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Previous message: patrick l mason: "[OPE-L:4049] Re: New Quiz!: Equalization of Profit Rates"
My ope-l 4043 responded to one aspect of John's 4041. Now I tackle another
aspect.
John wrote: "Let's suppose that a new machine costs $3000. Engineers predict
that it will last 6 years. Capitalists have found that the normal life for
this type of machine is 3 years. That is, they have found that they can no
longer use them profitably after 3 years since better machines generally come
on the market within that time frame. This means that after 3 years even if
the machine is fully depreciated it can no longer compete with a new machine.
"For me, this means that capitalists must depreciate the machine in such a way
that the $3000 is recovered as depreciation at the end of the 3 years. The
$3000 in value is transferred over that period of time given that capitalists
expectations are correct. Need they be? No. ...
"I do not think that '*firms deteremine* the value of their products by
determining the amount of moral depreciation transferred to the product.' The
key here is "knowing" how long fixed capital lasts. Indeed, that is what
connects the value of the fixed capital and the value transferred."
Together these last two paragraphs seems to mean that (a) firms do recoup what
they charge as depreciation, that (b) they charge as depreciation an amount
that they *expect* will fully recover the cost of the fixed capital, based on
their *expectations* of its economic (not technological) life; but that (c)
how long the fixed capital actually lasts (economically) is determined
independently of the firms.
This raises a number of questions. HOW are firms able to recoup what they
charge as depreciation? Doesn't this depend on the price they get for their
products? What then determines the price they get?
Why are the costs they are able to recover the original costs, not the
replacement costs? Why not any arbitrary amount?
If firms do not determine the rate and amount value actually transferred, what
then DOES determine them? In my interpretation, they are given exogenously,
based on the technological life of the stuff. But John denies that the
technological life matters. So what does determine them? Don't consider the
individual firm in isolation. Instead, either assume a single
state-capitalist, or that all capitalists are identical in an economy with
1-sector or with equal capital compositions. Then there is no apparent
external environment apparently determined by competition lurking in the
shadows onto which one can deflect the real process of determination. One is
faced with Monsieur Le Capital himself. What determines value transfer then?
I think that John's position implies a type of simultaneism, in which values
are constant and, given their constancy, value transfer is determined by the
physical coefficients and the actual economic life of the fixed capital.
To understand what follows, let me introduce some notation and definitions. A
machine is expected to have an economic life of n periods. Its expected
depreciation during period t (i.e, from time t to time t+1) is, in fractional
terms, Dt, which is greater than or equal to zero. The sum D1 + D2 + ... + Dn
equals 1, if the expectation of economic life is correct. (E.g., if n is 5,
we may have .2 + .2 + .2 + .2 + .2 = 1, or .3 + 0 + .5 + .1 + .1 = 1, etc.; no
particular depreciation schedule is assumed).
The price of a new machine of the same type at time t is Pt. How much is a
partially depreciated machine worth at time t (again assuming correct
expectations)? Well, a machine that was acquired at time 1 and used for one
period should be worth, at time 2, W2 = P2*(1 - D1). If used during period 2
again, it should be worth, at time 3, W3 = P3*(1 - D1 - D2). Thus, the
machine should be worth
Wt = Pt*(1 - D1 - D2 - ... - Dt-1) at time t
and
Wt+1 = Pt+1*(1 - D1 - D2 - ... - Dt-1 - Dt) at time t+1
(Note that the formula tells us that, at time n+1, the machine is worthless
[since the sum of D's then equals 1], which is right.)
At any time t, the firm charges as depreciation the amount Pt*Dt and, if
expectations are correct, this amount is transferred to the product and
recouped through sale at time t+1.
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. Symbolically,
Pt*Dt = Wt - Wt+1.
But this implies that
Pt*Dt = Pt*(1 - D1 - D2 - ... - Dt-1) - Pt+1*(1 - D1 - D2 - ... - Dt-1 - Dt)
or
Pt*(1 - D1 - D2 - ... - Dt-1 - Dt) = - Pt+1*(1 - D1 - D2 - ... - Dt-1 - Dt)
so that, if t < n,
(yes, you guessed it)
Pt = Pt+1, for all t and t+1.
This result might not bother some listmembers, but it makes me (and, I suspect
John) want to spit up. Simultaneous Valuation Expectorated :)
The result can be interpreted in a number of ways, all valid. If expectations
are correct, the price of the machine is constant throughout all time. Only
if prices are constant throughout all time will expectations be correct.
Turning the equalities into inequalities, if the price falls, the firm cannot
recoup the full loss of the machine's value (and it recoups more than that
amount if the price rises).
Thus, if prices are continually falling, there are only two possibilities.
Either (a) firms systematically overestimate the economic life of their
machines, or (b) John's view of value transfer is wrong. I cannot accept (a).
I can accept that expectations may be incorrect, but not that they will
continually be biased. Why should they be? (This recalls the Alberro-Persky
critique of the Okishio theorem, according to which the machines become
obsolescent prematurely, and Roemer's response.) Moreover, if (a) were right,
this would make falling prices dependent on, or at least indistinguishable
from, biased expectations. Instead of saying that prices fall due to
labor-saving innovation, we could say that prices fall because capitalists are
stupid. And why would the profit rate fall? Again because capitalists are
stupid.
EVEN MORE IMPORTANTLY, IT WOULD SEEM THAT THE RESULTS OF A SCENARIO WHICH
ASSUMES FIRMS' EXPECTATIONS ARE CORRECT WILL BE THE ACTUAL RESULTS FOR THE
ECONOMY IF THE ACTUAL SCENARIO IS DETERMINED *INDEPENDENTLY* OF THEIR
EXPECTATIONS (WHICH IS, I THINK, WHAT JOHN WISHES TO MAINTAIN). THEY JUST
GUESS ABOUT AN ECONOMY THAT IS NOT ALTERED BY THEIR EXPECTATIONS. THE PRICES
ARE THUS BEING DETERMINED (IN PART) BY THE ACTUAL TRANSFER OF VALUE, ITSELF
DEPENDENT ON THE ACTUAL ECONOMIC LIFE OF THE FIXED CAPITAL. BUT, IN THE ABOVE
SCENARIO, EXPECTATIONS ARE CORRECT, SO THEY ARE CORRECT GUESSES ABOUT THE
ECONOMIC LIFE OF THE FIXED CAPITAL AND THUS, IMPLICITLY, ABOUT PRICES. HENCE,
THE ABOVE SCENARIO IS THE ACTUAL SCENARIO, AND PRICES ARE ACTUALLY STATIONARY!
THE RECOVERY OF THE FIXED CAPITAL'S FULL VALUE REQUIRES IT.
Keeping in mind that we are looking at the actual economy (given that
expectations do not influence the actual valuation process), the stationary
price result also implies that value is not determined by labor-time. Assume
a sector that, for simplicity, produces machines by means of machines of the
same type plus living labor. Specifically, M machines and L amount of labor
produce 1 new machine each period, and the expected economic life of each of
the M machines is n periods. Measure prices in terms of labor-time. Assume
that expectations are correct. Hence, P1 = P2 = ... = Pn. But since
techniques are not changing, subsequent prices must also be the same (someone
who invests in period 2 faces P2 = P3 = ... = Pn+1).
Prices are determined as
M*P1*D1 + L = P2, in period 1
M*P2*D2 + L = P3, in period 2
..
M*Pn*Dn + L = Pn+1, in period n.
Since P1 = P2, then the first equation implies that P1 = P2 = L/(1-M*D1).
Since all subsequent prices are the same, the subsequent equations merely
serve to determine the D's, not the P's.
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.
But it is still the first equation, containing the original L, that determines
the price, and this price must still be P1 = P2 = L/(1-M*D1). And, since
price must still be constant throughout time, the reduction in living labor
requirements has no impact on the price of the fixed capital! This is a
classic simultaneist result. (Indeed, it is somewhat worse. Simultaneism
usually leads to the conclusion that changes in living labor requirements fail
to influence the rate of profit, the composition of capital, the rate of
surplus-value, etc., but they do usually influence values themselves.)
Again, if the actual scenario is determined independently of expectations,
then the above scenario, in which expectations are correct, is the *actual*
scenario, and prices (values) are *actually* determined independently of
labor-time.
I think the basic moral of the story is that successivism and Marx's value
theory are incompatible with the notion that anything which occurs in the
future can determine value in the present. This includes the future economic
life of fixed capital. (The technological life of fixed capital is determined
when it is produced.) Determination must follow the arrow of time.
Andrew Kliman