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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