[OPE-L:4056] RE: Simultaneism in Sheep's Clothing

andrew kliman (Andrew_Kliman@msn.com)
Sat, 25 Jan 1997 13:23:25 -0800 (PST)

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A reply to John's ope-l 4050.

John: "Have you no mercy?"

A little. I didn't actually call you a simultaneist. I just said "John's
position implies a type of simultaneism." Actually, I've been saying it all
along, but I had to doll it up with some math to get your undivided attention.

John: "My God, have I really slipped
back into the static world of simultaneous valuation?"


John: "You summarize some of what I have said about moral depreciation ...."

I'm glad I got it right. I wasn't sure.

John: "The economic life of fixed capital is generally determined socially,
not naturally."

This is NOT a difference between us. I agree with this statement 100%. The
difference is that, in my interpretation, the *transfer of value* is not
determined by the economic life of the fixed capital.

I note that John has not answered the questions I posed in ope-l 4050
concerning his position; he has merely reiterated it. The questions were:

(a) HOW are firms able to recoup what they charge as depreciation?
(b) Doesn't this depend on the price they get for their products?
(c) What then determines the price they get?
(d) Why are the costs they are able to recover the original costs, not the
replacement costs? Why not any arbitrary amount?
(e) If firms do not determine the rate and amount value actually transferred,
what then DOES determine them?

John: "in Andrew's OPE-4050, all we ever see is cheaper machines."

Huh? I proved that if (i) the amount of value transferred during a period
depends on the input price and the D coefficient (which is *any* number
greater than or equal to zero and less than 1), (ii) the firm recoups this
amount, and (iii) this amount fully compensates the firm for the loss of the
machines' value during the period, then the machine's value must be CONSTANT.
It never gets cheaper. Note that I proved this INDEPENDENTLY of any
assumption concerning technology and any assumption concerning better
machines. Whatever one assumes about technology and better machines, the
price of *this* type of machine cannot change.

If we distinguish between cheaper machines and better machines, then "cheaper
machines" means machines of the same type as the existing ones that cost less,
right? Given (i), (ii), and (iii), cheaper machines in this sense are

John: "The production process that uses the machine never changes. The whole
notion of capital using or capital saving technical change is
gone as there really is no change in technique."

Huh? number 2. First, as I've just noted, my proof holds for any assumption
concerning technology. Second, I then gave an example in which the technique
changes, in order to show that changes in living labor requirements wouldn't
affect the commodity's value, given that (i) through (iii) hold:

"Now imagine that techniques change throughout the life of the fixed capital;
specifically that less and less living labor is needed each period. Instead
of L being the second term in the above equations, we have L, L', L'', etc."

John: "Commodities produced by the machine and the machine itself are somehow

No. See above.

John: " ... It is to this world Andrew brings us in order to show the error
in my conception of depreciation. He assumes that the machine
will have a 'an economic life of n periods' as he begins to
reveal the fatal flaw. We might ask, "Why 'n'?", since the machine
is simply going to be produced more cheaply in period after period."

Again, there are no cheaper machines and, of course, n is arbitrary. How
could I *not* assume an economic life of n periods? Note that nothing I did
requires that the magnitude of n be specified ex ante. (I should mention a
minor point that I neglected, however. If n = 1, so that the machine is not
fixed capital but circulating capital, then my proof doesn't hold. The
equation needed to satisfy (i) through (iii) becomes p1*(1-D1) = p2*(1-D1).
Since D1 = 1 in this special case, we have 0 = 0, and the equation doesn't
determine prices.)

John: "Or we might ask, 'Why the life of the machine is not infinite since
its technical life is not to be considered?'"

I don't know. I'm not sure I understand the point. If it helps, assume that
a better machine appears at time n+1.

John quotes me: "John's position basically implies that, if the firm's
expectations are correct, the firm recoups in each new period an amount equal
to the loss of value of the machine during the prior period," and comments:

"I have no idea why capitalists do not assume that machines will get cheaper
(Especially here, since that's all they ever do.) and allow for it as they

Again, (i) through (iii) imply that the machine CANNOT get cheaper. Note that
*nothing* in (i) through (iii) places any constraint on capitalists'
expectations. They can be anything. However, if the firm is going to recoup
the loss of the machines' value, the price (value) of the machine can't
change. If the firm's expectations are correct, it then follows that it must
expect the price (value) to remain constant.

John: "[Andrew] shows that


... But why this result? To be sure, it astounded me at least as much as it
did Andrew."

It didn't astound me. I intuited it. Knowing the result is what led me to
verify it symbolically.

It is a wholly obvious result *once* one sees that the firms' expectations are
a red herring. If their expectations were correct (incorrect), then the
amount they charged for depreciation equals (doesn't equal) the actual amount
of value transferred. Hence, the actual amount of value transferred is
determined *independently* of their expectations. That's the FIRST crucial
thing to see.

What then determines the actual amount of value transferred? Well, we know
that if their expectations were correct, they charged as depreciation an
amount equal to the actual amount of value transferred. And we know that if
their expectations were correct, then they recoup the whole loss of value.
Thus, we know that the actual amount of value transferred would equal the
whole loss of the machines' value, if expectations were correct. But we also
know that expectations are irrelevant. Hence, the actual amount of value
transferred must ALWAYS equal the whole loss of the machines' value. That's
the SECOND crucial thing to see.

Then the whole thing is trivial: if you get back what you put in, price must
be constant.

John then goes into a detailed discussion that again presumes that the
machines are becoming cheaper, which is not the case and cannot be the case,
given (i) through (iii), so I won't comment on it.

It may help, however, to give a numerical example to illustrate exactly *how*
the value of the machines remains constant, even with changes in techniques.
*That* the value remains constant is, again, implied by the condition that the
original value of the machine is fully recouped, and it is therefore a
*premise* of the illustration below. I assume a 1 sector economy in which 5
machines and diminishing amounts of living labor are used to produce 1 new
machine of the same type each period, for 10 periods. After 10 periods, a
better machine comes along, or whatever, so that the economic life of the
machines is 10 periods.

The machine's unit value (price), P, will be measured in labor-time units.

The amounts of living labor, L used are, in periods 1 to 10: 38, 34, 30, 26,
22, 18, 14, 10, 6, and 2.

In each of the 10 periods, the value determination equation is

5*Pt*Dt + Lt = Pt+1,

where Dt is the as-yet-undetermined depreciation coefficient.

So we have 10 value equations in 21 unknowns, namely 10 D's and 11 Ps.

We can eliminate 10 unknown P's, however, since the price is always constant.
That leaves 10 equations in 11 unknowns. But the Ds must sum to 1, giving us
an 11th equation.

Substitute 38 for L1 in the first equation and solve for P in terms of D1: P
= 38/(1-5*D1). Plug this into the next 9 equations, and plug in the L's.
There remains in each equation one unknown, Dt, which can be solved for in
terms of D1. Add these 9 Dt's and D1 together, and set them equal to 1. So
there's one equation left, in one unknown, D1. Solve for D1. It equals .01.
Plug this into the expressions for the Dt's and solve. The D series is, then,
.01, .03, .05, .07, .09, .11, .13, .15, .17, and .19. Note that these do
indeed sum to unity. Plugging the solution for D1 into the P equation, we
find that P = 40. Plug all the numbers back into the value equations to see
that they check:

5*40*.01 + 38 = 40
5*40*.03 + 34 = 40
5*40*.05 + 30 = 40
5*40*.07 + 26 = 40
5*40*.09 + 22 = 40
5*40*.11 + 18 = 40
5*40*.13 + 14 = 40
5*40*.15 + 10 = 40
5*40*.17 + 6 = 40
5*40*.19 + 2 = 40

Despite the decline in living labor requirements, the machines' value really
is constant, not falling, because the value transferred increases each period
by the same amount that the living labor extracted declines.

The 5 machines are worth a total of: 200, 198, 192, 182, 168, 150, 128, 102,
72, 38, and 0, at the start of periods 1-11, respectively. They lose a value
of 2, 6, 10, 14, 18, 22, 26, 30, 34, and 38 during periods 1-10, respectively,
which equals the value transferred in each of these periods. No other sets of
depreciation coefficients and prices permit this to occur.

Andrew Kliman