There is an error of logic creeping into this discussion of TSS--or so
it appears to this lurker. Fred gives the case:
> 1. It seems that Andrew's "historical cost" price equation could be written as:
>
> p(t) = ap(t-1) + VA(t)
>
> where VA is the "value added" component of the price of commodities, which
> according to Marx's theory is due solely to living labor.
>
> 2. Now assume three periods of production: p(0), p(1), and p(2). Then the
> price equations for periods (1) and (2) could be written as:
>
> p(1) = ap(0) + VA(1)
>
> p(2) = ap(1) + VA(2)
>
> 3. Assume that there is no technological change in period (1), so that
> p(1) = p(0).
>
> 4. Finally, assume that there is technological change in period (2) that
> reduces the cost of material inputs, so that p(2) < p(1). However,
> assuming "historical cost' valuation, the constant capital component of p(2)
> and p(1) are equal, because p(1) = p(0). Therefore, it must follow that
> VA(2) < VA(1). In other words, VA has declined solely as a result of the
> change
> of the price of material inputs, without a change in the amount of living
> labor, contrary to Marx's theory.
>
> This has been Duncan's main point in recent posts, and I do not think it has
> yet been answered by Andrew or other TSSer.
The equation is incorrectly specified. If technological change is to
occur, then it must occur either in the productivity of labor (the VA),
or the input-output requirements of production (the a). If we accept
that we can separate the two components (labor productivity and
input-output requirements) then the equation should be stated as
p(t) = a(t-1)p(t-1) + VA(t)
The source of technology improvements must then be changes in a(t) over
time, so that a(t)-->0 as t-->infinity. If we accept the strict labor
theory of value (as compared to, say, Joan Robinson's), then we have to
accept that VA(t) is proportional to labor input, and that this does not
change when a(t) changes--i.e., that reducing a(t) does not simply
increase the RSV pari passu.
Mind you, this still won't necessarily free the TSS interpretation from
the the derivation drawn by Fred--that there's been a change in value
added without a change in the amount of living labour. I haven't tried
to see whether that is the end-product of the argument yet, but as
someone who argues that the labor theory of value is invalid, I wouldn't
object if that was the case!
Cheers,
Steve Keen