Andrew here, with a reply to Allin's matrix example.
First, the TSS interpretation does not just "choose" an arbitrary
money expression of value. The claim is rather this: the sum of
money prices will equal the sum of money values if the money expression
of value does not change during the period. If there's a discrepancy,
then that change is its source. This claim is just a differnent way
of stating some things I (and Alan) have said before about both prices
and values being measured in both money and labor-time. People found
it confusing. The above, which might be less confusing, is identical
in meaning. (Sum of money values in the above indicates the following
-- c(t) + MEV(t)*L(t). Sum of prices indicates p$(t+1)X(t).)
I'm not sure how this affects Allin's example, because I'm not sure what
it is meant to show. Allin himself seems not to be sure. The example
does seem to indicate that the sum of values = sum of prices in the
TSS interpretation will generally not equal the sum of values of the
standard interpretation, even when a price vector is found that equates
the sum of the standard interpretation's values and prices.
This is true. The TSS interpretation gives different quantitative results
for values (and for production prices).
Andrew Kliman