Re:
> Andrew: I don't see why a critique of Sraffianism needs 2+ sectors. The basic logic
> of Sraffianism is that of the corn model, as the Sraffians themselves say. A
> main point, if not the main point, of their theory is to show that relative
> price variations are of little significance and technology and distribution
> (conceived as independent of relative price variations) are of great
> importance.
Actually, I meant that the Sraffian critique of Marx required 2 sectors
(a la Steedman); but as it happens, the critique of Sraffianism I'm
doing benefits from multiple sectors, because this increases the
probability of nonlinearity.
To explain this briefly, Steedman decided to attack Kaleckian markup
pricing, using a circulating capital model of the form
p = (u+pA)(I+M)
where p is a (row) vector of prices, u of "exogenous costs" (including
labor), A the input-output matrix, I an identity matrix and M a
diagonalised matrix of sectoral markups. After the usual matrix
critique, he considers dynamics and concludes that his static analysis
"does not ignore time. It merely allows for changes to have their *full*
effects".
His dynamic equation from which this is established is
p[t] = (u+p[t-1]A)(I+M)
Part A of my response shows that his equilibrium is only stable if the
matrix A(I+M) has eigenvalues of less than mod 1. Part B shows that he
can't call this framework "Kaleckian" unless he has a variable markup
based on some inverse function of the rate of profit, which generates a
2 vector equation system with entries of the form
p[t-1]A(M[t])
which is nonlinear because of the pM cross products. As the size of A
increases, the likelihood that this system's equilibrium is unstable
also rises, to the stage where the equilibrium solution is irrelevant to
the short run and long run state of the economy.
(I'll send the full--but still incomplete--critique to you directly as
an attachment, once I convert the form of equations [but the easiest
would be if you can handle a psotscript .ps file])
Cheers,
Steve