Keen/Ernst discussion

Steve.Keen at unsw.EDU.AU Steve.Keen at unsw.EDU.AU
Fri Nov 3 15:58:22 MST 1995


Dear John,

After we were so rudely interrupted... and, to be honest,
after I've finished a large slab of work that stopped me
replying to your post immediately.

It's been over a week since your last post, so to make
it possible for you (and anyone else interested in this
genuine discussion--as opposed to the diatribes that
I've recently been embroiled in) to follow, I will
extract large sections of your Thurs 26/10 post. This will
also make reference to some aspects of your 1982 RRPE paper,
which I've read in the meantime.

You began by making the correction I suggested to your
own example, when you hypothesised that new technology
could triple output while only doubling capital input
(in the spirit of Marx's p. 383 Grundrisse example), but
in fact showed only surplus value tripling. So now we
start with:

Initial State  (Period I)
      c   +   v   +  s    =     w
    $100  +  $50  + $150   =  $300   (30 units
                                       at $10ea)
Period II (Case A)

    $200  +  $50  + $650  =  $900     (90 units
                                        at $10)
You then continue:

|How does Marx discuss the valuation in Period II.
|For him, the social value created or added to
|the constant capital is $700.  The individual
|value added is still $100.   Thus, if prices
|fell such that the individual value and social
|value added were equal, with the given wage we
|see that
|
|Period II (Case B)
|    $200  +  $50  + $150  =  $300     (90 units
|                                        at $3.33)

Granted, this reading is consistent with how Marx
discussed similar examples elsewhere; but it it NOT
how he discussed the example we are dissecting. There
he said:

"It also has to be postulated (which was not done above) that
the use value of the machine significantly greater than its value;
i.e. that its devaluation in the service of production is not
proportional to its increasing effect on production." (p. 383)

In this instance, Marx is not discussing how a technical change
might allow a capitalist to temporarily secure a higher rate
of profit by introducing new technology, with the inevitable
eventual result of a fall in the rate of profit to the point
where the original rate of surplus is restored (relative to
a higher organic composition of capital) with a lower rate
of profit. He is contemplating, as he clearly said, that
the contribution of the machine to output (13.33 in his
example, 500 in yours) exceeds its depreciation (10 in
his example, 200 in yours).

In Marx's example and discussion, he presumes that the
surplus enjoyed by capital II continues:

Production Paper  Press   Wage  Surplus  Output  Rate SV Profit
Capital 1     30     30     40       10      30  25.0%   10.0%
Capital 2    100     60     40    13.33     100  33.3%    6.7%

The lower selling price of Capital 2 (1.59 vs 2.76) drives out
Capital 1, but there is no mention in that example of the surplus
for Capital 2 falling back to 10, resulting in a still lower
rate of profit.

Your example also highlights that Marx's result--higher rate
of surplus but lower rate of profit--was an artifact of the
numbers he chose. If he had used the ones you provided, the
result would have been a higher rate of surplus value
(1300% vs 300%) AND a higher rate of profit (260% vs 100%).
[All this is without transforming the value of capital in
period II, which I believe is a much less straightforward
task than the Sraffians presume--something I think you
agree with.]

Of course, these are all just arbitrary numbers. The real
question is the one posed by Marx: is it true that "the use
value of the machine significantly greater than its value;
i.e. that its devaluation in the service of production is not
proportional to its increasing effect on production."

If that is true, then your suggestion that the example
is one where individual value > social value, but the two
will eventually come into alignment at the pre-existing
state of social value, is incorrect. However, as you are
aware, this presumption is fundamental to all numerical
and algebraic work by Marx and marxists (save this one
example). For example, you open your RRPE paper with that
same assumption:

"Thus, assuming the value of the constant capital is transferred
to the output of each period, the value of the gross product in
the period is

w(t) = c(t) + v(t) + s(t)" (p. 86)

Now if in fact *more* than the value of the constant capital is
transferred--because "the use value of the machine significantly
greater than its value; i.e. that its devaluation in the service
of production is not proportional to its increasing effect on
production"--then while c(t) will be the measure of the
depreciation of the machine, it will not be the measure of its
contribution to output. If that is going to appear anywhere in
the equation you have above, it will appear in the s(t)--which
is the way it does appear in Marx's example.

Referring to your paper again, this breaches a vital condition
in your analysis--which is that, effectively, value is conserved.
That is, if you presume that the machine simply adds to output
what it loses in depreciation, and if you have a fixed population,
then total value equals the total labor-time expended by that
population, and it is therefore conserved from one period to
the next.

If, as you hypothesise, technical change results in a higher
rate of surplus value, while the new technology continues, as
did the old, to simply contribute to production what it loses
in depreciation, then there is an upper limit to the amount of
surplus that can be generated--the total labor time which can
be performed by the population. Once this limit is approached,
the extra surplus squeezed out by new technology will necessarily
be swamped by the increased organic composition of capital, leading
to a decline in the rate of profit. And, as you say, if the
rate of growth of surplus at any stage is less than the rate of
growth of output, then the rate of profit will fall before this
asymptote is approached.

But if, as Marx hypothesises in that example, a machine can add
more to production (its use-value) than it loses in depreciation
(its exchange-value), then surplus is not conserved but increased--
there is no upper limit to surplus creation (or rather, the
surplus that can be generated is a function of technology and
population, rather tha population alone).

This means that the appropriate tools of analysis are no longer
conservative ones, but dissipative. This raises an issue which
I think has troubled you, and makes you believe that some
conservative law is needed to be able to link one time period
to the next.

This is not so. A conservative rule--such as that which applies
in mechanics--provides a very powerful "accounting check" on
such systems; but a dissipative system can still be modelled
dynamically.

I've included a simple example in one of the papers I've sent
you. Its basic mechanisms can be repeated here:

Investment as a lagged linear function of change in output:
I(t) = c * {Y(t-1) - Y(t-2)}

Output as a linear function of accumulated capital stock:
Y(t) = 1/v * K(t)   (where v is the "accelerator")

Capital as a function of investment:
K(t) = (1-a)*K(t-1) + I(t-1) (where a is the rate of
depreciation; this isn't in the paper I've sent you, so
I thought I'd include it here)

Put the three together and you get

Y(t) = 1/v * {(1-a) * [v *Y(t-1) + c * {Y(t-2) - Y(t-3)}]

which cancels through to

Y(t) = (1-a) * [Y(t-1) + c/v * {Y(t-2) - Y(t-3)}]

which generates both cycles and growth--but no prices,
of course, since it's a one commodity model.

You'll have to take my word for this for now--because
I've yet to write up the paper--but this can be extended
to a multi-commodity model with prices. So while I agree
that in the past, the "price" of working out prices
has been equilibrium analysis, this is a fault of
nonlinear thinking, rather than a necessary consequence
of working out prices (linear dynamic models of prices
always end up with impossibly divergent price behaviour).

I agree with you that "the LOV you want to
toss out should be tossed out, and replaced by one
more consistent with that found in Marx's work --
one that is dynamic, not static." However, this law
need not be--indeed should not be--a conservative one,
because the economy is not a conservative system (in
the mathematical sense): it is a dynamic dissipative
one.

Cheers,
Cheers,
Steve


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