I think that you are right about what Marx assumed. I think we have
to question to what extent the assumption is justified. I think there is
some
evidence for the formation of a general rate of profit, but that the
tendancy for this to form is not all that strong.
One has to take into account other complications:
1. The dispersion of profit rates within firms in a given industry
is also significant and can be large relative to the dispersion
between industries. This is generally left out of mathematical
models which use only a single method of production per
industry, with an associated single rate of profit.
2. It is not at all clear that the average rate of profit on invested
capital accross all industries will be relevant to a firm when
deciding on investment. It is equally plausible that it will be
the rate of interest that is taken into account. The rate of
interest is known, the average rate of profit is not.
3. Real capital, as opposed to money capital, has limited mobility
between branches of production weakening any tendancy
of the rate of profit to equalise.
4. An alternative model for price determination favoured by Kalecki
is that prices are determined by a markup on prime costs -
principally labour costs, if that is the case prices will tend to
shadow values.
5. A factor tending to favour a markup on prime costs as a
regulator is that the bargaining position of trades unions
is strongest with industries earning above average markups
on labour costs. This may tend to limit the dispersion of
prime cost markups.