Paul,
We may have hit the point where doing the transformation
backwards clarifies some differences. Here the dialog included
in your post is reproduced and my response follows.
Simon writes:
I don't understand the specification. Why should anything different happen
in Period II if the uniform rate of profit does not change?
John responds:
The relation between total price and total value changes since the
labor added in the production process of period II creates less or
more value than average since it is working with a capital of a
larger or smaller composition respectively. Living labor does not
add the same amount of value expressed in prices as before.
Paul C now replies
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The amount of value created by labour is quite independent of the
organic composition of the capital with which it works. The
price of production hypothesis is that goods produced under high
c/v ratios sell at prices above their values, not that their
values are higher.
John says:
I am starting with prices of production. How did I get there?
Start with the concrete and abstract from all else till you get
there. Now what do we have? Workers laboring for various
capitals of differing compositions each of which is earning the
same rate of profit is the object before us. Based on the
price of the net product of the total labor, we can say what
amount of "value" is created in the given period of production.
For that period, we could then say that the "value" added
represents so many hours of labor. From that number we could
establish the "value" of the capital inputs. (Given we are
moving backwards or, in other words, from the concrete to the
abstract, I'm not sure how else we can proceed.) With this
info, we could then assume a uniform rate of surplus value and
arrive at what we see in Vol. III prior to the transformation
of values into prices of production.
My point in the exchanges with Simon and Chai-on was that the
relative sizes of the various capitals involved seemed to
affect the determination of "value." Hence, to know the "value"
added by a given amount of labor, one would have to have already
abstracted from a certain price of production structure. But here
I see no other way of proceeding if we take seriously the idea that
the movement from the concrete to the abstract takes place prior to
that the presentation in CAPITAL.
John