Mathematical analysis of Marx's claims

Karl R. Peters u1006057 at warwick.net
Mon Dec 17 20:01:54 MST 2001


I was looking at an interesting article at:
http://www.wsws.org/articles/2001/dec2001/corr-d17.shtml
which attempts to explain, in Marxist terms, why capitalism
tends to suffer periodic economic collapses.  I decided to
try some formal mathematical manipulation of the terms involved,
and my results don't seem to bear out Marx's claims.  Am I
doing something wrong here, or is Marx wrong?

Let C = capital, P = Production, and W = wages.

Then we have:

Profit = P - W

and,

rate of profit = (P - W)/C

Now, the part which seems to suggest that Marx is wrong is
the "W/C" term.  (P -W)/C can be expanded to P/C - W/C.
W/C seems to be the ratio of labor to capital, which tends
to decrease (that is, capital tends to increase faster than
labor population; fewer labors employ more capital).  But
looking at this equation, a decrease in W/C would lead to
an increase, not a decrease, in the rate of profit.  Only if
P/C, the amount produced by a unit of capital, decreased
faster than W/C would the rate of profit fall.

Have I done something stupid, or is this analysis correct?
If my analysis is correct, it seems the limiting factor is
the P/C term, the amount of goods which can be produced
by a unit of capital.  If this begins to decline, then the rate
of profit will fall.

    <karl>



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