Real Sector
Households
The model includes a continuum of households, normalized to 1. Each of them solves the following standard utility maximization problem:

(1)

which depends on the current consumption and the labor supply . dDenotes the discount factor and is the inverse elasticity of labor supply.
The budget constraint of a household has the following form:

, (2)

which includes credits for entrepreneurs at time - , the interest on the same credits adjusted for inflation, but at time - , where is the inflation rate at time , and the interest rate is set by the central bank. The household gets from entrepreneurs the wage in exchange for its labor , she also pays lump sum taxes and owns retail firms, obtaining their profit - .
The first order conditions for the problem are standard, and have the following form:

(3)
, (4)

where (3) and (4) are the Euler equation and the labor-supply condition correspondingly.
Entrepreneurs
Entrepreneurs manage perfectly competitive firms that produce intermediate goods, and borrow from households in order to finance the purchasing of the capital for the production process at time . In the production process at time, they also use the labor of households ,; the production function of a representative entrepreneur is assumed to be of the Cobb-Douglas type:

, (5)

where the parameter represents technology process, and are the shares of capital and labor in the intermediate product, respectively, while denotes the share of households’ labor in the total labor. The amount of entrepreneurs’ labor is normalized talso , and the share of entrepreneurs’ labor is equal,
Wwith the probability an entrepreneur can become bankrupt in each period. Under this assumption, entrepreneurs always use for the financing of the purchase of capital, not only their net worth , but also credits from households in amount :

, (6)

where denotes the fundamental price of capital at time .
Bernanke and Gertler (2000) introduce the “financial accelerator” mechanism from BGG (1999), in which the interest rate for external financing is greater than the interest rate , because of agency costs and asymmetric information, and depends on the ratio of the market value of capital to the net worth:

, (7)

where it denotes the expected rate of external financing, is the market price of capital at time , denotes the parameter of financial accelerator mechanism. – is the ratio of the market value of capital to the net worth of entrepreneurs or their financial leverage.
The net worth of entrepreneurs is updated according to the following equation:

,(8)

where is the labor income of entrepreneurs. Entrepreneurs, who become bankrupt at time , consume the rest of the net worth in the amount .
It is worth noting, that the interest rate of external financing in (7) and the dynamics of entrepreneurs’ net worth in (8) depend on the market price of capital , which is changed as follows:

, (9)

where is the exogenous market change shock that is set by the interaction of traders on the financial market, who trader futures on capital. The setting of will be described further in Section 3.3. The equation (9) determines the size of the deviation of the market price of capital from the fundamental price of capital, and we suppose that without the market change shock, this change will keep the same size over time. This assumption seems very reasonable, because the prediction of financial markets is a very complicated problem, if it is at all possible. Financial markets can go up or down, so without proper prediction, it is the most suitable way to suppose that the deviation will be the same over time without exogenous shocks.
The following condition is fulfilled under the optimal demand on capital:

, (10)

where is the marginal return on capital. The first order conditions for entrepreneurs are as follows:

(11)
(12)
, (13)

where – is the markup of retailers at time , its description will be given further.

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