Empirical Studies








The relation between the growth rate and the rate of accumulation at various stages of technical progress has been thoroughly analyzed many times with the help of various growth models.  Let us now turn our attention to one of the aggregate growth models. It  can be easily shown that the growth of the rate of accumulation not only cannot be considered a general rule but that it is not even permanently possible

Y = national income,
K = capital,
L = labor force,
S = consumption fund,
A = accumulation fund,

and let us define the following parameters:  
a   =  A/Y   … the rate of accumulation;
b   = Y/K   … the efficiency of capital,
w   = Y/L   … labor productivity,
r    = Y'/ Y  …the growth rate of national income;

l    = L'/ L  … labor force growth rate
f   =  b
'/b   ... rate of change of capital efficiency 
   = w'/w  …rate of change of labor productivity

Note:  the primes ‘ indicate the derivative

with respect to time.
Technical progress is capital intensive  if  f < 0:
neutral    if  f =  0; 
and  capital saving if  f > 0.

Assuming that the labor force growth rate l is constant, we can express the growth model by the following system of equations:                            

(1)              Y   =   bK  

 (2)              Y  =    wL

 (3)               Y  =   S + A

 (4)               A  =   aY

 (5)               A  =   K’

 (6)               L  =   L0 elt


  From the production function (1) and equations (4) and (5) we can derive the growth rate:

(7)                       r  = ab + f

From production function (2) we can derive the relation for the so-called natural growth rate:

(8)                       rL = m + l

If resources of unused labor force exist, then r > rL is possible, but if these resources do not exist (which is the case of Czechoslovakia) the equilibrium condition for economic growth is

(9)                    r =  rL  

It follows from (7), (8) and (9) that

                 ab + f  =  m + l  

and from this                   

 (10)          a  = (m + l - f)/b  


If the dynamic balance of the economy is to be preserved, it is necessary that the rate of accumulation in time develops according to relation (10), which depends on the rate of growth of the labor force, the rate of growth of labor productivity and on the rate of change of capital efficiency. As long as we do not know the direction of change of these parameters, we cannot arrive at any conclusion about changes in the rate of accumulation over time. It is obvious from the model, that if the right side of equation (10) diminishes over time it will be possible to preserve balanced growth in the economy only at the price of a fall in the rate of accumulation. In this case real wages will grow faster than national income, but this does not necessarily lead to inflation or rationing in the economy, as Soucek maintains. In this case an  increase in the accumulation rate, and not a decrease would cause imbalances in the economy.

But Soska is not right either, if he draws conclusions about the development of the accumulation rate only from changes in capital efficiency (or its reciprocal value capital intensiveness). Even if we were to admit the  general validity of capital intensive technical progress, we cannot draw conclusions about the dynamism of a, as long as we do not  know how m and l change.   



From model presented above we find that:

a) from (7) it is obvious that with capital saving technical progress growth is possible even with no accumulation at all. On the other hand the capital intensive technical progress “absorbs” accumulation and consequently reduces the rate of growth.

b) from (10) we see that when the natural rate of growth m + l is constant capital-neutral technical progress requires constant rate of accumulation a.

c) from (10) we also see that with capital-saving technical progress and f > 0 the rate of accumulation can  permanently fall  without causing  a fall in the growth rate of national income.

d) with capital intensive technical progress f < 0 it is possible to secure a non decreasing natural growth rate m + l only if the rate of accumulation grows by   f  . This process, as can be easily shown, cannot go forever.

The rate of accumulation cannot grow infinitely  (since a has to be less than one) so that  capital intensive technical progress is inconsistent with a non-decreasing growth rate. 8 Thus either there will be permanent investment intensive technical progress but then, the growth rate will start to decline after some time (possibly with further negative consequences causing the imbalance of the economy), or it is possible to maintain a non-decreasing growth rate under socialism, but then investment intensive technical progress can last only for a limited period of time. 9







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