Dear Ian,
Thanks for your post (OPE-L 4954).
You write:
"As a bystander, I don't think I understand your request of Fred.
You state that prices and the rate of prfit cannot vary unless
physical quantities vary, but this is so only if the wage rate is
specified as a physical quantity."
Well, I of course think prices and the rate of profit *can* vary
independently of variations in physical quantities. It is only
when input prices are constrained to equal output prices, a
constraint I reject, but which Fred embraces, that prices and the
rate of profit are functionally determined solely by physical
quantities.
You say "this is so only if the wage rate is specified as a
physical quantity." What you seem to mean is that, if the money
wage rate varies, but technology doesn't, the simultaneist profit
rate will vary nonetheless. This is true. However, a change in
the money wage rate entails a change in another set of physical
quantities, namely the components of workers' consumption.
Formally, if we denote the money wage rate as w, the vector of
prices as p, and the bundle of workers' consumption components as
the vector b, workers' budget constraints are w = pb, so a change
in w entails a change in b.
It thus remains the case that simultaneist prices and the rate of
profit cannot vary unless physical quantities vary.
Your second point is one I found particularly interesting. I had
written:
"I still think it is accurate to characterize your [Fred's]
response
to Alan Freeman's demonstration as a non-response. He
showed that, when technology is changing, all variants of the
*physicalist* prices of production and profit rate FAIL to
constitute the center around which prices and the average
profit rate fluctuate, despite the common claims to the
contrary.
You responded:
"Why should Fred be worried by Freeman's demonstration?
I have always supposed that prices of production and profit rate
in the Sraffa or similar models only give values around which
market prices and the average rate of profit TEND to fluctuate.
This tendency would be realised only if technology is constant
for long enough .... Empiracal observation does not produce
uniform prices and profit rates of any description as centres
around which market prices and profit rates fluctuate. ..."
If I understand what you are saying, I agree fully. What I take
you to mean is this. Prices and the average profit rate WOULD
fluctuate around the static equilibrium prices and the static
equilibrium profit rate IF technology were not changing (rapidly
enough). IN FACT, however, prices and the average profit rate DO
NOT fluctuate around the static equilibrium prices and the static
equilibrium profit rate, because technology DOES change (rapidly
enough). In other words, the static equilibrium profit rate is
not the average profit rate that prevails at any moment, nor even
the time-average of the average profit rate.
I'm glad you understand this. I've found that very few people do.
They just do not understand the difference between the average
value of a variable and its static equilibrium value.
But once one DOES understand this -- and this is a question for
you -- of what use and what significance are the static
equilibrium results? They don't describe or predict what actually
occurs, nor do they even describe or predict what actually occurs
once we abstract from accidental factors and fluctuations that
compensate for one another over time. So what good are they?
Take the following simple one-sector case, for example. Define
the relative rate of variation in the unit price as
H[t] = (P[t+1] - P[t])/P[t],
where P[t] and P[t+1] are the unit input and output prices of
period t.
Assume the time-path of H is
H[t+1] = -2H[t] - 50(H[t])^2 .
Assume further that 10 units of corn input are required to produce
every 11 units of corn output. Then the rate of profit is
(11P[t+1] - 10P[t])/10P[t] = 1.1(1+H[t]) - 1.
Now the static equilibrium value of H is 0 (there is also another
fixed point, H = -0.06), so the static equilibrium profit rate
equals
1.1(1+ 0) - 1 = 0.1 = 10%.
However, for H[0] not too far from 0, H behaves chaotically and
averages -0.02.
The rate of profit thus also behaves chaotically and its *average*
over time is 7.8%. This is 22% below its static equilibrium
value. Simulations indicate, moreover, that two-thirds of the
observations are below the static equilibrium value of 10% and
only one-third are above, instead of half and half.
So who cares what the level of the static equilibrium profit rate
is? What use does it have? What does it tell us about the actual
economy?
I still haven't answered your question about why Fred should be
worried about Alan Freeman's demonstration. The answer is this.
Although, as we agree, Fred's (physicalist) profit rate is not the
actual "center of gravitation," when MARX referred to the general
or average rate of profit, he WAS referring to the actual "center
of gravitation." Hence Fred's average rate of profit and his
associated prices of production are NOT the same as Marx's. This
is contrary to what Fred has claimed, so he should be worried.
Moreover, Alan's paper also shows (by means of Monte Carlo
simulations) that temporally determined prices of production and
average profit rate are indeed the "centers of gravitation" of
actual prices and profit rates, even when technology is changing.
This is also contrary to what Fred has claimed, so, again, he
should be worried.
Ciao,
Andrew ("Drewk") Kliman
Dept. of Social Sciences
Pace University
Pleasantville, NY 10570 USA
phone: (914) 773-3968
fax: (914) 773-3951
Home: 60 W. 76th St. #4E
New York, NY 10023 USA
"The practice of philosophy is itself theoretical. It is the
critique that measures the individual existence by the essence,
the particular reality by the Idea."
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