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Model of economics - Vіtlіnsky V.V.

14.6. The fiscal aspect of the dynamics of the Borg

Rosglyano fiscal aspect for a deterministic process to budget deficit. It is permissible that scho financing of a budget deficit is more expensive for the taxis and new bargains. This means that the budget deficit and the state borg do not like to pay money and, therefore, do not have to give more information and more.

As a rule, officials of monetary nature, a secrecy of seniority * 2, every day, then the accumulation of sales of the singing period to the budget is an oath to the sovereign borg.

* 2: {Senyorazh - a side trip, of possessions by a sovereign skarnnitsa, or by a central bank as a VIP of pennies. Dear sellers of the nominee wartime of pennies and vitrats for емhnyu emіsіyu.}

For the burden of the sovereign borg in real (current) prices b = b ( t ) and the constantly up-to-date rate of return for the sovereign regions of r > 0 and the fact that there were more than zero (more than 0)


Vіdpovіdno until (14.17) the budget, which was underestimated due to deficiency D ( t ), is characterized by the appearance at the skin moment of time t of the sovereign borg with an oath of b ( t ).

Vinikaє in earnest: how great can the Borg’s swear, how could the state have no problems seeing what was repaid? It is empirically possible to give such a rank: evaluate the upper boundary for the pet borg, a kind of rosy mind, like an official borg (nominal) to GDP (nominal). To get involved, if I don’t overwhelm the pet Borg, 50-70%, then there are practically no problems with this payment system for the economical economy. Theoretically obruntuvannya vіdpovіdі є deso folding.

Significantly Pet Borg through :

de Y ( t ) is the oath of real GDP for the t- th rotsі.

Zmіna pet Borgu for several maliy perіod hour Dorivnyuvatime:


de - Zmіna real obyagіv Sovereign Borg for several years Maliy perіod hour; - Zmіna real GDP for a few maliy perіod hour; - the rate of growth of real income (GDP).

When (a little bit) the real boss at the time of hour t becomes the value of the budget deficit for the target:


The formula is simply the highest level of the sovereign Borg (14.17), which is the only differentiation after the hour t (i Navpaki).

The rights to the private property (14.19) - all the budget deficit, which is stored from the original price without a security deficit ( G - T ) and the payment according to the accumulated borg, which must be respected for the nominal rate of the state ownership. Pіdstavlyayuchi (14.19) at (14.18), we’ll remove the differential rivnyanno to the pet Borg:



de - the value (oath) of the original primal deficit (deficit without urachuvannya has been extended).

Rivnyanni (14.20) has a structural factor first pet deficit can be used for all the functions of the hour, scho, seemingly in vagueness, reality, reality, part-time rate, part time and frequency of change at the time. However, for the sake of simplicity of analysis with the most constant values, the value of the number is:

It is permissible that in the house and the value of the pet borg for the moment, it is necessary to take on the cob, so that z (0) = z 0.

At the current model (for the daily monetary bureaucrats) the budget deficit can be financed in the world of redistribution of taxes on more accurate government vitrates, so remember

as well as for a brand new posik.

From now on, having multiplied the offending part (14.20) by the minus one and by the value of budget profits, obsessively rіvnyannya fіnansuvannya budget defіtsitu (for vіdsutostі senyorazhu):

, (14.21)

at which deficiency is reduced to the payouts of the accumulated borg for a rate of income r > 0, which is averaged by a - the growth rate of real GDP.

For a growing economy, the parameter a is the current number, for the economy in stagnation it is zero, and for a depressive economy it is a number.

Rivnyannya (14.21) showing the budget deficit (per unit product) qz of security at the skin time hour net incomes of the state and new pet borgs .

Forgiveness of the vitrat for servicing the Borg for the rakhunok of the new Borgs є to finish the problem and make the problems low.

Let’s talk about the problem of financing the budget deficit without getting new ones, The camp of a steel (in hours) pet Borg ( ) є for the system (14.21) by the stationary camp * 3.

* 3: {For deacon’s economical people, writing about the "youth camp" is not certain, but the master camp itself can be as much as youth, so we’ll need to do it.}

For a new differential rivnian (14.21), to relate to an algebraic rivnian, which is different in function:


From now on, as a whole, purely profitable powers for the sale of unlimited period of time become , then the marketability of the flow of income is reduced to the current moment of the hour, dear to z *. Koefіtsієnt capіtalіzatsії maybutnіh streams in income_ - value , what is the hour for q = ( r - a )> 0.

Rivnyannya (14.21) є The sound of the heterogeneous first-order differential rivnyanny, which can be rewritten with the standard viglyad:


Rozv'yazkom (14.23) є the function of the pet Borg, which is the principle of obyagam yogo repaid:


After I have recognized the need for transfer of labor (14.24) the problem of servicing the Borg is that you need to pay regular payments for the first repayment, keep up to the last behavior of the pet borg: there is no other allowable borg, then the borgs can be butted together. In theprotector area, repayments are asymptotically not не impossible, and bankruptcy will become inevitable.

Don’t have a nice spin at the hour t = 0 pet borg, for example, I will overtake the size of the cob, Todi, the problem of repaying the Borgs is to start before they can’t help them. It is permissible that in the period of time (0, t 1), the payment on the Borg is not healthy, but it is repaired at the time t 1, if the stench is more expensive Yak viplivaє of rozv'yazku (14.24), Pete Borg spochatku zrostaє eksponentsіyno, and at the time t 1 stribkopodіbno skorochuєtsya, oskіlki pochinayutsya Yogo splats. However, don’t pour in the dynamics of the dynamics of the pet Borg, the growth of such a trivє, as shown in Fig. 14.2, deprived of the process of cob minds. From the analysis, it’s clear that such a nature of the work of the bargain is necessary q = ( r - a )> 0, which is the sacrifice of the average real estate income and growth rate of real income a . From now on, as a rule, the rate of income of the sovereign regional governments is that I transfer income to income (GDP and national income), then the pet borg grows up to inconsistency, the fragments of economical bills are not paid.

Dynamo of the Sovereign Borg

Fig. 14.2. Dynamo of the Sovereign Borg

Nagadaimo, scho senyorazh at this model viddsuty, and the economy is closed. For the sake of closure, the economy is not here, there’s no role, an appeal to the best dzherel finance of the sovereign borg for this model is not sutuvim.

Formally, the trajectory (14.24) takes into account those who have the system of paying the sovereign borg є nestіykoy. Navpaki, the dynamics of the borg style, so that the borgs can be more tightly knit, if the real income is higher, the lower is the rate of the remaining value servers, so far q <0.

In our opinion, the economic reserve of this gown is зв supremely important: for depressive economy, the Borgs cannot be butted together, fragments for a ? 0 system wait є unstable.

The value of the nutrition of the transformation processes in the economy, if a = a ( t ), lie down at the right time and є with a downward function:

abo abo skinny.