Читать книгу Probabilistic Economic Theory - Anatoly Kondratenko - Страница 12

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, p^D(t), which we will do below. We will do the same for the sellers, and their single averaged price trajectory we will designate as p^S(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, q^D(t) и q^S(t). However one should do this separately for the buyers and sellers as follows:

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 q^D(p^D) and q^S(p^S)), 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. q^D(p^D) and q^S(p^S) 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.