I shall argue two main points. The first is that although Marx is
conventionally taken to have formulated two different theories of
price in the the three volumes of Capital, labour values in volume
I and prices of production in volume III, there is actually a third
theory, hidden inside the reproduction schemes of volume II. This
theory is not explicit, but can be logically deduced from the constraints
that he presents on simple reproduction. It is not a theory of individual
prices, but a theory of relative sectoral prices.
I will go on to argue that this theory of sectoral prices allows us
to make probabilistic arguments about the relative likely-hood that
either production prices or labour values will operate at the level
of reproduction schemes. This paper provides a measure on the configuration
space associated with Marxian prices of production and labour values.
By use of random matrix techniques it shows that the solutions space
associated with prices of production is similar to that associated
with classical labour values.
In the latter part of the paper, a sample of reproduction schemes
is simulated over time, under assumptions of capital movement,
to see whether such systems dynamically converge on prices of production.
It is found that some converge, and some fail to converge
