Brief von Stanisław Gomułka an Josef Steindl Stanisław Gomułka 1538565550087
» - 2 - UK +L* The major oscillation, with a) in the range (O, ir) for O &lt; h &lt; 1 or/(0, n/2) for h &gt; 1, appears if and only if (o) &gt; a + b, that is iff 1 (6) (1 + r ) &lt; bh &gt; 1+h &gt; a + b n Condition (6) is a constraint on the parameters a, b and h. This condition is satisfied if and only if (7) a &lt; 1 (8) b JL &lt; b &lt; b 2 where b^, b^ are two non-negative roots of the equation &lt;J&gt; (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 (9) sin a) /h o sin w &gt; 1/b o where o) o is given by the equation &lt;&gt; (u3 q ) = a + b. Thus it is sufficient that b &gt; 1/h for the oscillation to explode. Case h = 1 (as in your letter). Condition (6) implies 2 /b &gt; a + b. Hence b^ ^ = 2 - a + 2 A-a. Since b &lt; 1 for a &lt; 1, the major oscillation exists ' and is damped iff b &lt; b &lt;1. The oscillation exists and explodes iff 1 &lt; b &lt; 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 &gt; a &gt; a &gt; O there is a lower bound h depending on a such that the major oscillation explodes for all b &gt; O and 0 &gt; h &gt; h. But in view of the proven possibility of all the oscillations being damped, I must and have withdrawn my paper on Kalecki from the OEP.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 &gt; 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