Ebook: Application of Dimensional Analysis in Economics
The modeling of economic phenomena and processes, in terms of their static and dynamic features and with regard to the characteristics of their course, is a major methodological trend in studies of the nature, properties and functioning of contemporary management systems. Models describing management systems must be of a multi-aspect nature, entailing aspects such as technical, economic and sociological factors on the one hand, and forecasting, planning, leading, controlling etc., on the other.
Developing a method for incorporating such diverse data into a system of analysis is, needless to say, a complex process. Dimensional analysis is a tool which might be useful in this process, but one which, up to now, has been little explored in the economic sciences.
This book explores the application of dimensional analysis in the field of economics. It has been structured in a way which corresponds to the formulation of economic quantities, and is divided into five sections: measuring of economic quantities, modeling of economic processes, principles of dimensional analysis, building of quantified dimensional models, and experiment and practical verification.
Modelling of economic phenomena and processes, in terms of their static and dynamic features and with regard to discrete or continuous characteristics of their course, is a major methodological trend in the studies of nature, properties and functioning of contemporary management systems. On various levels and in different areas, these systems comprise subsystems of programming, planning, organisation, motivation, implementation and control, both in the reality sphere as well as in the information and regulatory one. In practice, one may also find such perspectives of those subsystems which are focused in subject matter on economic and technical problems. All depends on what fraction or aspect of reality originating from the natural world or intentionally constructed by men constitutes the object of researchers' interest. The models being created may be of forecasting nature, thus continuing the retrospective study of phenomena and processes, or may emerge as solutions developed by disregarding the past experiences and analyses. A different approach to reality modelling is representing the existing state of matters as accurately as possible, and on such a basis, making an attempt to enhance the structures and functioning principles of the phenomena and processes studied. Two different concepts of model building may be assumed.
The first one, known as conceptual, is based on qualitative description of things, interactions, relationships, structures and phenomena observed, for instance, in abrupt changes of their functioning, leading to verbal representation of systems or subsystems.
The second one – mathematical, also known as formal, consists in representing descriptions of the same areas and levels in a formalised language of mathematics leading to development of analytic, stochastic, statistic and simulation models.
According to both approaches, the starting point may assume different forms: empirical knowledge (experience), analytical considerations, instrumental concepts, both normalised or integrating, leading to syntheses representing a holistic approach. The procedure itself depends on the methodology assumed as well as the researcher's knowledge on modelling of a reality fraction. Models describing management systems must be of multi-aspect nature, meaning that they should entail technical, economic, sociological and similar aspects, on the one hand, and forecasting, planning, leading, controlling etc., on the other hand. What matters particularly is that a large number of aspects to be taken into consideration, namely multiple sources shedding light upon the same problem, encounter taxonomic issues and may lead to indeterminacy. Solving measuring problems by using many factors decisive for the model formulation must ensure dimensionality of the quantities applied in the modelling. In order to describe the input characteristics explaining specific phenomena, things, and relationships, a multiaspectual language of categories matching the selected reality segment is used. Categories may be measurable and immeasurable. Measuring of quantities, being measurable categories, requires conscious application of the appropriate measuring principles and techniques.
Such a standpoint must give birth to a system of units of measure perceived from a technical, economic and information perspective, ensuring that all the characteristic base and auxiliary quantities can be described. In this study, the authors have proposed such a system of units referred to as SI-ETI. The problems related to measuring of economic quantities being discussed in the book require multilateral discourse and further study to develop them to the fullest extent possible, so that they constitute a basis for quantified models to be created. Building of mathematical models can be facilitated by means of dimensional analysis being a tool little explored in economic sciences. This methodology is relatively easy to apply and does not require considerable mathematical preparation, as it can be used without having profound expertise of the theory of algebra and mathematical analysis. Dimensional analysis uses such basic notions as dimensional quantities, i.e. measurable ones, whereas the instruments of its operational application contain only several theorems concerning dimensional functions. It should also be mentioned that dimensional analysis is a useful tool facilitating verification of mathematical models built on the foundations of other methods. Some of the main goals of this study included discussing the use of this technique, which may seem like a novelty to a Polish reader, in modelling of economic processes as well as its applicability in the theory and practice of economic sciences and management.
The examples of dimensional models of certain processes discussed in the book have been described assuming the accuracy of parameters or numerical functions. In order to obtain detailed (accurate) models, one should conduct an identification experiment based on statistical or forecasting data, applying the methodology discussed herein. The principal theses of the study have been described with reference to modelling examples for production processes, national income building, channelling expenses for consumer goods, problems of economic growth modelling in confrontation with the ways these problems are traditionally analysed.
This publication has been structured in a manner corresponding to formulation of economic quantities, thus providing grounds for their measuring and presenting methods of their determination. In terms of measuring methods, special importance has been attached to measurements of time and value. This section of the book is devoted to a new approach to modelling of economic processes, describing the principles of dimensional analysis and model similarity. The final sections of the study describe the principles of building quantified dimensional models and the related experiments and techniques enabling their practical verification. The content of the book has been delivered in a manner assumed to help the reader master this methodology self-sufficiently. The authors are hoping that the methods of applying dimensional analysis in modelling of economic phenomena and processed they have proposed will find appreciation and some followers. In order to describe and characterise real processes, one can use basic quantities expressing specific categories and providing sufficient characteristics of the following notions: supply, stream, circulation and cycle. They express actual physical flows, transformations, storage of things, men or their work in terms of economic and technical criteria. From the perspective of information-regulatory processes, these quantities are represented – for instance – by price, with reference to value, as well as efficiency, productivity and intensity corresponding to speed and rate of acceleration of changes taking place. Such an approach entails both the static and the dynamic nature of the said processes. If one should additionally add to the discourse the category of information, namely the quantity corresponding to it, i.e. the amount of information, then one would obtain enough categories to describe basic characteristics of both the real and the information-regulatory processes. There is a clear breakdown into categories and quantities shown in Diagram 1. The categories include value, speed, rate, stability, dynamism and information, whereas the quantities express only some of their characteristics or provide descriptions with reference to specific measuring criteria and options. For instance, price is used to express value in a limited way. Also information is described as a category in a limited manner using the information amount. What particularly matters for the considerations undertaken in this study is to find an answer to the following question: are the said quantities sufficient enough to subject an item to quantitative modelling of real and information-regulatory processes in economy? Practical experience related to building such models as well as their actual application implies that they form a limited yet sufficient set. Such a hypothesis requires further in-depth research which, however, is neither the subject nor the matter of interest of this study.