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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
The general solution of this equation has the form 
4-7) 
K = He”) + K 
where H is an arbitrary constant to be determined by the initial 
conditions and where the function A(#) and the constant K are 
given by 
(4-8) 
h(z) — 
»—æ)(1—y)(e -- = cos té + 
+ (1—a)(1—Y)a | e-s + 5 É, 
(4-9) 
IB 
I—à 
2 
It is seen that %(¢) is composed of a pure cyclical component 
and a trend element, while h(t) is a linear function of the pure 
cycle alone. From the constraints that we have imposed upon 
ko and kp, making them uniformly non-negative, it is obvious 
that H must be positive and that h(t) can never be negative. 
Inspecting our basic model equations we find that x, xo, and 
ko are linear functions of K alone, while xp, kp, y, and m are 
linear functions of K and K. From these considerations we 
can draw the following conclusions. 
Conclusion 1 
Even if fiscal policy is sufficiently « radical » to maintain 
full use of capacity (i.e. x=aK) at all times, the rate of growth 
will depend essentially upon the extent, (1-8), to which the 
(81 Haavelmo - pag. 10