I have to side with Jerry on the uselessness of trying to establish the
TSS case using a one sector model. While a couple of his points are not
exactly right--there are one sector models which don't have the
knife-edge effect (specifically nonlinear ones a la Kaldor & Goodwin,
and a reworked form of Hicks's bastardisation of Harrod)--he is spot on
that such a model simply can't make or break the TSS interpretation.
The simplest reason is that what the hell do prices mean in a one-sector
model? You need at least 2 sectors to have even relative prices.
Duncan's defence that the 1-sector model is a special case of the
general contains a fallacy. The one-sector neoclassical growth model is
a "special case" of a multi-sectoral model too, but that one-sectorality
was a large part of the critique Sraffa developed (which, Steedman
apart, we should never forget was developed specifically to undermine
neoclassical theory). More importantly, the "dimensionality" of a
problem can and normally does have a profound effect on it: a change in
dimension fundamentally alters the problem, so that a "n-1" dimensional
problem is not a special case of an n-dimensional one, but an entirely
different ballgame.
The best illustration here is the "3-body problem". The gravitational
influence of one heavy body on another can be solved analytically. That
of three heavy bodies on each other is insoluble, and gave rise to chaos
theory.
I would argue that TSSers should start with at least a 2-sector model
(Marx, after all, used 2 or 3 sectors), which makes it possible to bring
in relative prices based on the labor value of each sector. Technical
change which alters the production method for "constant capital" would
then have a price to alter.
Cheers,
Steve Keen