A reply to Alan's ope-l 3459.
Alan: "So far I have not found an instance where they [the difference in our
interpretations of valuation in Marx --- AJK] make a qualitative difference
except for one: the conservation of value in the case where fixed capital
is involved."
Also, when fixed capital is involved, the paths of your unit prices (values)
and mine can diverge systematically. This can occur if the ratio of fixed
capital to output is very large.
I agree that, subject to the qualification Alan notes and the one I just
noted, our results are very similar. Alan's post notes the important
similarities; I agree with everything he says in this regard.
Alan: "F(b-1) < Q-A"
Yes. Actually, Fo(b-1) </= Qo - Ao*b - wLo*c, if one uses my growth factors.
Alan: "Fo(b-1) = Qo - Ao ... gives physical meaning to the
bifurcations ...."
Huh? What bifurcations?
Alan: "The definition of F is ambiguous since we have to decide whether it
includes W, B and the circulating capital A in order to discuss the total
stocks of society."
I intended F to include none of them. Your K = F + A + W + B is basically
what I was thinking of. I have trouble, however, in thinking of B as existing
at the *start* of the period if there are no consumer durables. W is treated
by Marx as an advance, so I have no problem thinking of it as existing.
Alan: "My argument is that fixed capital participates in the formation
of social value from individual value on the same basis as newly-produced
commodities."
I don't think the issue has anything to do with individual and social value,
if by that you mean the value of commodities produced by individual producers
and the social average value of the commodities produced by all producers.
Let us assume a single capitalist exists, as Marx did in Ch. 9, Vol. III, or,
if you can't, assume they are all exactly alike. In either case, there's no
discrepancy between individual and social values. Yet we still get different
value measures from one another.
Alan: "In this way, no new value can be created in exchange other than by
living labour and any value destroyed in consumption appears either as the
value of W or the value of B.
I agree that your interpretation implies these things. But so does mine. My
interpretation does *not* imply that value is created in exchange. I agree
that Marx held that *exchange* conserves value. I don't think he maintained
that *changes in productivity* conserve value. My interpretation implies
that there can be a net change in the value of assets over the production
period, for the whole social capital, that differs from
value transferred + value added by living labor - value consumed.
But the net change has nothing to do with exchange. It all takes place in the
C ... P ... C' phase of the circuit. It occurs even if there is a single
capital, which therefore doesn't exchange with any others.
It may seem to you as if my interpretation implies value is created in
exchange because you identify only the following value processes: (a)
creation, (b) transfer (from constant capital to product), (c)
consumption/physical destruction, and (d) exchange. If a given change in
value doesn't fit under (a), (b) or (c), you classify it under (d), and say
value is being created or destroyed in exchange. I think there is a fifth
process: (e) devaluation/revaluation. I think there can be, in Marx's
theory, a devaluation/revaluation of the *total* social capital, so that
productivity changes lead to the non-conservation of aggregate value.
Alan: "Now when we come to the solution we have to reorganise it as
v(+1)(F+Q) = v(F+A) + L
".... In the case of your example F, Q and A are all growing at the same
rate. The solution behaves the same as yours, therefore, except that we
must replace your coefficient a =A/Q by the coefficient (F+A)/(F+Q).
Generally this will be larger (->1 as F->oo) and the rate of change of
value is therefore slower. ...
"That's the formal difference."
I agree with all this; but another formal difference is that the two unit
values do not converge. And, again, it is possible that they diverge
systematically. Using my growth factors, and assuming A = 0, there will be a
systematic divergence if Q <= F(b/c - 1), if I remember.
Alan: "Suppose for simplicity that F=90 and A=10, that Q will be 20 when
production has happened, and that L = 10. The coefficient a is thus
10/20 = 0.5. The equilibrium value is then 1. But suppose because of the
previous phase of rapid technical progress the actual current value is still
2. The total value of stocks in society is hence 2F + 2A = 200.
"We now find that in the first production period Andrew's equations yield
v = ve + (vo-ve)*(0.5) = 1 + (2-1)*0.5 = 1.5
"At the end of this period, however, there is in existence 90 units of F
that were not used up, and 20 units of Q that were produced. The result is
110 units valued at 1.5, being 165 units of value. The total value of the
stocks of society have declined by 35 even though living labour to the value
20 was discharged."
This is almost correct. The living labor extracted was 10. But Alan
understands my interpretation, and the other numbers check out. Why has the
total value of the stocks of society declined by 35? Well, the unit value
fell by -0.5, and so the 90 units of F are revalued downwards, for a total
devaluation of -0.5*90 = -45. On the other hand, living labor extracted is
+10. In sum, -45 + 10 = -35.
Alan: "But suppose, instead, that there was a temporary *decline* in
productivity, so that the starting value was not greater but lower than
equilibrium, so vo = not 2 but 0.5.
"In that case, the initial value of the stock would be 100*0.5 = 50.
Andrew's equations would yield
v = 1 + (0.5-1)*0.5 = 0.75
"But now at the end of this same period, the stocks in existence would
as before be 110 and their value would be 82.5, so that they have
*increased* in value by 32.5 even though L was only 10."
These numbers are also correct. Why has the total value of stocks increased
by 32.5? The unit value rose by +0.25, and so the 90 units of F are revalued
upwards, for a total revaluation of +0.25*90 = +22.5 Living labor extracted
is +10. In sum, +22.5 + 10 = + 32.5
Alan: "Value has been created out of nothing."
I don't accept this conclusion. This is a process of revaluation, not a
process of creation of value. Add a fifth process to creation,
consumption/destruction, transfer, and exchange, and there's no problem. If
technical change can lead to a devaluation of capital, it can also lead to a
revaluation.
Alan: "What puts people off my solution is the fact that the gross
value of current production can appear less than the value directly
consumed or added."
That is not my problem with it. My only problem with your solution is as an
*interpretation* of Marx's value theory. The specific difficulty is that your
interpretation doesn't conform to the notion that the value of the commodity
is determined by the labor-time needed to *reproduce* it (as I understand
"reproduce"). In your first case, the labor-time needed to reproduce was 1.5,
in the second case, 0.75, as I interpret Marx. (Note that I'm denying that
the fixed-point "value" is the labor-time needed to reproduce.) You may
disagree, and then we need to explore the meaning of "reproduce" in Marx
further. This is, I believe, where we last left off this discussion.
Alan: "Last point on the MEV: of course, in the last case, you might
still maintain that value conservation was not
violated, *if* you maintain that the MEV had meantime fallen."
No. I assumed you were working with labor-times or constant-MEV money values.
In any event, the numbers you give for my interpretation are indeed my
constant-MEV or labor-time values.
I maintain that value conservation *was* "violated." As I understand Marx,
the only processes that necessarily conserve value are the transfer of
constant capital-value, and exchange. I am aware of no textual evidence that
technical change conserves value.
Andrew Kliman