Probabilistic Economic Theory
Шрифт:
Fig. 3. Dynamics of the classical two-agent market economy in the two-dimensional economic price-quantity space within the first time interval [t1, t1E].
And now we turn from the simplest economy to a more developed economy, in which the farmer and hunter gradually switch from the discrete trade system (one trade per year) to the continuous trade system on the market. Generally speaking, negotiations are conducted continuously and transactions are accomplished continuously, depending on the needs of the buyer and the seller. This would continue for many years. Taking into account this new long-term outlook it is expedient to change somewhat the method of describing the work of the market. Namely, by quotations of a quantity of goods, it is now more convenient to represent a quantity of goods during a specific and reasonable period of time, for example year, if the discussion deals with the long-standing work of the market. In this case the dimension of a quantity would be represented by ton/year. We show in Figs. 4, 5 how it is possible to graphically represent the work of the market over a long span of time. We see that before the establishment of equilibrium at point E, transactions were of course accomplished, but probably did not bring maximum satisfaction to the participants in the market. This would induce agents to continue to search for long-term compromises in prices and quantities. After reaching equilibrium, the volume of trade reaches a maximum, and participants in the market therefore attempt to further support this equilibrium.
Fig. 4. The classical stationary and non-stationary two-agent market economies in the [T, P] and [T, Q] coordinate systems in the time interval t > tE.
Fig. 5. The classical stationary and non-stationary two-agent market economies in the [T, S&D] – coordinate system.
Here a fork appears in the following theory: – look at Figs. 5 and 6. If quotations cease to change, then the economy converts to a stationary state in which time appears to disappear. This is especially noticeable in Fig. 6, where this sort of stationary state is described by one point, E. We will label the economies in the stationary state simply the stationary economies. But if quotations vary with time, then the economy will be named the time-dependent or simply non-stationary economies. In Figs. 5 and 6 they are represented by two lines, which emanate from the equilibrium point E. If in this case the equilibrium quantity grows, then the economy is a growing one. But if it decreases, then the economy is falling one, which clearly is represented in Fig. 5. As a rule, in such cases, the total S&D behave similarly and this can be easily seen in Fig. 5. Let us note that their dimensions in this model have also changed, now equaling $ ton/year.
Fig. 6. The classical stationary and non-stationary two-agent market economies in the economic price-quantity space at t > tE.
4.3. The Many-Agent Market Economies
Now we will increase the level of complexity of the classical economies by examining how it is possible to incorporate several buyers and sellers into the theory. It is understandable that each market agent will have its own trajectories in the PQ-space. In principle, they can vary greatly. There is good reason to believe that there is much similarity in the behavior of all buyers in general. The same is valid of course for all sellers. The reason is as follows. There is the intense information exchange on the market, by means of which the coordination of actions is achieved among the buyers, among the sellers, as well as among the buyers and sellers. This coordination is carried out to assist the market in reaching its maximum volume of trade, since it is precisely during the process of trading that the last point is placed in the long process of preliminary business operations: production, financing, logistics, etc. This is exactly what we would have referred to earlier as the social cooperation of the market’s agents. For example, it is natural to expect that all buyers, from one side, and sellers, from other side, behave on the market in approximately the same way, since they all are guided in their behavior on the market by one and the same main rule of work on the market: “Sell all – Buy at all”.
Hence it is possible to draw from the above discussion the following important conclusion: the trajectories of all buyers in the P-space will be close to each other; therefore, the totality of all buyers’ trajectories can be graphically represented in the form of a relatively narrow “pipe”, in which will be plotted the trajectories of all buyers. It is also possible to represent all price trajectories of the buyers by means of a single averaged trajectory, pD(t), which we will do below. We will do the same for the sellers, and their single averaged price trajectory we will designate as pS(t).
We have a completely different situation with the quantity trajectories, since each market agent can have the very different quantities, bearing in mind the fact that the behavior of the buyers’ (sellers’) curves can be relatively similar to each other. Nevertheless, we can establish some regularities in the behavior of the whole market, being guided by common sense and the logical method. Since the quotations of quantities are real in the classical models, we can add them in order to obtain the quantity quotations of the whole market, qD(t)
where summing up of quantity quotations is executed formally for the market, which consists of N buyers and M sellers. In this case we understand that for the whole market we can draw all the same pictures as displayed in Figs. 1–6 for the two-agent market. Thus, for instance, we can represent the dynamics of our many-agent market by the help of the following pictures in Fig. 7. In it, the dynamics of many-agent market are depicted at the moment of equilibrium (curves qD(pD) and qS(pS)), as well as dynamics of the stationary economy (point E) and dynamics of the non-stationary growing and falling economies.
Fig. 7. Dynamics of the many-agent market economy in the price-quantity space. qD(pD) and qS(pS) are quantity trajectories reflecting dynamics of market agents’ quotations in time up to the moment of establishment of the equilibrium and making transactions at the equilibrium price.
4.4. The Classical Economies versus Neoclassical Economies
Let us call attention to the fact that, in Figs. 3 and 6, the quotation curve of the buyer, q1D (pD), has negative slope, and the slope of the quotation curve of the seller, q1S (pS), is positive. This reflects the natural desire of the buyer to purchase more at the lower price, as far as possible, and the natural desire of the seller to sell more at the higher price, as far as possible. Specifically, it is here we reveal the visual similarity of the classical economies to the known neoclassical model of S&D. But the visual similarity of picture in Figs. 3, 6 with the corresponding famous neoclassical picture in the form of two intersected lines of S&D is only formal; economic content in them is entirely different. In classical economies, this is a graphic representation of the real market process (which really occurs on the market at a given instant), while in the neoclassical economies, this picture expresses the planned actions of market agents on the market in the future. Note that in neoclassical economics it is namely the curves qS(pS) and qD(pD) that are called S&D functions. The economic content of these S&D functions can be roughly expressed thus: “the market is by itself, I am by myself”. If one price is on the market, then I purchase (or I sell) one quantity, and if it is another, then will I purchase (or I will sell) another quantity, and so forth. Thus, the market process is completely ignored in the neoclassical economic model. But we know that, in real market life, all market agents participate continuously in the market process, permanently changing price and quantity quotations, since each has made transaction price changes on the market. We will discuss neoclassical models in more detail in other chapters of the book. However, we will now develop an artificial classical economy that will be as similar to the neoclassical model as possible.
We will call this model the quasi-market economy with the “visible hand of the market” in order to distinguish it from the economies having self-organizing markets, or economies that exhibit the “invisible hand of market”. In the quasi-market economy, there is a definite chief (very strict and all-seeing by definition) of the market (visible hand of the market), to whom all agents of the market for the planned period, let us say a year, must pass very detailed and reliable plans with respect to purchase and sale of goods. These plans are compiled by agents and are given to the chief in the form of tables, which are formed according to the rule stated above. If just such a price is found on the market, then I will sell a particular volume; if it is another price, then I will purchase (or sell) another, specific volume, and so forth. These agent tables are represented in Fig. 8 for simplicity in the form of continuous straight lines, a factor which does not decrease their generality in this case.
Let us note that each agent passes its plan to the chief in the form of table, and chief itself unites data of these plans and presents them in the easy-to-use shape of the two straight lines in one picture. Common sense tells us that it is most profitable for the buyer to purchase more at the minimum price. But in this scenario the seller would want to sell less. The opposite would be true for both buyer and seller at the maximum price. Graphically, this is reflected in the fact that when point P1 is higher than point V1, and the point V2 higher than point P2, the consequence is that the slope of the curve of the buyer is be negative, and the slope of the curve of the seller, positive. It is obvious that these two straight lines will compulsorily be crossed at the point E (pE, qE), where the prices and quantities of the buyer and seller coincide. Next, the chief considers that these prices and quantities reflect certain equilibrium in the market, he or she calls the equilibrium price and quantity and declares that these values of price and quantity are set for the market year. Market process is, in this case, further completely eliminated from market life, in that the decisions of the market's chief completely substitutes it during the next year. We call this model economy a quasi-market one, since plans are compiled by market agents. However, they realize them in the prices and the quantities that are essentially dictated by the market’s chief.