[OPE-L:5029] RE: numerical example!!!

From: Drewk (Andrew_Kliman@msn.com)
Date: Thu Feb 22 2001 - 03:33:20 EST

Hi, Fred.

In reply to your OPE-L 5020:

"You are right that in my example I assumed
the money wage as given rather than the real
wage, as in Steedman."

That isn't the issue.  It doesn't matter what was given.  You
could have assumed a given money wage of 0.2685; you would have
gotten the same physical quantities as Steedman -- and also the
same prices and profit rate.

"However, I think what my example shows,
 at least, is that, if the money wage is taken
as given, then a given set of physical inputs
and outputs and the assumption of "stationery
prices" does not uniquely determine the rate
of profit."

This is a red herring.  No one has ever claimed that "a given set
of physical inputs and outputs" is enough.  The physicalists are
always careful to specify that the technical AND REAL WAGE
coefficients, together, uniquely determine the relative prices and
profit rate.  If your full set of physical quantities --technical
AND real wage coefficients -- are the same as the physicalists',
so too will be your relative prices and profit rate.  That's
because of your simultaneous determination of prices.

"My example shows that, with a given
money wage, at least two rates of profit
are compatible with the given physical
structure and the assumption of
"stationery prices" (and we could
compute more)."

No.  The physical structure includes real wage coefficients.

"there are an infinite number of rates
of profit that are compatible with the
given quantities of inputs and outputs."

Of course, but again, that's a red herring.  There's only one
simultaneist uniform profit rate compatible with the given
quantities of inputs, outputs, AND real wages.

"unfortunately, the system of
equations is more difficult to
solve under the assumption of a
given real wage.  ...  I will get some
software soon, and then we shall see
whether the result still holds under
the assumption of a given real wage.

"In the meantime, perhaps another
listmember who has the software can
solve this system of equations for us
and let us know the results.

"Assuming to begin with that the
rate of profit = 0.4, the equations

(1.4) [28 p1+ 56 (5/80 p3)]   =   56 p1

(1.4) [16 p1+ 16 (5/80 p3)]   =   48 p2

(1.4) [12 p1+  8 (5/80 p3)]    =   8 p3

Please solve for the three prices."

The reason you're having trouble solving this, Fred, is that it
can't be solved (for positive prices).  The top equation gives us
p1 = (49/168)p3.  The bottom gives us p1 = (73/168)p3.
Obviously, the only solution is that p1 = p3 = 0, which would also
make p2 = 0.  Apart from that solution, there isn't one.  For
positive prices, the top and bottom equations are inconsistent.

The reason for the contradiction?  You're using the wrong profit
rate.  There is only one simultaneist profit rate that corresponds
to the full set of physical quantities.  Steedman's.  52.08%.

"And then assume the rate of profit
= 0.25, replace the 1.4 in the above
equations by 1.25, and solve for the
three prices again.  Thanks in
advance for any help."

The top equation gives us p1 = (25/120)p3.  The bottom gives us p1
= (59/120)p3.  Again, the system cannot be solved, except with
zero prices all around.  But that would make v = 0.  Jerry would
not be pleased.

"Logically I don't understand why
this system of equations would not
be solvable for different rates of
profit.  This is a system of three
equations in three unknowns, which
should in principle be solvable."

Not necessarily.  It isn't solvable if two or more equations are
inconsistent, as your 1st and 3rd ones are.   A simpler case of
the same problem is

x + y = 0

x + y = 1.

Again, no solution.  To eliminate the inconsistency, you need to

(a)  Use 0.5208, Steedman's rate, as your rate of profit


(b)  Rewrite the equations so that the input prices and the output
prices differ.

Those are the only options, given the same physical quantities as

"Andrew, I don't understand why you
think that the money wage rate is not
equal across sectors.  The money wage
rate is assumed = 1 in all sectors.  From
which it follows that the real wage rate
will also be equal across sectors, since
the real wage rate = 1 / (price of corn).
Thanks for the clarification."

I plugged in your prices and profit rate, and solved for w in each
equation.  I may have made an error.  It doesn't matter, because
the inequality of the wage doesn't matter.  What matters is that
you had a different real wage from Steedman, which caused your
prices and profit rate to differ.



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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