I just pointed out that in Bruce's example (1556 of 26/03), on the
assumption of Okishio-behaviour, the capitalists would not switch to
the new technology.
What happens with what we might call Roberts-temporal behaviour after
more than one period? We could also call this one-period-marxist
behaviour. Bruce's capitalists are marxist enough to know that when
they employ more labour, the value of their output will rise, but not
marxist enough to know that it will subsequently fall.
If the capitalists' adopt this behaviour then as Bruce rightly notes,
the temporal paradigm predicts that in the next period they actually
will get more profits and a higher profit rate. Yet the equilibrium
profit rate is lower. Is this a contradiction?
In a temporal model based on this behaviour, it emerges that they
cannot sustain the higher profit rate for ever. Their expectations
would initially be satisfied and subsequently dashed. Their
'stupidity' is a consequence of Bruce's behaviour assumption, namely,
that they can only see ahead one period - they are in effect stupid by
definition. This is by no means the only behaviour they might adopt
as I have already indicated, but even if they do adopt it, the results
are illuminating and, I think, more realistic than the results of the
simultaneous paradigm.
We can study this by extending the number of periods. Bruce need not
fear continuing time for more than one period. This is not what is at
issue between the iterative and the sequential approach. On the
contrary, it provides a rather clear illustration of the difference.
In period two as Bruce notes, the capitalists make high profits
because the price of corn sold rises to $1.225, while the seed corn
was purchased at the old cost of $1.000. But in period three the seed
must be purchased at the new price of $1.225 and the profit falls to
$58.51, which it will be seen yields a profit rate of 0.7895.
This is nevertheless higher than the old rate. But it sinks in each
successive period. By period 6 it sinks to 0.6638, less than the
original profit rate.
Thus, they would discover their error, but with a lag instead of
instantaneously, as suggested by the simultaneous interpretation. That
is the 'real' difference between the two approaches. The temporal
approach does not suggest they never discover the consequences of
lower physical productivity, only that these consequences do not
always emerge instantaneously.
For what happens when the rate of profit falls below the original
0.6667? A very simple behavioural assumption leads to a permanent
cycle, which has no parallel in any simultaneous model.
Suppose the capitalists remember that they secured a higher profit
with the old technique. When the temporal rate on the new technique
fell below this level they would switch *back* to the old technique.
The rate would then recover (though likewise not instantaneously) and
after a while price would adjust to the point where once more the
capitalists can once *again* make a (temporarily) higher profit by
taking on more labour and adopting technique 2.
This switching between the two techniques would go on for ever in a
stable limit cycle. Such courses of events arise with the most simple
behavioural assumptions in temporal models but are almost
inconceivable in simultaneous models.
In this case
(i) the result is *not* an interative solution because it does not
converge. The capitalists keep switching between techniques,
disrupting the convergence
(ii)with a temporal model of the utmost simplicity we have
demonstrated what the Sraffians laboured so long to establish; that
capitalists can switch *back and forth* between different technologies
depending on the price regime. But in our case this behaviour is
occasioned not by changes in the real wage but by the endogenous
properties of the system.
(iii)reswitching does not depend purely on technology but on the
process of reproduction as a whole. This is in fact very obvious; if
some resource is temporarily very expensive, the capitalists will not
invest in it even if it is physically more productive; this is why
many switched away from oil during the OPEC period.
Again such phenomena are absolutely commonplace in temporal models,
which are very rich in the variety of phenomena they can account for.
Note that I am in no way implying that the capitalists would actually
adopt such behaviour; I am simply pointing out this behaviour is
compatible with the temporal paradigm and indeed, produces interesting
results with some empirical verisimilitude.
And in general it illustrates one of the most important features of
the temporal paradigm: it is *simpler* conceptually but *richer* in the
phenomena it can explain.
Alan