Probabilistic Economic Theory

Novosibirsk, 2015

INTRODUCTION. Probabilistic Economic Theory

“The market economy is the social system of the division of labor under private ownership of the means of production. Everybody acts on his own behalf; but everybody’s actions aim at the satisfaction of other people’s needs as well as at the satisfaction of his own. Everybody in acting serves his fellow citizens. Everybody, on the other hand, is served by his fellow citizens. Everybody is both a means and an end in himself, an ultimate end for himself and a means to other people in their endeavors to attain their own ends.

This system is steered by the market. The market directs the individual's activities into those channels in which he best serves the wants of his fellow men. There is in the operation of the market no compulsion and coercion. The state, the social apparatus of coercion and compulsion, does not interfere with the market and with the citizens’ activities directed by the market. It employs its power to beat people into submission solely for the prevention of actions destructive to the preservation and the smooth operation of the market economy. It protects the individual's life, health, and property against violent or fraudulent aggression on the part of domestic gangsters and external foes. Thus the state creates and preserves the environment in which the market economy can safely operate… Each man is free; nobody is subject to a despot. Of his own accord the individual integrates himself into the cooperative system. The market directs him and reveals to him in what way he can best promote his own welfare as well as that of other people. The market is supreme. The market alone puts the whole social system in order and provides it with sense and meaning”.

    Ludwig von Mises. Human Action. A Treatise on Economics. Page 243

Exactly how is our economic market world arranged at the deepest micro level, at the level of individuals and businesses, buyers and sellers on markets? How does the market economy function? According to what laws and rules do people make decisions about price and quantity of bought and sold goods? How does a market price eventually become established, and how can one and the same volume of goods be sold regularly each year at this price on the market? How and why does this regularity change over the course of time, and how and why do markets grow or fall? We attempt to answer these and many other similar questions in this book within the framework of a new economic discipline, namely, physical economics.

In general terms, at the conceptual or descriptive level, the answers to these questions are known from classical economic theory. They are obtained with the aid of the logical method of economic theory and they are given in this book in epigraph form to the parts and the chapters. These answers represent by themselves extensive quotations from the fundamental work of Ludwig von Mises [1]. But other questions agitate us more. Where can we search for the answers in this book, and how can all these answers of classical economic theory be expressed in terms of the natural exact sciences, i.e., in mathematical language? Therefore, in the book we attempt to develop quantitative methods of calculation for economic systems, as well as their structure and dynamics, which would make it possible to speak about the further development of quantitative economic theory.

Contemporary, real, economy is a complex dynamic system. It is therefore possible and necessary to attack the problem of studying its structure and dynamics in different ways and from different points of view. Our point of view is such that we look at the economy primarily as a collection of an enormous number of reasonably thinking and actively acting people, each of them “is not only homo sapiens, but no less homo agents” [1] simultaneously. To solve their problems and achieve their goals, these people are forced to constantly make important decisions for themselves about production, purchase and sale of goods, organization of logistics and marketing, control of other people, etc. As reasonable people, they attempt to make specific decisions that would bring more benefit and a large return for their efforts. Such rational decisions can be made only on the basis of having sufficient information regarding factors that concern their interests Therefore, people are constantly searching for and processing new, relevant market information. But we never possess completely adequate information about the things interesting us in view of the time constraints at our disposal, or in view of our obviously finite mental and technical abilities. It is our deep belief that human nature, and also the nature of market economic systems, is such that all our market decisions can only be approximate. In more technical terms, they can only be of a probabilistic nature. Furthermore, according to our vision of the market economy, all economic processes and phenomena are nothing more than the result of the actions of all players in the economy. There seems to be no escaping the conclusion that all economic processes and phenomena in the market economy are, to some extent, also probabilistic by their nature. Hence, there is only one step prior to obtaining the fundamental conclusion that the market economy is not simply a complex dynamic, but that it is still probabilistic [2–5]. Therefore, in order to be able to give a sufficiently complete description of such complex probabilistic systems, adequate economic theory must also be probabilistic to a considerable extent. For this, it is necessary to incorporate into the classical economic theory the uncertainty, as well as probability at the appropriate mathematical level, i.e., to develop probabilistic economic theory adequately in relation to the contemporary economic reality. Specifically, the present study is devoted mainly to this purpose.

In this book we have limited ourselves to the study of the probabilistic aspects of functioning markets in a sufficiently free market economy. More accurately, we study the details of supply and demand, as well as the mechanisms of the formation of prices and the establishment of equilibrium in the markets. Emphasis is given to the description of probabilistic nature of these fundamental market categories and notions. All these market concepts have been the subject of intensive investigations and critical rethinking in the book within the framework of the main paradigm of physical economics, which can be briefly formulated as follows.

All markets consist of people, buyers of some goods and sellers of other goods, simultaneously. Everything that the markets do, these people do, and it is precisely the action of all these people in the market that determine all results of the work of that market [1]. We have defined five fundamental or general principles of physical economics (and probabilistic economic theory naturally): the cooperation-oriented agent principle, the institutional and environmental principle, the dynamic and evolutionary principle, the market-based trade maximization principle, and, finally, the uncertainty and probability principle. These determine, in essence, the work of markets in our physical economic models. The cooperation-oriented agent principle speaks about the unique moving role of the market agents and significant role of social cooperation in modern market economy. The institutional and environmental principle expresses the fact that the interaction of agents with the various institutions and external environment must be taken into account simultaneously with the interaction of the agents with each other. The dynamic and evolutionary principle reflects the fact that the market behavior has, to certain extent, a deterministic character and consequently can be described with the aid of the equations of motion. The market-based trade maximization principle determines the direction of the motion of the free market as a whole under the influence of internal market forces. The uncertainty and probability principle tell us that all market phenomena are probabilistic in nature and thus help us to understand what a mathematical apparatus must do in order to adequately describe market behavior under uncertain conditions. We refer to the appropriate approach to as probabilistic economic theory, and since this theory is built by analogy with the “probabilistic physical theory” (quantum mechanics) of many-particle systems, we designated it more precisely as quantum economy [4]. Since the picture of the market economic world is built in physical economics at the micro level in approximately the same way as in physics, there is, in principle, a possibility of developing the quantitative methods of calculating the market economies by analogy with the calculation methods in physics. Consequently, it becomes possible to fruitfully use natural science concepts and speak natural science language to describe and analyze market structures and dynamics. In this book, we widely explore these great possibilities that help us to look at economic reality from the natural science points of view and discover new perspectives of economic theory for investigation and development.

In conclusion, it is natural that the direct mechanical transfer of methods and concepts of physics into the economic theory would be impossible. We only can accurately borrow and transfer general concepts and formal methods, since economic and physical phenomena are principally different in their essence and content. In this book and within the framework of this approach, the basic concepts and general principles of physical economics are developed and described. On this basis, we have developed the complex of the principally new quantitative methods of calculation and analysis of many-good, many-agent market economies that we named probabilistic economic theory.

References

1. Ludwig von Mises. Human Action. A Treatise on Economics. Yale University, 1949.

2. Emmanual Farjoun and Moshе Machover. Laws of Chaos: a Probabilistic Approach to Political Economy. Verso, London, 1983).

3. Philip Ball. Physical Modelling of Human Social Systems. Complexus 2003; 1:190–206.

4. A.V. Kondratenko. Physical Modeling of Economic Systems. Classical and Quantum Economies. Nauka (Science): Novosibirsk, 2005.

5. K.K. Val’tukh. Development of a Probabilistic Economic Theory. Herald of the Russian Academy of Sciences, 2008, Vol. 98, N 1, p. 51–63.

PART A. The Agent-Based Physical Modeling of Market Economic Systems

“In the course of social events there prevails a regularity of phenomena to which man must adjust his actions if he wishes to succeed. It is futile to approach social facts with the attitude of a censor who approves or disapproves from the point of view of quite arbitrary standards and subjective judgments of value. One must study the laws of human action and social cooperation as the physicist studies the laws of nature. Human action and social cooperation seen as the object of a science of given relations, no longer as a normative discipline of things that ought to be”.

    Ludwig von Mises. Human Action. A Treatise on Economics. Page 6

CHAPTER I. Fundamentals of the Method of Agent-Based Physical Modeling

“For a social collective has no existence and reality outside of the individual members’ actions. The life of a collective is lived in the actions of the individuals constituting its body. There is no social collective conceivable which is not operative in the actions of some individuals. The reality of a social integer consists in its directing and releasing definite actions on the part of individuals. Thus the way to a cognition of collective wholes is through an analysis of the individuals’ actions”.

    Ludwig von Mises. Human Action. A Treatise on Economics. Page 43

“The whole market economy is a big exchange or market place, as it were. At any instant all those transactions take place which the parties are ready to enter into at the realizable price. New sales can be effected only when the valuations of at least one of the parties have changed”.

    Ludwig von Mises. Human Action. A Treatise on Economics. Page 231

PREVIEW. What is the Main Point of the Concept of Agent-Based Physical Modeling?

The concept of agent-based physical modeling is based on taking the known, fundamental concepts of classical economic theory, and uniting and eventually converting them into probabilistic economic theory. It is described with the help of formal approaches and methods borrowed from theoretical physics, beginning with the method of equations of motion for many-particle physical systems. The role of the theoretical physics methods is only to provide the framework for physical economics and eventually for probabilistic economic theory. This theory is developed step-by-step with the creation of the more complicated models, each subsequent step building on the last. It includes and increases the number of concepts and principles of physical economics, and reflects on one or more of several fundamental features of the market economy. The first one, the cooperation-oriented agent principle, is the cornerstone of all the physical economic models which holds that all market phenomena have their origins in agents’ actions. To put it differently, since the action of the market as a whole is a result of the actions of all the market agents and nothing other, the market agents and their actions must be at the basis of the physical economic models. In other words, according to the agent principle, all market phenomena have their origins in agents’ actions.

1. The Concept of Agent-Based Physical Modeling

It is well-known that the method of conceptual modeling of economic systems has long and widely been used in economic theory. According to the new physical economic mode of thought, the main requirement for such economic models, which determines their basic predestination, is skill, with which several important basic concepts and principles must harmoniously, competently and simultaneously be incorporated into the theory. The latter is very important since, by the definition of the problem, all concepts and principles play roles that compare their significance in the economy under study.

Despite their simplicity, the first and most well-known conceptual theories of neoclassical economics, such as supply and demand (S&D below), contributed significantly to economic science. They helped economists to better understand the basic elements of the economic world, and they gave rise to graphic conceptualizations that aided the transfer of this knowledge to others, especially students. Early on, conceptual modeling had, and continues to have, great significance. This is also the case in Austrian economics, where it bears the name method of imaginable constructions and it is considered as the basic method in economic inquires. In theoretical physics, it is not acceptable to accentuate attention on the use of models, since theoretical physics itself can rightfully be considered as the conceptual mathematical modeling of physical systems. Specifically, in theoretical physics, the most advanced methods of theoretical modeling of complex systems have been developed. Moreover, there is the required inclination towards conducting the quantitative numerical, and, as precisely as possible, calculations of structure and properties of these models. The deep structural and dynamic analogies between the many-particle physical systems and the many-agent economic systems are exploited in this book to transfer concepts and analytical methods from theoretical physics to economics.

2. The Main Paradigm of Physical Economics

For the achievement of larger clarity, let us again mention the main idea in physical economics regarding the use of analogies with physics. For this purpose, we once more express the thought of the main paradigm of physical economics as follows: physical systems consist of atoms. As was well known long ago, all that the physical systems do, atoms do. Market systems consist of market agents, buyers and sellers. And it is also known that all that the markets do, the market agents do. Both the physical and market economic systems are the complex dynamic systems, whose dynamics are determined by interaction between the elements of the system and their interaction with the environment in the widest sense of this notion. In our view, the very existence of such structural and dynamic similarity gives rise to the possibility, in principle, of building formal, many-agent physical economic models by analogy with the theoretical models of the many-particle physical systems, for example, of polyatomic molecules. It is here that the physical economic model could include all basic concepts and principles which define the work of the economy. As a result, it could sufficiently, simply, and adequately describe both the main structural features and principal dynamic characteristics of the economy being modeled, a target at which this study is precisely aimed, since no model can immediately describe everything completely. The study of economic systems by means of physical modeling must be carried out gradually, step by step, incorporating into the model ever finer effects and properties in the way that theoretical physics has done over the course of theoretical studies of complex physical systems. Thus, physical economics borrows formal approaches and model structures from theoretical physics. In other words, physical economics uses the very body or framework of the theoretical models of the many-particle systems, but not the results of theoretical studies of the concrete real physical systems. Namely this is the essence of physical modeling of economic systems. In conclusion, the obvious structural and dynamic analogy of the many-agent economic systems with the many-particle physical systems is basic to the formulation of fundamentals of the method of the agent-based physical modeling of the many-agent market economic systems in the formal economic space, and eventually, of the five general principles of physical economics as well as probabilistic economic theory.

3. The Axioms and Principles of Physical Economics

Generally speaking, our attitude towards the problem of adequate quantitative description of the agent behavior in the market as well as market S&D and price formation is based on the two rather simple axioms of a very general character.

1. The Agent Identity Axiom.

All market agents are the same, only the supplies and demands they have different. The axiom says that all market agents share common properties, depending primarily on agent revenues and expenses, or more strictly, on supply and demand (S&D below) for traded goods and services. It is these agents’ S&D that mainly determine the rational economic behavior of agents on the markets, and eventually the behavior of the whole markets. It shows a possibility of building rather common and accurate models of behavior of agents in the market, and hence the total market as a whole. It sets us on the right track for the identification and examination of the common properties in the behavior of market agents that ensure appearance of the common patterns and regularities in the course of market processes. It gives us the ability to build theoretical economic models on a fairly high scientific level by using physical and mathematical methods, which is the primary goal of physical economics and economic theory in general. We are certain that only these types of common market phenomena and processes are rightly a matter for exact scientific economic enquiry. In other words, it focuses us on building economics as an exact science in the image and after the likeness of the natural sciences.

2. The Agent Distinction Axiom.

All market agents are distinguished. The second axiom works when the first axiom fails. Thus, it defines those areas and aspects of the agents’ behavior on the markets that are the subject of the studies of other sciences of more applied nature, such as marketing, behavioral science, managerial economics, psychology, policy, etc. In other words, these social sciences are concerned with the specific nuances and peculiarities in the behavior of concrete people, agents and communities in different markets and situations, etc.

Let us stress that in economics we do not study real people, but rather the real actions of these people on markets. The people can be different but market decisions and actions of these people can be the same, depending primarily on their supplies and demands on markets. It is this fact that lies in the background of the agent identity axiom.

Hence, we will sum up everything we have stated above in the form of the five general principles of physical economics and probabilistic economic theory as follows:

1. The Cooperation-Oriented Agent Principle.

The most important concept concerning markets is as follows: every market consists of market agents, buyers and sellers, all strongly interacting with each other. There are never any mysterious forces in markets. Everything that markets do, the cooperation-oriented market agents do, and therefore only the cooperation-oriented, agent-based models can provide the reasonable and justified foundation for any modern economic theory.

2. The Institutional and Environmental Principle.

Markets are never completely closed and free; all the market agents are under continuous influences and under such external institutional and environmental forces and factors as states, institutions, other markets and economies, natural and technogenic phenomena, etc. The influences, exerted by each of these forces and factors on the structure of market prices and on the market behavior, can be completely compared with the effect from inter-agent interactions. Moreover, the action of strong external institutional and environmental factors can significantly hamper the effective work of market mechanisms and even practically suppress it in a way that results in the breakdown of the market’s invisible hand concept, well-known in classical economics. Therefore, the influence of institutional, environmental and other external factors must be adequately taken into account in the models, as well as simultaneously with the inter-agent interactions.

3. The Dynamic and Evolutionary Principle.

Markets are complex dynamic systems; all the market agents are in perpetual motion in search of profitable deals with each other for the sale or purchase of goods. Buyers tend to buy as cheaply as possible, and sellers want to obtain the highest possible prices. Mathematically, we can describe this time-dependent dynamic and evolutionary market process as motion in the price – quantity economic space of market agents acting in accordance with objective economic laws. Therefore, this motion has a deterministic character to some extent. This motion can and must be approximately described with the help of equations of motion;

4. The Market-Based Trade Maximization Principle.

On relatively free markets, the buyers and sellers consciously and deliberately enter into transactions of buying and selling with each other, since they make deals only under conditions in which they obtain the portion of profit that suits each of them. It is in no way compulsory that they aspire to maximize their profit in each concluded transaction, since they understand that the transactions can only be mutually beneficial. But they do attempt to increase their profit via the conclusion of a maximally possible quantity of such mutually beneficial transactions. Thus, it is possible to assert that the market as a whole strives for the largest possible volume of trade during the specific period of time. Consequently, we can make the conclusion that market dynamics can approximately be described and even approximate equations of motion for the market agents can be derived in turn by means of applying the market-based trade maximization principle to the whole economic system (more exactly, this principle is system-based).

5. The Uncertainty and Probability Principle.

Uncertainty and probability are essential parts of human action in markets. This is caused by the nature of human reasoning, as well as the fundamental human inability to accurately predict a future state of the markets. Furthermore, market outcome is the result of the actions of multiple agents, and no market is ever completely closed and free. For these reasons, all market processes are probabilistic by nature too, and an adequate description of all the market processes needs to apply probabilistic approaches and models in the economic price – quantity space. The uncertainty law results from this principle.