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.
We assume that, from one side, these five general principles are capable of sufficiently and adequately describing the basic structural and dynamic properties of market economic systems and the market processes within them. From other side, they can be regarded as the basic pillars of physical economics, which carry on constructing step-by-step the bodies or frameworks of our physical economic models. These principles and their substantiation will be repeatedly discussed in more detail and step-by-step in this book. Concluding, let us stress that new probabilistic economic theory has been built on the basis of these principles in this book.
4. The Classical Economies
4.1. The Two-Agent Market Economies
As mentioned previously, below we will sequentially introduce into the theory the new concepts of physical modeling. They will be the building blocks in the construction of the body or framework of our models, which will also be filled step-by-step with new, concrete contents. We will start with the construction of the simplest physical economic models. In this paragraph we will create this with the use of analogies and formal methods of classical mechanics. These physical economic models will be referred to as the classical economies. Naturally in construction, we will use only first four principles, since only they have analogues in classical mechanics.
As we know, market agents are the buyers and sellers of goods and commodities, and as such are the major players in the market economy. They strongly interact with each other and with the institutions and the market’s external environment including other market economies. They continuously make decisions concerning the prices and quantities of good, and buy or sell those in the market. All the market agents’ actions govern the outcome of the market, which is the essence of the agent principle. We believe the agents to behave to a certain extent in a deterministic way, striving to achieve their definite market goals. This means that the behavior of market agents is, in turn, governed by the strict the economic laws in the market. The fact that these laws have until now been of a descriptive nature in classical economic theory, and they have not yet been expressed in a precise mathematic language, is not of key importance in this case. What is really important is that we believe all the market agents to act according to the economic laws of social cooperation that can be approximately described with the help of the market-based trade maximization principle.
Every market agent acts in the market in accordance with the rule of obtaining maximum profit, benefit, or some other criterion of optimality. In this respect, we believe the many-agent market economic systems to resemble the physical many-particle systems where all the particles interact and move in physical space. This is also in accordance with the same system-based maximization principle, such as the least action principle in classical mechanics which is applied to the whole physical system under study. The analogous situation exists in quantum mechanics (see below in the Part F).
The main drive of our research was to take the opportunity to create dynamic physical models for market economic systems. We construct these physical economic models by analogy with physics, or more precisely by analogy with theoretical models of the physical systems, consisting of formal interacting particles in formal external fields or external environments [1]. Let us stress that these particles are fictitious; they do not really exist in nature. Therefore, the physical systems mentioned above are also fictitious and they do not exist in nature either. They are indeed only imagined constructions and served simply as patterns for constructing the physical economic models. Thus, these physical economic models consist of the economic subsystem, or simply the economy or the market. It contains a certain number of buyers and sellers, as well as its institutional and external environment with certain interactions between market agents, and between the market agents and the market institutional and external environment. Moreover, according to the dynamic and evolutionary principle we assume that equations of motion, derived in physics for physical systems in the physical space, can be creatively used to construct approximate equations of motion for the corresponding physical models of economic systems in the particular formal economic spaces.
Let us briefly give the following reasons to substantiate such an ab initio approach for the one-good, one-buyer, and one-seller market economy. Let price functions p1D (t) and p1S (t) designate desired good prices of the buyer and seller, respectively, set out by the agents during the negotiations between them at a certain moment in time t. Analogously, by means of the quantity functions q1D (t) and q1S (t) we will designate the desired good quantities set out by the buyer and the seller during the negotiations in the market. Below, for brevity, we will refer to these desired values as the price and quantity quotations, which can or cannot be publicly declared by the buyer and the seller, depending on the established rules of work on the market. Note that the setting out of these quotations by the market agents is the essence of the most important market phenomenon in classical economic theory, namely the market process leading eventually to the concrete acts of choices of the market agents, being implemented by the buyer and seller through making deals (see below). Graphically, we can display these quotations as the agents’ trajectories of motion in the formal economic space as will be shown below. In real market life, these quotations are discrete functions of time, but, for simplicity, we will visualize them graphically (as well as supply and demand functions, see below) as continuous linear functions or straight lines. This approximate procedure does not lead to a loss of generality, since these functions and lines are necessary to us. They are only for the illustration of the mechanism of the market work and for the most general graphic representation of the motion of the market agents in the two formal economic spaces, corresponding to the two independent variables, price P and quantity Q. We will refer to this agent motion as market behavior, for brevity, and sometimes the evolution of the economy in time. All these terms are, in essence, synonyms in this context of the discussion. And for simplicity we will call these spaces the price space and the quantity space, respectively, as well as the united space as the price-quantity space.
By setting out desired prices and quantities this way, buyers and sellers take part in the market process and act as homo negotians (a negotiating man) in the physical modeling, aiming to maximum satisfaction in their attempts to make a profit on the market. This is the first market equilibrium price pE1 and quantity qE1 at a moment in time t1E at which the agents’ trajectories intersect, the deal takes place, and the interests of both the buyer and seller are optimally satisfied, taking