Probabilistic Economic Theory - страница 17

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.

Let us call attention to the fact that, in Figs. 3 and 6, the quotation curve of the buyer, q_>1^>D(p^>D), has negative slope, and the slope of the quotation curve of the seller, q_>1^>S(p^>S), 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 q^>S(p^>S) and q^>D(p^>D) 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.