[OPE-L:3075] RE: assumptions, assumptions, assumptions

andrew kliman (Andrew_Kliman@msn.com)
Sat, 21 Sep 1996 14:33:59 -0700 (PDT)

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This is a reply to the aspects of Jerry's ope-l 3070 that addressed points in
my ope-l 3068/3069 up to my signature. As I've noted, I had meant to delete
the rest.

Jerry: "You seem to imply that I am 'picking' on you, i.e. that I am
unfairly singling you out for criticism. This is not the case."

OK. I accept this. I got the contrary impression because your critique was
addressed specifically to me; it wasn't just a comment-to-all concerning my
post. Now we seem to be clear: you object to all discussion of the maximum
profit rate "except in the special case where v=0 is employed to critique a
theory that likewise uses that assumption" or "to simplify the equations." In
the latter case, you contend, "the 'results' are formally dependent on the
assumptions made." (Actually, I'm not entirely clear; I understand
"dependent," but not "formally dependent.")

I do not agree. v = 0 is a limiting case, and I think it is often helpful to
clarify the implications of certain propositions and concepts by considering
limiting cases.

In the present context, we are considering a theory proposed by a certain
individual who Jerry prefers I not mention, a theory which contends that the
magnitude of the capital advanced to production (the denominator of the profit
rate) is potentially unbounded, while the magnitude of profit (the numerator
of the profit rate) is bounded from above by the amount of living labor
extracted. This theory further contends that rising productivity and the
factors that enable it tend, ceteris paribus, to drive profit to its maximum
level and to increase capital advanced. The conclusion is that reductions in
v may not be able to raise profit sufficiently to counteract increases in
capital advanced, so that the profit rate tends to fall. One way of gaining
an understanding of these propositions, and testing their consistency, is to
examine the limiting case, i.e., the magnitude of the profit rate when profit
is at its maximum level. One does so by setting v = 0. One finds that the
upper bound on the profit rate is the reciprocal of the ratio of constant
capital advanced to living labor extracted, so that if this ratio rises over
time, there is a falling maximum level to the profit rate. Hence, if the
"initial" profit rate was greater than this maximum level, the profit rate
must fall. Moreover, one finds that, although the profit rate can be written
as (s/v)/(c/v + 1), so that it seems as though a sufficiently large rise in
s/v can always counteract a rise in c/v and make the profit rate rise, this is
not correct. One finds that when v = 0, s/v is infinite, but the profit rate
is finite, and can fall is the above-mentioned ratio rises.

I do not think these are trivial conclusions. What enables one to draw them?
The use of the v = 0 assumption in a context that Jerry does not sanction.

I also do not agree that the results obtained by use of the v = 0 assumption
are always dependent on that assumption. What is true is that *often* one
cannot correctly *infer* that the results obtained by means of an assumption
also hold true in the absence of that assumption. But it is also incorrect to
infer that the results fail to hold true! The results may or may not hold, in
other words, so that additional work is needed to find out. Moreover, note my
use of the word "often"; *some* inferences obtained by use of an assumption
also yield conclusions for cases in which the assumption does not hold. For
instance, the above use of v = 0 did permit valid inferences to be made
concerning the magnitude of the profit rate when v > 0.

I also think there are at least two other valid uses of v = 0 that Jerry's
strictures exclude. One is that the assumption may be used to test claims
when v = 0 is among the cases which the claim covers. This is not the same as
critiquing a theory that uses v = 0. For instance, the Okishio/Roemer claim
concerning the pre- and post-innovation profit rates *covers* the v = 0 case,
though I wouldn't say that it "uses" v = 0. Nor do I think the Okishio
theorem is a "theory," or intended to be one, in the usual meannig of
"theory." It is even more clear that Duncan was not propounding a theory when
he claimed that, in certain cases, the ratio of output to input prices does
not fall over time unless technical change accelerates. The case of v = 0 was
among the cases his claim covered, and I used that assumption to test the

The other valid use is this. When one is studying a question or questions the
answer(s) to which one *knows ahead of time* do not depend on whether the
magnitude of v, or whether it is rising, falling, or constant, I think it is
quite legitimate to abstract from changes in v by setting v = 0. One does so
not (or not solely) because it is thereby "simpler to get formal, quantitative
'results'." One may be doing so because one is thereby able to study the
question(s) at hand in their "pure" form, without the intrusion of extraneous
factors, and not because one cares about the numerical results. That is the
case when one studies certain *qualitative* implications of simultaneous vs.
temporal valuation on the magnitude of the profit rate-the relative sizes of
the two rates, the possible divergence in their movements over time, etc. Or
one may be doing so because one is concerned to discuss the operationalization
of certain concepts or measures under particular conditions in which the size
and movement of v is a minor issue that can be dealt with later. That was the
case in the extended discussion Duncan and I had on the internal rate of
return under conditions of a falling unit value. In most of that discussion,
neither of us was concerned to get correct numerical results for the impact of
falling values on the IRR.

Jerry: "Third: there is no point in 'scribbling', i.e. jotting down numbers
building models, until we can agree what the purpose at hand is and what
would constitute legitimate assumptions. If we can not agree on that
point, then we could easily generate an infinite variety of models along
the lines of 'the tendency of rain to fall.'"

Again, I don't agree. Why should I have to accept either the purpose or the
assumptions of your model before you write it down? All development of
models would be paralyzed forever if anyone waited for the agreement of
his/her audience.

Moreover, what we are discussing at present are the implications of temporal
vs. simultaneous valuation and pricing. If you don't like the (non-)models
you've seen, but you have even the slightest doubt that the conclusions drawn
from comparative statics fail to hold true (in all but peculiar special cases)
when one moves to a dynamic context, then *you* write down a model that you
*do* like, with assumptions that you *do* consider legitimate, and your doubts
will be ended. If they aren't, then post the model. Alan has graciously
agreed to help end your (and everyone's) doubts; I'll also be happy to pitch
in. Neither of us wish to criticize your assumptions. The point is to study
the implications of temporal vs. simultaneous valuation and pricing, to show
that your own model, whatever it is, will generate rather different results in
these two cases (I am stating Alan's conjecture in its strong form, about
which I have already expressed reservations). I can't see what possible
objection you could have to understanding better the implicit models you
already carry around in your head.

Jerry: "it is entirely legitimate to scrutinize and critique a model based on
the assumptions made."

It depends on the purpose of the model. If the purpose is to predict, and the
model predicts well, then why criticize the assumptions. If it does not
predict well, then it is legitimate to point to the assumptions as a reason
for this failure, but then one is critiquing the model for failure to meet its
objective, not the assumptions per se. (I know Friedman said this already.
Up to this point, he was right.)

More importantly, I do NOT think it is legitimate to scrutinize and critique a
NON-model based on the "assumptions" made, and least not by the same means as
one uses (legitimately) to scrutinize and critique a model. Ted and I have
suffered this treatment for over ten years now. Alan has indicated that he's
suffered it for a rather long time, too. I don't fault anyone for this. I
think that people simply do not understand the difference between *models*, on
the one hand, and *illustrations* and *examples* of properties governing
transitions between one dynamic state and another. The former operationalize
certain assumptions concerning the behavior of agents and/or the
interconnections of certain assumed processes and structures. Their results
depend on the assumptions made. The latter employ particular assumptions
because *some* set of assumptions is needed for illustrative purposes, but
they do not constitute a claim that the assumptions mirror reality, even
approximately, and the results they are meant to illustrate do NOT depend on
the particular assumptions made. Therefore the critique of the assumptions
is utterly irrelevant.

One example of the latter are Ted's and my illustrations that supplies and
demands can be equal, simple reproduction can take place, and a uniform profit
rate can be achieved, if exchanges take place on the basis of nonstationary
prices. It is very easy to miss or fail to confront the implications of this
if one starts picking at the assumptions of the illustration as if it were
meant to be a model of how capitalism works. Why simple reproduction?-that's
not realistic. Why a uniform profit rate?--that's not realistic. Why no
fixed capital?, why are workers paid in kind?, why is there no technical
change? why only two departments, why?, why?, why?, why?, why? Amidst this
continual din, Sraffianism falls in the forest but there's too much noise to
hear it, the purpose of the illustration is lost, the whole thing is reduced
to an absurdity. Having themselves made a model out of a non-model, people
forget one simple point: none of the particular assumptions have any bearing
on the results whatsoever.

Again, I don't hold this against anyone. People just don't get it. I think
the main reasons they don't are that they are so used to doing comparative
statics, in which the problem of transition from one state to another never
arises, and they're so used to dealing with models that any set of numbers or
equations is taken to be a model, to be scrutinized and critiqued on the basis
of its assumptions.

But I feel like Alan does: it is getting downright tiring. So I would like
to implore you all: Get It!

But we have already tried that. It hasn't really worked. This seems to
suggest that people won't get it until they begin to *see* the difference for
themselves. And they won't do that until they start having to confront the
problem of how you get from here to there. And that requires that they have
experience scribbling down their own equations and numbers (which some on this
list do). Until then, I think Alan is right, there will continue to be this
big communication gap. Until then, no matter how much people want dialogue,
they'll think challenging v = 0 or a uniform profit rate, or ... is dialogue.
It isn't.

Jerry: "I reject the proposition that the whole working day can be
appropriated by capital, or that necessary labor can equal 0, or that wages or
v can be equal to 0."

So do I.

Jerry: "if we are to agree that the subject of _Capital_ is capitalism, this
[assumption] is illegitimate."

I don't know how I can respond to this. A little earlier in his post, Jerry
had just rejected my proposal on how to continue the v = 0 discussion, writing
"Let's first discuss the meaning of the v=0 assumption *independently of the
question of whether Marx utilized that assumption, when, where, and for what
purpose*. Let's then discuss under what conditions and as part of the analysis
of what subjects this assumption is legitimate and/or illegitimate. *After
that*, we can discuss the questions of whether Marx employed that assumption
and whether it was legitimate for the subject and purpose at hand." Now I am
supposed to agree with a statement concerning the relationship between v = 0
and the subject of _Capital_, which he supposedly doesn't want to discuss
except at the end.

Which is it, Jerry?

Jerry: "to vacate wages and v from the analysis entirely requires us to
*fundamentally* depart from both Marx's analysis and the analysis of
capitalism itself."

Again, you're violating the order of discussion you yourself proposed. You
are now discussing Marx and saying v = 0 fundamentally departs from his
analysis. How should this claim of yours be TESTED? I would suggest we look
and see whether he makes this assumption in _Capital_. What would you
propose? Or are we going to slip back into the morass that Ted addressed, in
which what Marx said, wrote, and meant is assumed to be unknowable in
principle, the night in which all interpretations are black?

Jerry: "I *did* respond -- repeatedly -- to the textual question of whether
Marx utilized the v=0 assumption, when, and for what purpose."

True, but this does not contradict what I wrote about our discussion of v = 0:
"you broke it off several months ago. Basically you said let's agree to
disagree, instead of responding to my critique of your textual analysis, in
which I noted, inter alia, that the following imply one another: the whole
working day appropriated by capital, necessary labor equal to 0, and wages
(or v) equal to zero." If you could explain to me that the first doesn't
imply the third, then I'd agree that Marx didn't utilize v = 0 in a passage I
have heretofore claimed he did and you have claimed he didn't.

Jerry: "let me note that neither Alan, John, Ted, or yourself have attempted
to answer my question posed in the 'Developing Marx' thread concerning the
ways in which each of you believe one can 'develop' Marx from a TSS

John has since done so. I agree fully that the issues John raises are
unresolved and extremely important. I'm not sure, however, that this
qualifies as "developing Marx" (a phrase I don't really understand anyway). I
*have* mentioned on a number of occasions what I see as the most important
link between the TSS interpretation of Marx's value theory and the return to
and development of Marx's Marxism: the allegations of Marx's internal
inconsistencies imply that there is no Marx's Marxism as a totality, that it
must be corrected and completed. By refuting these allegations, the TSS
interpretation challenges the non-existence of Marx's Marxism and enables it
to be reclaimed, concretized, and developed.

I'll also add that the TSS interpretation is far too particular for it to be
the basis of a return to or development of Marx's Marxism.

Andrew Kliman

(sorry, no surprises this time either)