Date: Fri, 01 Dec 1995 06:47:38 +1000 From: Steve.Keen-AT-unsw.EDU.AU Subject: Re: Marx's limit cycles (fwd) Chris asks for a definition of "limit" in "limit cycle". The term itself is a mathematical one, and refers to a class of solutions which, rather than ending up in a point, or a system which heads off infinitely in one direction or another, ends up in an ever-repeating cycle. The cycle is therefore the "limit of the system as time goes to infinity", hence "limit cycle". There are many types of limit cycles, ranging from rigid ones (like the one in Goodwin's 1967 paper) where the system traces out exactly the same path time and time again, to ones where if the system starts "inside" the cycle then it gradually converges to it, ditto outside, and finally ones like my 1995 extension to Goodwin, where the system converges to the cycle from both inside and outside it (it spirals around the eventual cycle, moving ever closer to it). They are one of the foundations of coupled systems, where the rate of change of x depends upon the value of y, and the rate of change of y depends upon value of x. There is thus feedback from one to the other, and to me they are the mathematical expression of "dialectics", where the x/y system forms what Marx would have called a unity. The cycle described by Marx in Ch. 25 is clearly a limit cycle, with the wages share of output being one axis (the x) and the rate of employment being the other (the y). The way Marx describes it implies that he doesn't see it as a rigid cycle, but as one which can take a range of values, though ultimately the cycle will again occur: workers share will never rise to 100%, nor will it ever fall to zero, while wages themselves may rise or fall. As to whether what the "capitalist system comes up against repeatedly in its cycles, is a somewhat elastic sort of ceiling of the total exchange value of the society", the last time Westernc capitalism really approached that barrier was in 1973. Since then, unemployment has cycled about an increasing trend, while wages share has cycled about a decreasing one, and the turning points have been well before wages share ever began to challenge capitalist profits, and in my opinion driven by issues of the realisation of surplus (rather than its generation) and finance. Under the 1945-1973 system, then Goodwin's cycle was an apt characterisation--hence the limiting feature you're looking for, Chris, was the share of surplus. Since then, I'd argue that it is crises in effective demand, and finance, that have determined the cycle. Cheers, Steve --- from list marxism-AT-lists.village.virginia.edu --- ------------------
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