Publications 
1.1 The main aim of this study is to estimate production functions for Soviet industry on the basis of the perfor
(1) Y(t) = F(K,L,t) 
(2) I(t) = aY(t) 
(3) dK/dt = I(t) 
(4) dL/dt = lL(t) 
Here Y, K, L, I represent output. capital stock, labor and investment respectively
a is the share of investment in total output and
l is the rate of growth of labor force.
(1a)  Y  = 
or its special form (for w = 0), the CobbDouglas production function
(1b)  Y  = 
Some alternative assumptions about the form of A (t) will be used.
(5a)  g_{e}  = 
(5b)  g_{e}  = 
The rate of technological change is very important for determining the longrun growth potential, however, the other parameters of the production function namely the elasticities b and g are important as well. This is very rarely acknowledged. Many economists tend to judge the growth potential of the economy only according to the ‘dynamic efficiency” which is frequently identified with the rate of technological change. The importance of the parameter b and g for the evaluation of the long run growth potential can be easily illustrated on the following example:
A: b_{A} = .2 g_{A} = .9 r_{A} = .045
B: b_{B} = .7 g_{B} = .1 r_{B} = .025
Let us further assume that the rate of growth of labor force is for both countries the same
l_{A} = l_{B} = .01.
Using the formula (5a) we find the growth potential of the economy B is greater than the growth potential of the economy A
g_{eB} = .0866 > .0675 = g_{eB }
although both the rate of technological change and the degree of economies of scale were greater in the economy A.
1.4. The case in which the equilibrium rate of growth is not constant, is even more relevant for Soviettype economies. Changes in g_{e} may result from two different causes:
(a) The rate of technological progress may vary
(6)  r  = 
If we still assume that the elasticity of substitution is equal to 1 than the equilibrium rate of growth will be
(7a)  g_{e}(t)  = 
g_{e}(t) would be declining if r(t)is declining and it would be increasing in the opposite case. In empirical studies it is usual to approximate r(t) by the linear function:
(6a)  r(t)  = 
This approximation will be used also in the present paper. We should stress, however, that if the “true” function r(t) is nonlinear then the linear approximation (6a) may not be suitable for the long run forecast of economic growth, even if it explains the rates of growth in the observed period quite well. Obviously the discrepancy between the “true” function r(t) and its linear approximation (6a) can become enormous at very high t’ s. Suppose, for example, that the. “true” function r(t) is a monotonous decreasing function which asymptotically converges to a value r* > 0. If the function r(t) (6a) is estimated from, let us say, 20 observations, then the estimated value of the parameter r_{0 }will be positive end estimated value of r_{1 }will be negative. The linear approximation of r(t) extrapolated beyond the year t =  r_{ 0 } / r_{ 1 } would be negative and therefore inconsistent with the above assumption.
(b) The equilibrium rate of growth g_{e} will not be constant if the elasticity of
(8)  h_{K}  = 
In the case of low elasticity of substitution (i.e. if w > 0) h_{K} is declining along the equilibrium path. If on the contrary the elasticity of substitution is high (w< 0) the capital elasticity of output will increase. The labor elasticity of output h_{L} will change in the opposite direction.



