Full text: Distribution and Growth

Let us take for example a difference equation of the 
second order which will represent the cycle provided 
the parameters have the right sign and are within the 
right range. On the right hand side we put a growth 
term, an exponential term; in order to prevent the damping 
of the cycle we ought to have also a term representing 
random shocks; they will simply produce new initial 
conditions again and again and thereby change the phase and 
amplitude of the cycle. For the purposes of the following 
discussion we can leave out this term. The equation is thus 
A y(t) + B y(t-1 ) + C y(t-2) = c ( 1 + g )* (1) 
There will be a particular solution representing the 
trend. This solution in full is 
y(t) = 
c( 1+g 
A(l+gf+B(1+g)+C ( 1 + g } 
The parameters of the equation A,Band C do not affect 
the direction of the trend which is given by g. 
Thus the trend is entirely imposed from outside, 
it is purely historical and independent of the 
internal structure of the economy ( such as,for example, 
the distribution of income or the response of investment 
decisions to a change in profits or in utilisation ).

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