The model of the economic system which is discussed in this paper is based on the assumption of the existence of the heterogeneous structure of economic agents. During this assumption, we analyze the general economic equilibrium model with incomplete asset market, the existence of monetary equilibrium and the emergence of financial instability of the economic system, as well as actions that are necessary for overcoming economic instability. The private sector is observed as a set of participants who have different utility functions. Also, it is assumed that there are more commercial banks, where each bank has their own portfolios, which reflect the different preferences the risk / profit. In the market conditions, each bank analyzes the credit worthiness of each borrower, and on the other side each borrower faces different credit markets. Therefore, in this paper, instead of the only market for deposits/loans, development of model will be conducted by analyzing more than one market for deposits and more than one market for loans. The private sector and commercial banks maximize their utility functions, while the role of the Central Bank and the public sector is exogenously given. Further, in the model, we look at money as the conditioned medium of exchange, whereby the Central Bank and the government have a monopoly on the issue of controlled money as a widely accepted method of payment. Also, depending on what is the function of money in the markets funds, we observe the same physical structure as endogenous or exogenous size.