Grossmann's key contribution to political-economic theory was his book, The Law of Accumulation and Breakdown of the Capitalist System, a study in marxian crisis theory. It was published in Leipzig months before the Wall Street Crash of 1929.
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2 Career 3 Contribution to Theory |
Early life & Education
Grossmann was born into a relatively prosperous Jewish family in Cracow, then a part of Austrian Galicia. He went to Vienna to study, where his tutors included economist Eugen von Boehm-Bawerk and the "orthodox" marxian historian Carl Grunberg. With the destruction of the Austro-Hungarian empire at the end of World War 1, Grossmann became an economist in Poland, with communist sympathies acquired during the war.
Career
From 1922 - 1925, Grossmann was Professor of economics at Warsaw University. He emigrated in 1925 to escape persecution at the hands of Pilsudski's regime. He was invited to join the marxian Institute for Social Research in Frankfurt by his former tutor, Grunberg. From 1930 onwards, after Max Horkheimer took the helm at the Institute, Grossmann rapidly became disenchanted with what appeared to him to be a degeneration into non-marxist or even anti-marxist projects of the Frankfurt School.
Though apparently never a member of the German Communist Party, Grossmann had remained a supporter of the USSR longer than his colleagues in Frankfurt. Hitler's accession to power in 1933 forced him first to Paris, and then via Britain to New York, where he remained in relative isolation from 1937 - 1945. He spent the last five years of his life in East Germany.
Grossmann's work was finally made available in English translation in 1979 by Jairus Banaji, for an Indian Trotskyite organisation, the Platform Tendency. A recent edition is: ISBN 0745304591
Contribution to Theory
While at Frankfurt in the mid-1920s, Grossmann contended that a "general tendency to cling to the results" of Marx's theory, in ignorance of the subtleties of "the method underlying Capital", was causing a catastrophic vulgarisation of marxian thought - a trend which was undermining the revolutionary possibilities of the moment.
The Law of Accumulation was his attempt to demonstrate that marxian political economy had been underestimated by its critics - and by extension that revolutionary critiques of capitalism were still valid. Amongst other arguments, it sets forth the following demonstration (for a complete definition of the terms employed, the whole book is recommended):
... Apart from the arithmetical and logical proofs that we have been given already, mathematicians may prefer the following more general form of presentation which avoids the purely arbitrary values of a concrete numerical example.
Meaning of the symbols
c = constant capital. Initial value = co. Value after j years = cj
Further, let
and let
After j years, at the assumed rate of accumulation ac, the constant capital c reaches the level:
At the assumed rate of accumulation av, the variable capital v reaches the level:
The year after (j + 1) accumulation is continued as usual, according to the formula:
whence
For k to be greater than 0, it is necessary that:
k = 0 for a year n, if:
The timing of the absolute crisis is given by the point at which the consumption share of the entrepreneur vanishes completely, long after it has already started to decline. This means:
whence n =
This is a real number as long as s > av
But this is what we assume anyway throughout our investigation. Starting from time-point n, the mass of surplus value S is not sufficient to ensure the valorisation of c and v under the conditions postulated. The logical and mathematical basis of the law of breakdown
v = variable capital. Initial value = vo. Value after j years = vj
s = rate of surplus value (written as a percentage of v)
ac = rate of accumulation of constant capital c
av = rate of accumulation of variable capital v
k = consumption share of capitalists
S = mass of surplus value, being:
Ω = organic composition of capital, or c:v
j = number of yearsThe formula