1a
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 ).