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.

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