[OPE-L:4096] RE: Another Sheep?

andrew kliman (Andrew_Kliman@msn.com)
Wed, 29 Jan 1997 16:03:10 -0800 (PST)

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A reply to John's ope-l 4077.

John: "I still feel we are caught in a discussion limited to cheaper
machines. Witness your demonstration of that p1=p0 in which you show that the
price of a new machine, p0, at t0 is equal to the of new machine at t1. The
comparison is meaningful as we assume that the two machine are the same save
for their ages."

True, but if Po = P1, then we're not discussing *cheaper* machines.

John: "It is not altogether clear that there are not instances where w0=0.
Consider two identical pentium computers of today. Does it really matter
which is older? Is there really wear and tear? Would not one using it in
profitable endeavors not expect to discard long
before it wears out?"

Clearly there *are* instances in which Wo = 0. Microprocessors may be an
example; for practical purposes, software surely is. It doesn't matter in
such cases which is older. There is not really wear and tear. It will be
discarded before it wears out if something better comes along before the end
of time. So I fully agree with you. A generally valid conception of value
transfer cannot be based on this special case, however.

John: "I'm still not sure how 'moral depreciation' fits into calculations you
would make concerning the rate of profit. Are you subtracting the losses due
to moral depreciation from profits prior figuring s/(c+v)."

Again, I think there are a number of things one may validly mean by "rate of
profit," and a corresponding number of valid calculations. One is to count as
c the *original* value invested, and count only s from production in the
numerator. Another is to measure c as the current, depreciated value of the
capital stock, but to subtract moral depreciation from s in the numerator.
(The simultaneist "profit rate" mixes and matches these invalidly, by using
the new value of the capital but ignoring the fact that the firm has accrued a
capital loss or gain.)

Then John presents an example which I find enormously interesting, which he
wishes me to "place ... within the value context." I've found this to be very
challenging, partly because he "left some play in this thing so that you can
assume whatever relative to the creation of value," and partly because it
makes me think through a number of tricky concepts in a way I hadn't done.
I'm going to try to meet the challenge, but what I'd urge others interested in
these matters to do is to try to work through the problem themselves, on their
own, independent of what comes below, and then we can compare answers. I
think it may help clarify our thinking in this area. It has helped me.

First, a minor technical problem. John's 2nd IRR:

2005.529 = 900/(1+.1) + 800/(1+.1)^2 + 700/(1 + .1)^4 + 600/(1+.1)^4

isn't right. The LHS and RHS aren't equal, nor are they equal when the 3rd
RHS term is corrected to be 700/(1 + .1)^3. I think John's intention is to
use the RHS to determine the LHS. The LHS, the cost of the new machine that
appears at the end of the 1st (original) period, then equals 2415.07 (rounding
to the nearest cent, as I'll do throughout). I'm not sure it will matter
qualitatively, but the 10% IRR may be important, so I'll assume 2415.07 is
indeed the cost, not 2005.529 (or 2005.259).

Second, I need to make clear that, because the problem is actually a very
complex one, I'm going to brush past a lot of issues, a couple of which I
recognize, most of which I probably haven't. Hence, there will be some
unstated assumptions in the background and what follows can be legitimately
picked at in a number of ways.

OK. John writes: "Ignoring all costs save those of fixed capital ...." I'll
take this to mean all other costs = 0. Sorry, Jerry, but you'll have to take
it up with John. It's his assumption.

John: "... let's assume a capitalist buys a machine for 2732.053, expects to
use it for 4 periods and also expects that the prices for the total output
produced in periods 1,2,3,and 4 are 1000,900,800, and 700 respectively. At the
end of the 4th period, it has no scrap value."

Fine. I'll also assume that these expectations would be correct were the new
machine not to have appeared (and may or may not be fulfilled given that it
appears; more on this below). I'm uncomfortable with the implication of this,
that the actual output price is determined exogenously, but I'm pretty sure
examples could be constructed in which this is the case, so I'll go with it.
I'm also going to assume that the reduction in the price of the product does
not cause a change in the price of the original or new machine in subsequent
periods. I have a similar problem with this -- it is another partial
disequilibrium assumption. But again, I think examples could be produced in
which this is true.

John has allowed me to stick in some additional assumptions. One of these
will be that prices = values. More precisely, the price of the product, of
the original machine, and of the new machine will be assumed to equal the
monetary expression of the weighted average (i.e., socially necessary)
labor-time needed to reproduce it.

Thus, given the correct expectations and the price = value assumption, here's
what we'd have if the new machine had NOT come along.

t used C L C+L
--- ---------- --------- --------
1 683.01 316.99 1000
2 683.01 216.99 900
3 683.01 116.99 800
4 683.01 16.99 700

Used C = 683.01 = 2732.05/4, which is the value transferred according to my
interpretation. The output values, C+L, are given. The L figures are not
assumed; they are derived by subtraction. If C+L is true, these must have
been the Ls.

With sales at value, the value transferred (used C) compensates for the full
loss of use-value, so that, at the end of period 4, the firm has no machine,
but 2732.05 in money capital (assuming for simplicity only that the value
transferred and recouped is not invested). The IRR is 10%.

John: "At the end of the first period, a new machine becomes available that
sells for [2415.07] that can produce the same output as the other machine. The
output prices expected in its 4 periods of life are 900,800,700,600."

I take the last sentence to mean that its life is (not just expected to be) 4
periods. Now, because prices = values, and values are social averages for a
kind of use-value, we have to ask whether the new machine is the same kind of
use-value as the original machine, which makes it a *cheaper* machine. I
think so. It lasts just as long, and it produces the same amount of output
per period (I think John implicitly assumes this; if not, I will). So it is
*functionally* indistinguishable from the original machine. I cannot but
conclude that it is the same kind of use-value. But may it not be a *better*
machine? Yes, if we mean by "better" that it lowers unit costs, it is a
better machine, since the machine costs are the only costs and output is
identical. So it is both cheaper and better.

But since it is cheaper, i.e., the same use-value as the original, its
coming-into-existence affects the value of the original machine, because value
is determined by (weighted) average labor-time. To proceed, we thus need to
know what the social value of this kind of machine will be.

One extreme case, CASE A, is that 1 new machine has been produced while
zillions of the old machine continue to be produced or, equivalently, that 1
machine is produced at a value of 2415.07 while zillions continue to be
produced (are RE-produced) at a value of 2732.05. In this case, the social
value of the machine remains 2732.05. Note that the social value of the new
machine is also 2732.05.

Another extreme case, CASE B, is that only the new machines are produced; no
old machines are produced during period 1 or thereafter. Equivalently, in
period 1 and thereafter, the machines are all produced at a value of 2415.07,
so that the value of the original machine, determined by the labor-time needed
to RE-produce it, falls immediately to 2415.07 at the end of period 1.

Among the many, many other intermediate cases is CASE C, in which half of the
machines produced from period 1 onward are "old," and half are "new," or,
equivalently, that half are produced at one value and half at another. The
social value of this machine from the end of period 1 onward is (.5)2415.07 +
(.5)2732.05 = 2573.56.

Note that the above cases are not distinguished by the number of old machines
relative to new machines actually *employed* in production, or on the relative
amounts *in existence*, but only on the relative amounts *produced* at the end
of each period. The latter alone is what determines the value of the
commodity (machine), i.e. the monetary expression of the weighted average
labor-time needed to re-produce it. (Here I think my interpretation may
differ from Alan's.)

I will assume that, in all these cases, the series of living labor
requirements is the same whether the old or the new machine is used, and it is
the same as above. I could assume something different, but why not this?

Let us then examine CASE A. Whether the old-style, or the 1 new machine, is
used in periods 2-4, the results are the same, and they are the same as those
above. No moral depreciation: the full value of the old machine is
recouped. The IRR is still 10%.

Now CASE B. Again, assuming sale and purchase at value, we will have

t used C L C+L
--- ---------- --------- --------
1 683.01 316.99 1000
2 603.77 216.99 820.75
3 603.77 116.99 720.75
4 603.77 16.99 620.75

Firms that employed the original machine in period 1 will recoup the sum of
the used C, equal to 2494.31, so the sum of the moral depreciation is 2732.05
- 2494.31 = 237.74. The IRR will be 6.67%. The period 2-4 figures are the
same whether a particular firm uses the original or new machines, or some

Note that the price expectations were not correct and could not be correct,
given that output price = output value.

In CASE C, we will have

t used C L C+L
--- ---------- --------- --------
1 683.01 316.99 1000
2 643.39 216.99 860.38
3 643.39 116.99 760.38
4 643.39 16.99 660.38

Firms that employed the original machine in period 1 will recoup the sum of
the used C, equal to 2494.31, so the sum of the moral depreciation is 2732.05
- 2613.18 = 118.87. The IRR will be 8.36%. Again, the period 2-4 figures are
the same whether a particular firm uses the original or the new machine, or
some combination.

Here again, the price expectations were not correct and could not be correct,
given that output price = output value.

Note that there is no advantage or disadvantage to using the new machine. It
is obviously unprofitable to throw away the old machine if it still functions.

John wrote that "I have constructed the above in such a way that there appears
to be no losses due to moral depreciation." I don't know from this whether he
thinks there is or isn't moral depreciation, but I think there is, except in
CASE A. The fact of moral depreciation lowers the IRR, and the more the moral
depreciation, the more the IRR is lowered.

Obviously, these are only 3 of many, many cases. In particular, I should
note, even if the value of the machine falls to the value of the new machine
immediately, there is no reason to expect that the price of the machine will
fall as much immediately. Since the price of the machine affects value
transfer, the CASE B results do depend crucially on the price = value
assumption, and not just the fact that the new machine-producing technique
reigns. I could have put in a different assumption, of course.

I'm sure there are other implications of the above that can be drawn, but I
can't think of them at the moment. Again, I found John's example very
thought-provoking, though I expect that this response may have undergone moral
depreciation in the last several hours, i.e., become less valuable, given the
rapid diffusion of new innovations on this topic (SOS and Mr. Wolf).

Andrew Kliman