I'd like to comment on some aspects of Alan's long essay.
I find myself somewhat perplexed in this discussion, because I agree with a
great many points that Alan makes, and believe that they are far more
widely accepted than he judges. On the other hand, there are some claims he
makes that as yet I do not see the support for in the argument, and some
that I doubt. I'd like, if possible, to focus the discussion around the
issues that remain puzzling to me.
1. I have no problem in principle with Alan's critique of static and
stationary methods of analysis as approaches to a dynamic and ever-changing
reality. These criticisms have been made frequently in the economics
literature of the last 50 years, starting with papers of Richard Goodwin
and John Hicks, and continuing through the work of Frank Hahn, Jess
Benhabib and Richard Day, and others in "mainstream" economics. The
technical problem Alan alludes to, the relation between the path of the
stationary solution with changing parameters to the actual dynamic path of
a system, is well-understood at a mathematical level. Perhaps these points
are less familiar to Marxist economists, but there's no reason why we can't
educate ourselves about the advances in the general literature on this
front.
Alan considers a general parameterized dynamical system S(t) =
f(S(t-1),H(t)), where H(t) are potentially changing parameters, and
contrasts the path of the stationary solutions satisfying S*(t) =
f(S*(t),H(t)) with the actual dynamic path followed by the system itself. I
think Alan is correct in his claim that these are two different concepts,
and that under some circumstances these paths may diverge in various
senses. It is also true that under some assumptions about the parameter
path H(t) the paths may not diverge. Given this observation it seems that
the critical next step is to understand the behavior of more specific
systems of interest, like the price equations for a capitalist economy.
What is true of one example (like the cobweb with exponentially changing
supply and demand curves) may or may not be true in another context, and
the only way to find out is to work out the models. This is one case where
Alan says something I think is true, but seems to believe that it proves
something else that I remain uncertain of. Just because the divergence is
true in some dynamical systems, it does not follow that it is true in all,
or in any particular one, such as the price formation process in capitalist
economies.
2. It's not at all clear to me what investment "the people who pay the
economists" have in stationary solutions to dynamical systems. I don't see
why stationary solutions "express in pure form the notion that a free
competitive market automatically and without external interference arranges
for a set of prices and quantities at which all goods are sold." Any market
clearing path of prices, stationary or not, has this property.
3. I agree with Alan that money profit rates will be lower when prices of
output are falling than commodity profit rates, that is, profit rates when
price per unit of commodity is constant. Consider a purely circulating
capital, one-good model in which it requires a(t) units of output in period
t-1 to produce 1 unit of output in period t. (Suppose for simplicity that
the goods consumed by workers are included in the coefficient a(t).) Then
capitalists invest p(t-1)a(t) in period t-1 and have sales of p(t) in
period t. The profit rate in money is r(t) = (p(t)-p(t-1)a(t))/p(t-1)a(t) =
(p(t)/(p(t-1)a(t)) - 1. If prices were stationary (p(t) = p(t-1)), or if we
reckoned with output as the numeraire, which amounts to the same thing) we
would get a profit rate r*(t) = (1/a(t)) - 1. If p(t) < p(t-1), r(t) <
r*(t). This illustrates Alan's point that the path of the stationary
solutions is not the same as the dynamical path of the system, and confirms
his claim that the money numeraire profit rate will be lower than the
commodity numeraire profit rate. (Much the same result appears in Money,
Accumulation and Prices, in the sections considering the impact of changes
in the value of money on the circuit of capital.)
But unless the rate of technical change (and hence the rate of fall of
money prices of output) is accelerating, this model does not yield a
falling rate of profit. The money rate of profit is lower than the output
rate because of the falling money value of output, but the difference does
not diverge, and the money rate of profit does not decline just because
there is technical change.
4. When I read some of the postings on the list I get the sense that some
people may be claiming that all cost-reducing technical change lowers the
rate of profit, whether it is labor-saving or labor-using or capital-saving
or capital-using, simply through its effect of lowering the price of
output. I don't understand this claim. It also seems to me to be sharply at
odds with Marx's discussion, which mentions possible offsetting tendencies
to the falling rate of profit, which clearly envisions technical changes
that do not lower it.
5. I have trouble with one other aspect of Alan's discussion, which I may
not understand completely, the part touching on the calculation of embodied
labor coefficients. I myself don't think embodied labor coefficients play a
very central theoretical role in the labor theory of value, as we've
discussed on the list already. But it seems to me that the "Sraffians" want
to talk about the labor embodied in commodities as a property of the
current technology A, and therefore coherently define labor values as a
property of the technology through the equation v = vA + l. This also seems
to me in line with Marx's explanation that exchange value represents the
labor required to reproduce the commodity at current good-practice
technology, not the labor historically expended to produce the inputs to
the commodity. I agree with Alan that it is important to distinguish these
concepts, which coincide only under the unrealistic assumption that
technology is stationary, but I'm not convinced that the interpretation he
puts forward is the only consistent or even the most relevant one.
(I wish I could think of a neat slogan to sign with, but I can't)
Duncan