^>Е and quantity q_>1^>Е of goods can be specified in the contract. Let us assume that in this bargaining model it makes some sense to call these price and quantity values the market price and quantity of the commodity and to assume that the market itself comes to or reaches its equilibrium state at these price and quantity values. Formally, this is described using the following equations for the market price and quantity:

So, for the two-agent model we obtained this trivial but significant result: the very fact of reaching equilibrium makes it possible to conduct a transaction and maximize the volume of trades in monetary terms. In this simple case the conclusion is quite obvious: no agreement, no equilibrium, no transaction, trading volume is zero. But we will further show that this conclusion has a rather universal nature, which agrees with the postulated trade volume maximization principle. By the way, it is easy to show that in the framework of the neoclassical theory the maximum trade volume in natural terms, i.e. the maximum quantity of traded goods is reached at the equilibrium point.

Further on, since life does not stand still, the buyer and the seller can meet again and make new deals, but under new conditions and, obviously, with other prices and quantities, then for convenience we will call р_>1^>Е the first market price, and q_>1^>Е the first market quantity. Thus, at time t_>1^>E, the interests of the buyer and the seller have coincided for the first time, and they have been optimally satisfied by concluding a sale-purchase transaction. In this case agents, naturally, in the course of the market process (negotiations and changes in quotations) implicitly took into account the influence of the external environment and institutional factors on this and other markets, i.e. the economy as a whole. Here one can notice a similarity in the motion of the economic system in economic space, described by the trajectories of the buyer р^>D(t) and q^>D(t) and the seller р^>S(t) and q^>S(t), and in the motion of the two-particle physical system in real space, described by the trajectories of particles x_>1(t) и x_>2(t), which, by the way, are also the result of a certain physical maximization principle, namely, the principle of least action on the physical system.

The noted analogy with the physical system suggests using a similar mathematical body, analytical and graphical. In Fig. 1.3, to begin with, we provided a graphical representation of these trajectories of agents' motion as a time function using suitable coordinate systems time-price (T, P) and time-quantity (T, Q), similar to the construction of particle trajectories in classical mechanics. Please, note that figure 1.3 reflects a certain standard situation in the market, when buyer and seller intentionally meet at a point in time and start discussing a potential deal by mutual exchange of information about their conditions, first of all, desired prices and quantities of goods. During the negotiation, they continuously change their quotations until they agree to final terms on price р_>1^>Е and quantity q_>1^>Е at the time t_>1^>E. Such a simple «negotiation» market model is applicable, for example, to the economy of a fictional island on which, let us say for certainty, once a year there is a negotiated grain trade between a farmer and a hunter. To introduce some certainty, let us assume that they use the American dollar, $, for settlement. For clarity, in Fig. 1.3, as in the following figures, we use arrows to reflect the direction of agents’ movement during the market process.