Growth Strategies
 RESOURCES OR INCENTIVES FOR ECONOMIC GROWTH? by Oldrich Kyn Planovane hospodarstvi, Vol. XX - 1967 No. 4. pp. 70 - 80

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 show that the growth of the rate of accumulation not only cannot be considered a general rule but that it is not even permanently possible

Let
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
m   =  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 > r 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

FOOTNOTES

1       Planovane hospodarstvi, 2/1967  [1] back

2     Planovane hospodarstvi, 8 – 9/1968  [2] back

3   “A general expression of their creation and use is the fund of accumulation”  Planovane hospodarstvi, 8 – 9/1968, p. 143.  back

4 For example on pages 148 and 152 op. cit. he says that inflation “accelerates the expanded reproduction of growth resources” by which he means, as follows from his preceding presentation, that inflation causes redistribution of national income in favor of accumulation.”    back

5  These are mainly the following  articles: O. Sik,  A Contribution to an Analysis of Our Economic Development, Poiticka ekonomie, [3], 1/1966; J. Goldmann and J. Flek, An Economic Growth Model in Socialism and a Criterion of Planned Management Effectiveness, [4], Planovane hospodarstvi  3/1996; V. Nachtigal, Extensiveness and Effectiveness of Czechoslovak Economic Development, [5], Politicka ekonomie, 4/1966; M. Hajek, M. Toms, The Production Function and the Economic Growth of Czechoslovakia 1950-1964, [6], Politicka ekonomie 1/1967      back

6 A similar criticism of this law we find in works of  Feldman, Dobb,  Kalecki and others. See e.g., O. Kyn, Chapters from the History of Economic Thoughts, part III, Theories of Economic Growth, [8], SPN, Prague, 1966.     back

7 Collection Theories of Economic Growth and Present-Day Capitalism, pp. 23-24, NCSAV Prague [9]     back

8 Michal Kalecki writes in his  Outline of the Theory of Growth of a Socialist Economy [6]. (NPL, Prague.1966) on page 96. about the process of growth acceleration by raising investment intensiveness: 'In no cease can it be opportune to prolong  this process ad infinitum. In such a case permanent growth of accumulation would gradually lower the share of consumption to zero, which is absurd... Sooner or later it will be necessary to stop the growth of investment intensiveness."     back

With permanent capital intensive technical progress at non-decreasing rate of growth, the rate of accumulation need not grow boundlessly (there could be lim a < 1 for t approaching infinity ) only if the growth rate of investment intensiveness would approach sufficiently quickly zero. But then there would exist a time period after which the rate of change of capital intensiveness  would be less then  any arbitrarily small number. This means that in such a case it is possible to find a period after which the growth of capital intensiveness will be so minute that technical progress would be  virtually neutral.     back

10  The initial efficiency of capital  b = 0.5.     back

11 Many economists proceed from this opinion, especially those who use the Cobb—Douglas production function. See e. g. R. M. Solow.A Contribution to the Theory of Economic Growth. Quarterly Journal of Economics, February 1958, or J.E. Meade, ‘A Neoclassical Theory of Economic Growth.’ London, Allen and Unwin, 1961 and others. The Idea of a choice of technique we find even among the models which are not based explicitly on the Cobb—Douglas production function; e.g., A. K. Sen. Choice of  techniques; Maurice Dobb, An Essay on Economic Growth and Planning; Nicholas Kaldor, Essays on Economic Stability and Growth; Joan Robinson  Essays in the Theory of Economic Growth; etc.    back

12 The same explanation of the dynamics of the capital coefficient is given by H. Flakierski, see the above quoted collection, p. 143. The falling trend is still more expressive with the marginal capital coefficient in the U.S.A.which according to the estimate of W. Fellner, reproduced by H. Flakierski was 5.08 in 1919, 3.30 in 1929, and 1.2 – 1.5 in 1950.    back

13 Productivity Trends in the US, Princeton, 1961.    back

14  This indicator is identical with the parameter f in our mathematical model     back

15     V Kudrov C. Shpilko: Tempi i proporcii obsschestvenogo proizvodstva v SshA, Moscow 1966.‘    back

16 V Kudrov C. Shpilko op. cit. p 117    back

17 These considerations are taken from the Z. Chrupek’s article.    back

18 Z. Chrupek in the quoted collection: Theories of Growth p. 275.    back

19 In a somewhat different form this idea maintained itself for a long time among Marxist economists as the dogma of the growth of the organic composition of capital.     back

20                This process can clearly be seen in the table, mentioned by Kendrick, op. cit. p. 121.   back

Relative factor prices in the U.S.A. (1929- 100)
Year            Labor            Capital
1899             90.7                 130
1919             97.6                 106.6
1921           100                    100
1937           113.3                  72.5
1948           105.8                  85.2
1957           124.3                  53.9     back

21 See E. D. Domar, "Depreciation, Renewal and Growth." seventh essay from  “Essays in the Teory of Economic Growth” Oxford University Press, 1957, and also Oskar Lange. The teory of Reproduction and Accumulation. NPL 1965.    back

22 These relations are very clearly seen in the table on page 110 of the above-quoted work of Oskar Lange      back

23 See e. g. the above quoted article by M. Toms and M. Hajek: “Determinants of Economic Growth and the Integral Productivity”    back

24 See e.g.. the lecture of A. L.Vainshtain at the Econometric congress in Warsaw     back

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