Paul writes (OPE-L:1343 of 6/3):
"I have no doubt that one can construct hypothetical examples in
which the super profit of the producers of new models of machine
exactly equal the losses on moral depreciation, but why should
this happen in reality. Why is there any necessary relationship
between the two sums?"
Because of the conservation of value. Whatever is gained in one
place *must* be lost in another in the absence of production.
Conversely, whatever is lost in one place *must* be gained in
another, in the absence of consumption.
All I have done is extended this law, I think more or less in the
form which you and Allin express it in your paper on the measure of
value, to the dynamic case, that is, enquire into how the law
operates between periods. The key to this operation is to consider
the effect of stocks on the distribution of value. Stocks are the
means by which dead and untransformed value is transferred between
periods.
Whether statically or dynamically, the same law applies: Only
production can create value, and only consumption can destroy it, in
the system as a whole.
Therefore, I would put the question the other way round. The issue
is not 'why should this happen in reality' because we know that it
*must* happen in reality. That is, we know that the value lost in
one place must surface somewhere else. The issue is not 'whether' or
even 'how' but 'where'?
Thus: we know that value is conserved, and we know that in moral
depreciation, value is lost to an individual producer. We also know
that, since this loss is an effect of circulation (of the formation
of a uniform price and a uniform value for commodities of the same
type), the value is lost only to the individual producer and not to
society. Therefore, it is a necessary consequence of the law of
conservation of value that the lost value *must* appear as the
superprofit of *somebody*. Just as, a necessary consequence of the
law of conservation of energy is, that if a body gets cooler, the
loss of energy in one form *must* reappear as a different form of
energy somewhere else.
So I have not constructed hypothetical examples in which,
for some arbitrary reason, the value lost and the value gained just
happen to balance. We *know* they balance. The problem is to find
out where the lost value goes to. When I constructed the examples
that I posted, all I did was to apply the law of conservation of
value, extended to stocks. I didn't set my computer a complex linear
programming problem to hunt through all possible numbers until I
found the set which justified my argument! Anyone can try this, just
by varying the numbers in my example and applying the law of
conservation of value. It is not very difficult at all.
At any rate it is no more difficult than accepting that the earth
moves around the sun, though I hope the idea finds a more rapid
acceptance.
Of course, this law (though still valid) may operate in a more
complex manner if, in addition to the technical change we discussed,
there are technical changes going on in other parts of the economy.
It will also operate in a more complex manner if prices diverge from
values.
The postulates I adopted were:
(i) prices equal values
(ii) no technical change anywhere else.
(iii)constant value of money
On these postulates the effects of technical change in the
production of a given machine in a given period is that circulation
redistributes value between four groups of people, and only these
four groups of people:
(1) users of old machines
(2) users of new machines of the same type
(3) producers of new machines
(4) producers of old machines.
However it is true that this analysis is valid only for one period.
In the next period, the products of the machines themselves become
cheaper and there is a diffusion of the effect throughout the system
over time. One of the reasons for using a sequential method is that
it allows us to trace through this process of diffusion, instead of
assuming at the outset it is already complete, a necessary
presupposition of the equation v = vA+L and another reason for
abandoning this equation.
Alan
Postscript on differentials
===========================
Of relevance to the point which Mike and Andrew have started
discussing is the following:
In the limit the dynamic process can be represented as a
differential equation, if the period of reproduction is reduced to
zero, thus:
v'K + vX = vC + L
where:
X is the matrix of outputs
C is the matrix of consumed constant capital (including pure
material depreciation)
K is the diagonalised matrix of capital stock (summed over
commodities)
v is the vector of unit prices (equal to values in this case)
L is the vector of living labour-power
' means 'first differential with respect to time'
In all cases these magnitudes in a differential formulation are
rates of flow, eg bushels per hour. L is thus simply worker-hours
per hour, or just 'workers currently employed'
If v' = 0 this reduces the equilibrium case (of exchange at values):
vX = vC + L
It can thus be seen that equilibrium is a special case of the
dynamic form.
The term v'K, which I term the 'stock adjustment term' is a purely
dynamic term which does not appear in equilibrium analysis. It is an
equivalent, for example, of forces of motion in mechanics such as
the Coriolis force or where there is a velocity potential, as in the
magnetic force operating on a moving charged particle.
Where values of any input are declining, the unit values of any
product in which this input is *used* as a means of production are
correspondingly *smaller* than predicted by the equilibrium
analysis. That is, the equilibrium measure *overestimates* value (by
wrongly portraying v'K as a cost)
This is proved rigorously in the last chapter of 'Marx and
non-equilibrium economics'.
The law of the falling rate of profit follows from the above
equation (modified to include exchange at values other than prices)
and a second identity, which connects the loss and creation of use
values (stocks and flows) which I term the 'time-dependent stock
identity'.
This may be further extended to the case of a changing value of
money. A further extra term
(m'/m)vK
then appears, where m is the (nominal) value of money.
The equation above only expresses transfers between sectors and
does not distinguish between different producers of the same
good, as in the first part of this post. This is mathematically
more difficult to capture because it obliges us to deal with
a non-reduced or rectangular matrix with more producers than
commodities, and a constraint that the several producers of the
same commodity must sell at a common price and hence produce at
a common social value.
Alan