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The behavior of stock market prices as a response on the variation of external conditions is very complicated problem. We begin our investigation of that problem from research of very simple mathematical models of stock market in the periods when variations of a external conditions for the stock market are small. The model of market of one commodity, in which there is in each moment of time the same quantity of goods and the same quantity of money was formulated and researched in this paper. Each participant of the market in the one moment of time can be in one of three statuses: to be buyer, be seller and do not take part in trade in this moment of time and can to change his status and price, by using the personal information about trade in the previous moment of time only. The convergence of trajectory of our system to stationary set of states with average price of trade which is close to some constant was established by series of experiments with computer realization of the model. Some cases of the herd behavior of participants were considered in this investigation. This text can be useful for the scientists and for the students of economics and mathematics.