Aleksander Jakimowicz

Ekonomista 1 / 2009 p. 15-48


The paper consist of two parts. In the first one author presents to the readers some general information on the very modern and very peculiar approach to economy or rather to the macroeconomics’ modeling. This is set against the classical approach, which is more similar to the classical physic, closed within the borders of thermodynamics and the rule of energy preservation. The classical approach in the natural sciences looks for the simple linear interdependence within the limited number of variables. The economists who try to cope with the macro-relations in economy have used the same approach so far, unfortunately to no effect. No effect means that there were a lot of significant discrepancies between the mathematical models and economic reality. This gave rise to critic of the keynesizm. However modern approach in the natural science observe the enormous complexity of the explained phenomena and its chaotic character. This conclusions led to the discovery of the set of mathematical tools, useful to describe complexity and chaos. In the first part readers are getting familiar with the beginning of the researches over complexity and its first trials to use its results in very different fields of science. Interdisciplinary studies seem to become a prevailing model of practicing science contrary to what was suggested by Kuhn. We may learn that there also are researches regarding economics based upon the presumption that the economy itself constitutes a complex adaptive system (Gell – Mann) and its main feature (apart from its complexity) is that the set of principles describing the behavior of the system is not stable but evolves. The conclusion of the first part of the paper is that we may use some tools worked out due to describe complex system in order to formalize and correct some Keynes theorems e.g. the part of general theory of employment, interest and money which claims the existence of function binding domestic product with the aggregate consumption expenditures, investments and governmental expenditures. The application of those tools is theoretically allowed because of some logical homologies which are specified.

The second part of the text consists of the complex mathematical equations, where one of the main variable, significant in the model – ultimate consumption propensity is not stable but expressed with the nonlinear function. Depending on the parameters of that variable we may observe how the model work. The conclusion is that it works non-stable, typically for the chaotic models, and the relatively non-remarkable changes in the shape of consumption functions changes the macroeconomics indicators in the entirely unpredictable way.


The article is very interesting and convincing. Especially its first part where the most important features of the modern science and the most important problems of economics are accurately caught. The researches over complexity and chaotic systems, which were rather intuitively pointed by the greatest minds in the XX century (Popper) as the field that should be explored by the science, seem to be the most accurate direction, especially in economics. The conclusion however is not very encouraging. The so called “Lapunov time” determines the maximum period when, based on the model, any prediction of the variables’ values is possible.  Any extension over the Lapunov time leads us to terra incognita. The main thesis of Keynes, that the market may not spontaneously approaches the stability, therefore governmental intervention is required is undermined. Such intervention looks tricky and may lead the economy astray. His main adversary, Hayek, may have been right.


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