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Modeluvannya ekonomiki - Vіtlіnskiy V.V.

14.6. Фіскальний аспект динаміки боргу

Roslyn'mo fiscally aspect for the deterministic process deficit to the budget. Pripimo, scho fіnansuvannya budget deficit zdіysnyuetsya Lisha for rahunok podatkіv i novih borgіv. Tse means, but the budget deficit and the sovereign borg do not viklikayut zbilshennya groshovoi Masi, otzhe, do not melt the dovgoterminovih inactivnyh naslіdkіv.

Yakshcho chinniki monetary nature, zokrema sejnorage * 2, videsitn, then the accumulation of simplification of the first period deficit to the budget is the oath of the state bogu.

* 2: {Senjorage is a pributok, possession by the sovereign of the central bank for a penny. Dorіvnyuє різниці між номінальною варістю гроше та витратами на їхню емісію.}

For the needs of the state borgo in real (current) prices, b = b ( t ) and non-perennially accrued pre-tax rates for the provision of electricity, r > 0 that triwalih terminov terminovі accumulated defitsitu (practically zero porchatkovo borgu b (0) = 0) має місце співвіdшення:

(14.17)

Up to (14.17), the budget, cotrii, is not identified with the deficit D ( t ), it is characterized by the presence of the moment b of the state b bargaining trough b ( t ).

Vinicaci listened to the nurse: you can boast of great bugs of the Borgiev, you can not have problems with your problems at the state. It is recommended to be given such a rank: to be uppermost for a pitugogo borgu, a clear rosy summery of the borg (nominal) to GDP (nominal). Vvazhaetsya, scho if the pitomii borg is not overloaded by 50-70%, then with yogo waplays, it is practically not a problem for zrostayuchoi economy. Teorotichne obryuntuvannya vidpovidі є дещо складнішим.

Significantly, the Borg through the :

De Y ( t ) is the real GDP in the t- th rotsi.

Зміна питомого боргу за нескінченно малий період часу Дорівнюватиме:

(14.18)

De - a change in the real landscapes of the state borough for an unquestionably short period of time; - The real GDP for an unspecified number of hours per hour; - Growth rate of real income (GDP).

Pririst (nezinkincheno male) of the real borgu at the time of the hour t becomes for viznachennyam the size of the budget deficit:

(14.19)

The formula is simply a new viraz of the pivot of the state borgh (14.17), yoga yodo prodifferentiating after hour t (i navpaki).

The rights of a part of the district (14.19) are the budget deficit, the cotry of storing in the initial chi of the insolvent deficit ( G - T ) and the payments for the accumulated borgo, which is due to the nominal rate of the pre - admission of the regional oblasts. Підставляючи (14.19) у (14.18), отримаємо диференціальне рівняння stasovno to pitomogo to the borgh:

Abo

(14.20)

De - the magnitude (octagon) of the pituitary primary deficit (deficit without urahuuvannya naryschenih vidsotkiv).

At рівнянні (14.20) structures it's a factor І pitomium primary deficit Mozhut bouti with the active functions of the hour, scho, vzagalі kazuchi, vidpovada real, oskilki rates vidsotka, tempi zrostannia і chastki defitsitu zmіnjutsya u chasі. However, for proskazhnya analizu vvazhatimemo їх postійними значениями, значення котрих відомі:

It is permissible, however, to take the value of the pythome borg for the hour at hand, to take care of the cobble, toto z (0) = z 0.

In the given model (for the sake of budgetary deficit), the budget deficit may be financed in the world by overreaching the taxes on the above-mentioned,

And so for a new rake of new poses.

Otzhe, multiplied by the offending part (14.20) at minus odnitnju and having learned through The amount of budgetary proficiency, obsessively rivnyannya fіnansuvannya budget deficit (for відсутності сеньоражужу):

, (14.21)

In which the deficit is to be generated before the payments to the accumulated borg for the rate of income r > 0, scoring by the amount of a - the rate of growth of real GDP.

For the economical economy, the parameter a is the number, for economics in stagnation is zero, and for depressive numbers, the number.

Рівняння (14.21) show, the budget deficit (on oditnitsu product) qz of baits at the dwellings of the hour to the net incomes of the state and the new pitomimi borgs .

Zaoschadzhnya vitrat on observogovuvannya borgu for rahunok novih borgiv є досить цікавим і порожує низкоку проблем.

Roslygno spochatku problem fіnansuvannya budget deficit without zaluchchennya noviks posek, tobto for umovi The mill of the old (in hour) pitogogo borgu ( ) - for the system (14.21) the stationary camp * 3.

* 3: {Do the economical economists write about the "stiysky camp," it's not exactly accurate, but the station itself can be very strict, so it's unstable, it's a risky thing.}

For nyogo difentsitsialnoe rivnyannya (14.21) redukuetsya to algebraic rivnyannya, rozvozykom kotrogo є funktsіya:

(14.22)

Otzhe, yakshcho chisti prihodi vlasy vprodizh neskinchennogo periodu chasu to become a value , Then rinkova vartіst flow tsig income, is reduced to the current moment of the hour, dorivnyuatime z *. Coefficient of capitalization in Maybutny flows , Which means that the time for q = ( r - a )> 0.

Рівняння (14.21) є звичайним разновиідним диференціальним рівнянням першого порядку, you can rewrite the cotra from the standard viglyadі:

(14.23)

Rozv'yazkom (14.23) - the function of the pitugogo borgu, scho vidpovidayot yagos otasheng:

(14.24)

Після знаходження розв'язку чи траєкторії (14.24) The problem of the service of the borg, the tobt of the regular plots for yoga repayment, to be brought to the notice of the trajectory of the pitugogo borgu: the remaining remains straight to the job of the ordinance (stacionary points of the station), but I do not overhear the top Permissible borgu, then the burgs can be assembled. In the case of a protracted razii, asymptotically, it is not possible to mimic, but bankruptcy is unimportant.

Have a look at the time of the moment, t = 0 ptomium borg, for example, shift the value to kopatkovu, tobto Тоді проблема сплати боргів зводиться до того, щоб з'ясувати, зростає chi зменшується ця різниця у часі. It is permissible, but at the end of the hour (0, t 1), the bargain in the borgo is not to be built, but to start at the moment t 1, if there is a sprinkling of additional water Yak viplivaє z rozv'yaku (14.24), pitomiya borg spota zrostaє eksponsentsionno, and at the time of t 1 it is squeezed sublimely to speed, oskilki poychayayutsya yogo razliti. However, one can not plow into the dynamism of the Pitomogy Borgu, but there is no triviality, as shown in Fig. 14.2, Lisha for zmіni pochatkovyh minds of this process. It is clear to the analyst that it is clear that this type of trajectory is given to the government q = ( r - a )> 0, but it is itself the share of the real estate rate in the worlds of r and the growth rate of real income a . Отже, якщо rate дохідності державних облігацій r перевищує зростання доходу (GDP chi national income), then питомий борг зростає до нескінченності, оскільки економічних джерел покриття боргів не існує.

Fig. 14.2. Dinamika of the Borgoux

Nagadaymo, scho senjorazh at the given model is vidsutniy, and the economy is closed. Зрештою, замкнутість економіки тут не відіграє ніякої ролі, апелювання до звнішніх джерел фінансування державного боргу для даної моделі не є сутєвим.

Formally, the trajectory (14.24) will be imposed on those systems for the splitting of the state borgue œ not sustainable. Navpaks, dynamika borgu stіyka, tobto borgi mozhut bouti plachchenі lishe todi, if real dokhid zrostaє shvidshe, nizh value of the rate of availability of the most valuable paperns, toto if q <0.

Economical zmist danygo visnovku, in our view, is extremely important: for the depressive economy, the Borg can not be combined, the aksliki for a ? 0 system zavzhdi є нестійкою.

Цікавим є й питання трансформаційних процесів у економіці, if a = a (a) lie in the hour and fall off function:

Abo Abo In other words.