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Model of economics - Vіtlіnsky V.V.


13.1. Solow Model

Small-scale non-linear models for the development of new trends and officials in the development (transformation) of the economy. The small number of sectors allowed allows for a similar analysis on the model of economic growth with adequate coverage of non-linear deposits of large amounts of resources due to a significant loss of cost.

Solow model є one-sector model of economic development. Your model has an economical system that looks more like one, more than one product is excluded, which you can survive, and invest. A model to achieve an adequate performance, macroeconomic and aspect aspects of the process. Export — Import Do Not Fly At Explicit Wiggle * 1.

* 1: {Kolemaev V. A. Mathematical Economics: Textbook for universities. - M.: UNITY, 1998.}

The economy in the Solow model is set by five endogenous winners: X is the gross suspension product (VSP), C is the fund for non-psychological living, I is investment, L is the largest investment, K is the funding fund. I’m surrounded by the model, in the model, I’m also able to specify the position of the system) indicators: v - the primary growth rate of the number of employees, m - the frequency of the longest stretch of the main viral products, a - the number of products that are directly sold, - the rate of accumulation (a part of gross investment in GDP). Between exogenous parameters:

Robbery is allowed, but endogenous changes at a time (the argument is vipuskatsya, ale vіn, as a rule, є present for the appointment). Exogenous knowledge of living in the hour. To get involved, is the norm, which is the norm accumulated by a curative parameter, but at the right time of the hour t 0 = 0 you can become a cherished organ of the system on a certain level in the range of acceptable values. The hour t is imperative to uninterrupted and such, what to do in the rocks. For the metrics L = L ( t ), K = K ( t ), it’s worthwhile to reach the natural ones, fragments, in principle, whether it’s possible to take into account the number of people involved in the inventory and establish the oath of taking the main virological funds. A significant indicator of the type of flow is X = X ( t ), I = I ( t ), C = C ( t ) at the moment of time t = [ t ] + { t } can be seen from the viewers with a long stretch of rock, which can be fixed at 365 { t } dnіv pіznіshe 1 sіchnya roku [ t ].

Robbery is allowed, and now there is a quick release at the skin moment of an hour that means a linear-one-neoclassical neoclassical func- tional function of two types of resources K and L.


Let’s take a look, as the resource indicators for the sale of small business hours D t . Згідно з to the designated rate of increase in the number of employees


otzhe, zdіysnyuyuchi integruvannya, mamo:

Victorist to the cob of mind L (0) = L 0,

The knowledge of the fund and investment of the road to the city is m K t I I vdpovodno, and by the hour D t - vidpovidno m K D t , I D t , the increase in the fund for the sale of the whole hour

Zvidki otrimaєmo differenti rivnіv rivnyannya:

Oskilki industrial product to become aX , then the gross domestic product is expensive (1 - a ) X.

Investments I = r (1 - a ) X , and the fund is C = (1 - r) (1 - a ) X.

Otzhe, we canceled such a formalized Solow model in absolute terms:


In fig. 13.1 is a diagram of the functionality of the economy from the model Solow.

Fig. 13.1. Functional diagram of the economy for Solow

We will also see the following indicators:

- capital recovery;

- Narodnospodarska productive pracі;

- pet investment (per one borrowed);

- srednododushovoy residency (per one occupied).


then the Solow model of the nabuvaє such form in pet (casual) indicators:


Overwhelmingly, absolutely leathery, the absolute chi indices are visible in the hour, so that you can conduct a motion about the system trajectory in absolute chi indices. They say that they say that they are stationary , but the indicators do not vary in the hour:

It’s unimportant to keep track of the formulas (13.3), and set the capital recovery at the correct posture to bring to the exit to the stationary traction.

On stationary traktory to that

, (13.4)


If the function F ( K , L ) is neoclassical, then f (0) = 0, f ? > 0, f ?? <0.

Yakshchos, okrym tsyogo, ask mind then rivnyannya (13.4) matime єdiniy vіdmіnniy vіd zero zero linking k 0, which can be shown in fig. 13.2.

Fig. 13.2

In fig. 13.2, at the point k 0, showing the statutory ryven fundraising, through the level of asset recovery has been designated, for which speed is the function g 1 ( k ) = l k and g 2 ( k ) = r (1 - a ) f ( k ) є better, to - korin rivnyannya