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“Economics is not about things and tangible material objects; it is about men, their meanings and actions. Goods, commodities, and wealth and all the other notions of conduct are not elements of nature; they are elements of human meaning and conduct. He who wants to deal with them must not look at the external world; he must search for them in the meaning of acting men”.

Ludwig von Mises. Human Action. A Treatise on Economics. Page 92

PREVIEW. What are Functions of Supply and Demand?

In the present Chapter the notion of supply and demand functions in the market, traditional to economics, is exposed to critical rethinking from the point of view of the uncertainty and probability principle. The Stationary Probability Model in the Price Space is developed for the description of behavior of a seller and a buyer in the price space of a one-good market in an economy being in a normal stationary state. Within the framework of the model, the terms supply and demand have changed their meaning; a new definition of the seller’s supply and the buyer’s demand functions is given. These functions are probabilistic in nature and they are normalized to their total supply and demand expressed in monetary units. In other words, they are the seller’s and buyer’s probability distributions in making a purchase/sale transaction in the market for a certain sum of money, respectively. Further, with the help of the proposed additivity and multiplicativity formulas for supply and demand, the Stationary Probability Model in the Price Space is extended to economies having many goods and many agents in the price space. With this strategy the probabilistic supply and demand functions of the whole market are constructed. As a main result of the work, we have laid the groundwork for probability economics. It is defined as a new quantitative method for description, analysis, and investigation of the model as well as real economies and markets.

1. The Neoclassical Model of Supply and Demand

An old joke in a well-known economics textbook says that creating an economist is as simple as teaching a parrot to pronounce words “supply” and “demand” (S&D below). My former managerial economics lecturer shared his own humor on this subject: If one understands the theory of S&D elasticity, you‘ve got yourself a new economics professor! These jokes reflect an important role which is played in economics by the S&D concept, the formal realization of which we will call the traditional neoclassical model of S&D. Below we will give the most widespread version of the description of this model from the textbook [1]. To start with, we will see how economics defines the demand of each individual buyer [1]. It is possible to present demand in the form of a scale or a curve showing quantity q of a product that a consumer desires, is able to buy at each given prices p, and at a certain period of time. Further, the radical property of demand consists of the following: at an invariance of all other parameters (ceteris paribus), reduction of price leads to the corresponding increase of the quantity demanded. And, ceteris paribus, the inverse is also true; an increase in price leads to the corresponding reduction of the quantity demanded. In short, there is an inverse relationship between the price p and the quantity q demanded. Economists call this inverse relationship the law of demand.

The simplest explanation of the law of demand: a high price discourages the consumer to buy, and a low price strengthens their desire to buy. The additivity rule is used to obtain the demand function of the whole market, i.e., all individual demand functions are simply summarized for obtaining the market demand function D(p). The graph of the traditional demand function for a grain market is displayed in the Cartesian (P, Q)-plane in Fig. 1.

This example is intentionally taken from the textbook [1] where it has number 3–1. In order to avoid misunderstanding, we will make some remarks concerning this and all other drawings in this work. First, unlike the textbook [1], we plot price p on the horizontal axis P and quantity q on the vertical axis Q in the Cartesian (P, Q)-plane because price is an independent variable in all our theoretical constructions and conclusions. In exact sciences, an independent variable can only be plotted on the horizontal axis. Second, we measure quantity of grain in metric tons (ton) per a year (ton/year), and the price in American dollars ($) per ton ($/ton).

Fig. 1. Graph of the traditional neoclassical demand function D(p) for the model market of grain [1].

Thus, according to the textbook [1], demand is simply the plan or intention of a buyer concerning product purchase which is expressed in the form of tables (or curves). We will discuss in detail later how adequately such tables and curves can reflect the behavior of buyers in the market, and we will now make some remarks concerning the form of representation of buyer’s intentions in the given model.

First, the law of demand itself follows from neither an experiment, nor a theory; it is a statement as a whole which is consistent with common sense and elementary conclusions from real life. However, all of these conclusions are the result of observations of the behavior of real market prices and demand in the day-to-day activities of markets. In the market we only concern ourselves with real prices, real transactions, and the real sizes of these transactions. Sometimes, attention is given to total demand, but not at all to market demand functions or tables. Therefore, direct transfer of this empirical law on a quite abstract, uncertain and obscure demand function of an individual buyer is unnecessary.

In other words, the law of demand means the reflection of real market processes connected with continuous changes of S&D in the market over time. The traditional demand function is an attempt to describe a situation in the market where nothing changes. It is not a dispute about how correct or incorrect a traditional agent’s demand function is. Instead, we can say that there is no basis on which to consider this model, reasonably, logically, or empirically. In principle, it is impossible to deduce a traditional agent’s demand function from the data concerning the whole market. And there is no convincing empirical data, testifying that a buyer’s behavior in the market is reflected by such a downward-sloping demand curve in the interval of all possible prices from zero to infinity. To understand our logic, the reader can try to draw on paper a demand curve of a buyer who wants to buy a new Mercedes car at a price of 100 000 $/car, or to buy shares at the stock-exchange for 100 000 $. We are sure that he or she will meet obstacles and recognize that there is something wrong with the traditional model. Moreover, logically it is impossible to construct a traditional function of the whole market making use of empirical data for the same reasons as that for functions of an individual agent. We will concern ourselves with this question once again in the end of Chapter.

Second, our main objection against the traditional demand function is that when real buyers enter a real market, they “keep in mind” not a concrete demand function on a whole interval of prices from zero to infinity, but a concrete desire to buy a certain quantity of demanded goods at a price acceptable for them which is near a known “yesterday’s” price. This is illustrated by an example of an ordinary buyer in a consumer market, who needs a certain amount of sugar in a week – but no more and no less. It is also true for a business company in a wholesale market: it should buy exactly as many raw materials and goods as are necessary for production, without creating superfluous stocks and with delivery “just in time”. Therefore, the demand function of an individual buyer can be distinct from zero only in a small interval of prices, near a known “yesterday’s” market price. In order to obtain market functions it is necessary to summarize these rather narrow functions, instead of traditional functions, distinct from zero in the whole interval of prices from zero to infinity. Moreover, the fact that in the traditional model practically all authors have the demand function converging to a maximum near the zero price (some authors even have it diverging to infinity), seems, in our opinion, to be an artificial property of a person – to take the maximum “for free”. In a real market buyers do not behave like that, and in practice no life is observed in the markets near zero prices. It is a dead zone; there is neither supply nor demand there.