On Thu, 7 Mar 1996, Alan Freeman wrote:
> 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.
>
I'm a little nervous about this way of putting the conservation of value.
Value is conserved in the exchange of newly produced products, but not
necessarily in the values imputed to assets, as the example of fictitious
capital (capital values attributed, say to government bonds which have no
real production process behind them) shows. For example, if the interest
rate falls, existing capital assets are all given a higher imputed value,
but no new value has been produced. Likewise, technical change may wipe
out part of the value imputed to existing stocks of assets, without
consumption or production taking place. This is one reason why it is
safer to focus on value added (representing new value produced) in
thinking about the conservation of value in exchange and the creation of
new values in production.
Duncan
> 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
>
>
>
>