Baizakov S.V., Mohamediev B.M.
Dynamics of the Balanced Growth with the View of Non- definite Influence of the Scientific and Technical Progress on Production Efficiency.
Journal "Vestnik KazGU". Serial of Economic Siences. Almaty, Kazakhstan, 1998, 11.

When the labour time fund acts as the only restriction of development of the economy, the increase of the output of products at the rate of per unit of the labour time becomes the source of its acceleration. . The increase of production efficiency and its acceleration are determined not only by the quantity of the accumulated labour of the past but first of all it depends on the ability to increase the public labour productivity, which, in its turn, influences the decrease of the labor intensive products.

The achievement of high rates of the economic growth is the priority task set in the "Strategy of Development of Kazakhstan up to 2030". We cherish the hope to build an independent, politically stable state to improve the well-being of the population, to solve acute social problems (poverty, unemployment, criminality), to introduce high-tech and to join the world economic system.

For managing the macroeconomic dynamics it is necessary to determine the intercommunications between the economic indexes. Labor product at consumer costs is characterized by the physical volumes of the aggregate public good W, production factors: the common fund of labor time L and production funds F, but its cost characteristics are the produced national incomes Y, and the fund of reimbursement c. The derivatives are determined by the following indexes: f- the fund on employment, - materialized labor productivity;- the average annual wages at the rate of per unit of the labor time; - the level of overtaking of the public labor productivity compared with payment; - the level of exceeding of the labor fund over the payment expenditures; - the fund return at the rate of per unit of materialized labor. The effective management of macroeconomic dynamics presupposes the stable tendency of changing all the aggregates.

The current development of productive forces is characterized by lagging behind of the growth rate of the public labor productivity from the growth rate of the labor fund provision, i.e.

,

where - derivatives on time indexes. The equilibrium of the productivity rate and the labor fund provision would mean the stabilization of the fund return on materialized labor, because

(1)

It will be possible when the equal growth rates of the public labor productivity and of the labor fund provision are reached:

, (2)

and also the indexes q and h:

, (3)

as in this case .

The ratios (2) and (3) show the proportional change of the macroeconomic indexes in time, and consequently, the movement of the economy along the path of the balanced growth.

In general, the ways of management of macroeconomic dynamics may be formulated like this. Suppose that at the moment of t0 the real ratio between the growth rates of the public labor productivity and its fund provision is expressed by the equation (1), i.e. 10. On the basis of the qualitative improvement of the technological sphere of production it is necessary to reach the equilibrium of their growth rates, i.e. to lead the economy along the path of the balanced growth, where the main indexes of the macroeconomic dynamics increase at constant rates (see Fig.1).

l

l0

l*

t0 t

fig. 1

There are two quite different approaches to modeling of the macroeconomic dynamics. In one of them the production function is used. So, in the models of Harrod and Sawlow the scientific and technical progress is treated as an exogenous factor, which does not depend on the state of the economy. All the new processes are introduced apart from the economic decisions.

In case of the second approach the entrepreneurs choose the optimal way of behavior not at once but step by step, gaining experience. The more possibilities they have, the sooner it happens. Thats why they say the more the volume of the capital investments, the higher the rates of the technical progress.

Referring to this statement Calder B.G. suggested the function of the scientific technical progress, which shows the direct dependence between the investment growth rate per one worker and labor productivity growth rate of workers using the equipment of the latest design. In the equilibrium the investment growth rates must be equal to the labor productivity growth rate. The correlation of the models of Calder-Mirleece enables us to determine the required characteristics of the balanced growth (see [4]). But at the same time there is still a problem for the economy to go on along the path of the balanced growth.

The main function of the scientific and technical progress at work [2] is suggested to establish quite differently, i.e. as the dependence of the change rate of the fund return on the materialized labor l from the change rate of the organic structure of production h: (4)

For simplification lets assume the dependence (4) as linear, i.e.

, (5)

where are the factors determined by the econometric methods as

(6)

and which show that the wages growth rate must not exceed the growth rate of the public labor productivity. Only then it will be possible to establish the interdependence between the main macroeconomic indexes. In particular, the main function of the scientific and technical progress may be shown in the following way:

(7)

At present the dynamics of changing of the index 1, characterizing the productivity of the scientific and technical progress, has the negative growth rate, i.e. i < 0. For the monosectoral model of the extended reproduction in [5], the linear equation of movement is accepted:

i = -Rl + u, l(t0) = l0, t0 t

where R is the coefficient reflecting the susceptibility of the economy to the scientific and technical progress, u is the parameter of management which shows the norms of the accumulation and the dynamics of other macroeconomic indexes. Thats why it cannot take the arbitrary sense.

Going into the path of the balanced growth may be achieved by stabilizing the index of the fund return on materialized labor, i.e. when i=0.

Suppose 1* is the level at which it is expected to stabilize the index 1 during the period T. For the linear model (1) at work [5] the meaning of the managing parameter U is given, which ensures the transition from level 10 to level 1* during the period of T = t0 :

(8)

But it should be noted that the scientific and technical progress and its influence on the economic development cannot be forecast for a long period of time.

Besides, the managing parameter u = u(t) may be, to a certain extent, changed, depending on the circumstances, i.e. depending on the variable 1=1(t) which has been realized by the time t.

Lets see the way of transferring to the regime of the balanced growth in view of non-definite influence of the scientific and technical progress.

i = -Rl + u, l(t0) = l0, uu, RRR,

t0t, l*-l()l*+. (9)

The given restriction shows the requirement of going into the level 1* with the precision of . The hypothesis of being well-informed is accepted : at the moment of t, while choosing the form of management U during the period (t, t+), the realized variable becomes known 1(t). The meanings of the factor R(t) are not definite, but it is supposed that they can change within RR(t)R for all to t0 t

Together with the system (2) lets make the discreet variant out.

, uuiu, RRiR,

. (10)

Here equals T/N,where N is the number of periods of time. On the basis of the approach (6) for the discreet system (3) it is possible to make the following calculations and get the needed conditions:

, (11)

These conditions determine the aggregate meanings of li, under which the economy may be led to the level with the index l = l* (with the precision ) during the left N-i years. And the variables ensuring such kind of transition ui show the below given non identity

(12)

In particular, under the ratios (11) the conditions for the initial state 10 and the required number of steps or stages N can be determined. If to assume that uncertainty, i.e. R=R=R is absent, management is constant, u=u=u. And it is possible to transfer to the limit N, then the formula (8) will come out of the ratios (12). It may be also possible to obtain the appropriate conditions for the uninterrupted system (2) from inequalities (11) by the limiting transition.

(13)

Thats why it may be possible to formulate the following task: to determine the minimum time during which the economy might be led to the level of the balanced growth from the level 1=1*

Below the results of the numerical calculations are given, compiled with the help of Excel table. The interval [ul, ul] in Table 1 gives in conformity with (12) the aggregates of the possible management u1 during the first year in order to lead the economy out on the path of the balanced growth.

Table 1.

l0

l*

R

R

u

u

eps

N

ul

ul

0,699

0,699

0,699

0,699

0,699

0,699

0,691

0,691

0,691

0,691

0,691

0,691

0,2993

0,299

0,29915

0,2993

0,299

0,2993

0,3007

0,301

0,3008

0,3007

0,301

0,3007

0,207

0,207

0,207

0,2065

0,2065

0,207

0,209

0,209

0,209

0,2095

0,2095

0,209

0,001

0,001

0,001

0,001

0,001

0,0007

9

-

15

5

7

13

0,20700

-

0,20700

0,20650

0,20650

0,20700

0,20847

-

0,20778

0,20869

0,20950

0,20798