Full text: Brief von Stanisław Gomułka an Josef Steindl

- 2 - 
UK +L* 
The major oscillation, with a) in the range (O, ir) for O < h < 1 or/(0, n/2) 
for h > 1, appears if and only if (o) > a + b, that is iff 
(6) (1 + r ) < bh > 1+h > a + b 
Condition (6) is a constraint on the parameters a, b and h. This condition is 
satisfied if and only if 
(7) a < 1 
(8) b JL < b < b 2 
where b^, b^ are two non-negative roots of the equation <J> (D) = a + b. It may 
also be noted that (0) - (a + b) has a maximum/for b = 1/h. 
N wiR -fe b 
From the definition of n (m) it follows that the major oscillation, if 
exists, explodes when 
sin a) /h 
sin w 
> 1/b 
where o) o is given by the equation <> (u3 q ) = a + b. 
Thus it is sufficient that b > 1/h for the oscillation to explode. 
Case h = 1 (as in your letter). 
Condition (6) implies 2 /b > a + b. Hence b^ ^ = 2 - a + 2 A-a. Since 
b < 1 for a < 1, the major oscillation exists ' and is damped iff 
b < b <1. The oscillation exists and explodes iff 1 < b < b^. The same 
conditions hold for the oscillations of the higher order. There is no periodic 
oscillation for b outside the range (b , b^)• 
I was unable to get any general result of the kind that given 1 > a > a > O 
there is a lower bound h depending on a such that the major oscillation explodes 
for all b > O and 0 > h > h. 
But in view of the proven possibility of all the oscillations being damped, 
I must and have withdrawn my paper on Kalecki from the OEP. 
I do not know how to proceed now. It is clear that my criticism of Kalecki * 1 * * * s 
trend equation (see his Eq. 35', footnote 2, p. 146): b ^ 
X t+1 - 5 *t + " Vh t " x t T ' i ' i 
remains valid for some values of n* notably for frl > J-/h, but i£ is not valid 
generally. This relativeness of the results makes me think that perhaps we 
should try to estimate n and h from actual data? 
Anyway thank you again for your letter. You ^ v-vooP 
VAjsA^J /V t/V V^h/ , 
Yours sincerely, 
Stanislaw Gomulka

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