# Parametric control of macroeconomics - System theory and system analysis

## Parametric management of macroeconomics

But in addition to the spontaneous perturbations described by equations (7.11) and (7.12), the economy is also experiencing control actions on the part of its controls.

Actually, these impacts are realized by changing the parameters of the economic system τ, n and L by investment, therefore, economic management belongs to the class of parametric controls, although a direct variation of Н by improving the quality of products, which, however, requires a lot of time.

Formally, the differential equation of a macroeconomic system under the conditions of parametric control of it differs little from (7.11a). It is only necessary to enter the corresponding parameters under the sign of the derivative

(7.11c)

However, if we expand the brackets in (7.11), then, for example, when we control only the resistance we get the turnover

(7.11y)

in which, unlike (7.116), and depend on the time.

This means that during the transient process caused by the change in x, the fluctuations in the turnover will vary both in the period (frequency) and in the attenuation, which under the condition becomes negative and can lead the system first to overheating, and then to the collapse of the economy.

So, if we want to reduce resistance to turnover from to by investing in modernization of production, then according to the law of diminishing efficiency of capital investments one can expect an exponential decrease

(7.14a)

where a is a measure of the decrease in management efficiency.

Accordingly

(7.146)

and

(7.14c)

Now, taking into account (7.14)

(7.15a)

(7.15b)

From these relations it follows that, although in the steady state , i.e. the turnover assumes the expected sizes, but before this mode the system may not survive, because it can collapse in the transitional process, if only , which is quite possible, especially at the beginning of the process for small t) •

In the latter case, becomes negative, and I can go beyond the permissible limits for the life of the economy, the more likely the larger the desired limits < img border = 0 src="images/image1160.jpg"> ι, the capacity n of the system and the initial efficiency of capital investments for t = 0.

As for the specific behavior of I in the process of controlling it by τ, it is formally described by the previous relations (7.12), but with the new values ​​ T and δ taken into account.

We now investigate the behavior of the system, if it is managed by increasing n by raising prices without changing the quality of the goods.

The equation of the system takes in this case the form

, i.e.

(7.11y)

where ;

If we assume that n will grow according to the exponential law (where - initial efficiency of stimulation of needs; - new (desired) value of n; - original ) the value of n), then

(7.16a)

a

(7.16b)

This means that in the case of the period of fluctuations and the decay of the economy become imaginary and at that time the economy can be severely stalled and thrown out of service.

If we manage the inertia L of the system, by reducing it by introducing flexible manufactures and promotions that shake the stereotypes of production and consumption, then the corresponding investments will give the effect , where - the new (desired) value of L; - its original (old) value; y is the initial efficiency of investments.

In this case, the equation of processes in the economy, caused by a change in the inertia of the system, takes the form

(7.11d)

where

(7.17a)

(7.17b)

From these expressions it is obvious that both and can change the sign in the transient process, that means that excessive growth, then a sudden decline, i.e. possibly unacceptable shocks, which I would like to know in advance by exploring the model of the economy.

Of course, it is possible to manage the economy in all parameters η, τ and L simultaneously and then the consequences of this will be superimposed on each other, creating absolutely fantastic system reactions that are speculatively impossible predict.

These reactions are described by equation (7.11b) if we take the derivatives of all parameters in parentheses in it, which is not difficult, but leads to cumbersome expressions that we will not write out, leaving this procedure for readers if they have such a need.

So far, our reasoning about the management of the economy has been a warning against unintended interference in its processes.

In other words, it was about the inadmissibility of managing the economy on the basis of good wishes for the final result, because on the way to it in the transitional process it is possible to go beyond the range of the system's operability with irreparable consequences.

This means that the consequences of intervention in the economy should be carefully examined beforehand on its model, not only in static, but also in dynamics.

Now we put the question differently: how to achieve that in the transition process to ensure more or less continued economic growth?

The point is that the system itself, described by a second-order differential equation with positive coefficients n, x and L (7.11a), is always stable, i.e. with any perturbations, sooner or later it comes to stagnation and can not develop itself.

Another thing is that, for example, with a continuous decrease in x due to investments in expanding production and consumption, the turnover could increase continuously.

But, because of the decreasing efficiency of investments, the change in τ can be only exponential, i.e. limited in magnitude, then the increase in turnover Δ I will be limited with subsequent stagnation, although at a higher level than the original one.

Of course, all sorts of technological breakthroughs restore the efficiency of investment, but they do not always happen on order, but more often they have to wait a long time, staying at this time in stagnation.

It only remains to hope that the economic willfulness of the system within the transitional process in it will be able to be channeled into the desired channel of economic growth over a sufficiently long period of time, which, ideally, could be prolonged by a proper change in the parameters n, τ and L.

The event is rather risky, since after a significant growth the turnover should still return to the established new value determined by n n, tn, L H, which inevitably will be accompanied by a recession turnover, which can be prevented if, during the growth of the economy, take care of the development of a product that is more efficient in meeting the needs of products, thereby increasing H to the level that secures the turnover achieved in the growth process.

In general, swinging the system one way or another, and having the opportunity to stimulate it with any of the remaining funds, it is necessary, firstly, to connect these growth reserves only at the time when the trend towards an economic recession manifests itself, and, in the first place Second, varying n and L, ensure the smoothness of the system's behavior when the reserves of its growth are exhausted, which will postpone its inevitable approach to stagnation.

If it is necessary to reflect the impact of the world economy on the national economy, then at the top level of macroeconomic generalization, the matter is formally reduced to the additional introduction of interaction factors into the model: - resistance to the turnover of goods and money between the world and national economies;

- the capacity of inter-economic turnover; - the rigidity of inter-economic turnover, i.e. the sensitivity of the national economy to changes in the world economy.

Then the mathematical model of macroeconomics will take the form

(7.11e)

where and are the parameters of the world economy that affect the national economy, to the extent of its respective elasticities . However, this effect is more clearly reflected by the symbolic chain diagram (Figure 7.6), where the national economy is on the left (see Figure 7.3), to the right is a similarly shaped world economy, with a docking node with parameters (customs, visa services, etc.), and - the resulting (total) flow of values ​​between economies.

This scheme corresponds to a system of equations

Fig. 7.6

(7.11f)

whose solution leads to (7.11 e), but with an explicit expression of elasticities through the parameters of both economies.

So, for example, the kinetic elasticity has the form , and as a result , That in the absence of interaction of economies, i.e. at ; at , i.e. with a free flow of values, we get ; and at this elasticity can become negative if .

Similar conclusions can be drawn from similar expressions for static and dynamic elasticities obtained from (7.11): .jpg ">

Note that according to the model in Fig. 7.6 in static, equipotential economies with , in general, do not interact, because they are in equilibrium competition, but equipotential economies, i.e. at , can fully interact if

Of course, in the framework of the model considered, the absence of interaction does not mean isolation from each other, but implies a complete balance of interchange processes.

If in the circuit in Fig. 7.3 to divide production (index 1) and consumption (index 2), we get the structure shown in Fig. 7.7.

Fig. 7.7

where - total exchange, i.e. mutual essence of the economy, and - aggregate consumption, i.e. system essence of the economy, - the integrity of the economy, - the degree of freedom of consumers in the acquisition of goods and services , and - the basic law of systemology (3.28), (3.32), (3.33).

The generalized macroeconomic model of an isolated national economy considered allows us to study the features of the turnover behavior as a whole without dismembering the commodity and financial components.

Meanwhile, only the relationship between commodity and money turnover can explain, for example, an important process such as inflation or relations with the world economy, which calls for an appeal to the developed structure (functional stratum) of commodity-money circulation, which we will now do.

But the stratification of macroeconomics implies the existence of an industrial stratum, to which we will address later.

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