I can't say that I follow all of what Andrew says regarding aggregate
equalities of this and that. But I have worked a little example and I'd be
interested to see if anyone is able to confirm or disconfirm the results, and
perhaps to comment on their significance, if confirmed.
Let's keep things really simple, with a static technology and just two
commodities. Let the A matrix be
0.15 0.40
0.30 0.20
(so far as I'm aware there's nothing "funny" about this matrix), and let the
vector of direct labour coefficients l = (2 10)'. The vector of values in
the standard sense (v = Av + l) is then, according to my calculations,
v = (10 16.25)'
Let the economy produce one unit of each commodity. The sum of values is then
26.25. Now let us postulate a set of prices such that the sum of prices
equals the sum of values, but there is an arbitary divergence between
individual prices and values. I choose p = (16.25 10)'. Applying the
formula v* = Ap + l (I denote Andrew's values by v*), we get, I think:
v* = (8.44, 16.88)'
for a sum of 25.31, not equal to the sum of the v's or p's. Now, on Andrew's
procedure one is free to choose a "value of money" or MEV such that the sum
of the p's equals the sum of the v*'s. But that's your degrees of freedom
used up: you can't at the same time force this common sum to equal the sum of
the v's, i.e. the sum of actual labour-time embodied.
Allin.