Re: cambridge criticism

[Julio Huato <juliohuato@xxxxxxxxx>]

Michael Lebowitz,

> True, the neo-Walrasian approach did bypass that critique, but for me
> that response was always the 'bait and switch' approach. What has
> done ideological service has never been the neo-walrasian GE stuff
> but, rather, the good old marginal utility everyone gets what she
> deserves (as long as....) mantra.

IMO, our *main* task is to confront the results of high theory, as
opposed to vulgar versions or textbook rehashing.  The results of high
theory are in flux.  The "social norm" shifts constantly.  JB Clark's
interpretation of marginal productivity theory as a "theory of
deserts" (as A Sen called it) was refuted and abandoned long ago. 
See, for example, Samuelson's 1950 paper "Economic Theory and Wages."

In many current applications, economists continue to use -- as a first
approximation -- the notion that a factor's income is proportional to
its marginal product, and that competition enforces it.  But, as far
as I know, there's no claim that the marginal product is an ethically,
politically, or economically *fair* measure of the factor's
contribution to production.  I say "as a first approximation," because
there's a broad recognition (lots of conventional theories showing it)
that, under mildly realistic conditions, a factor's income deviates
from its marginal product and that the deviations may or may not be
systematic.

As for the issue of "desert," I think the current view is that "one's"
marginal productivity is largely contingent upon events one doesn't
control.  Basically, one's efforts interact in very complex ways with
the efforts of everybody else in a firm and (particularly, in an
economy with pervasive externalities) in society at large, the
availability of other inputs, existing technology (which is constantly
changing), etc.  Technology changes, technological applications
change, and input prices change; and all these changes interact in
complex ways to determine "one's" marginal productivity.  So, what
current economic theory suggests is that the nexus between our
individual talents, efforts, etc. and "our" marginal productivity is
very very thin and uncertain.  That's my reading of the current view.

> So, a challenge to the idea that
> the return that capital is determined by its marginal contribution on
> the basis that the very summing of capital requires the interest rate
> did make folks a bit uneasy  (a LOT more than-- what are you assuming
> about perfect knowledge, absence of uncertainty?). Those were the
> days (long past) of raising a hand in class and seminar and asking,
> excuse me, sir, when you use the term capital here, do you mean the
> sum of productive equipment employed or the stock of money
> invested...? The sophisticated response (not many of those)
> ultimately was bait and switch--- ie., on to GE theory.

[...]

> what does this [the Cambridge capital critique] -- have to do with
> relative flows of value and labour allocation in the 2 departments?

Producing better theories and educating economists (particularly the
younger generations) need not be mutually exclusive.  So I understand
the need to confront toxic interpretations disguised as textbook
material and reinforced by teachers and academic environments with
strong pro-capitalist biases.  But I insist this shouldn't be our main
concern with regards to economics.  Advanced economic theory is too
useful to leave it only to the economists.  More to the point, it's
not a good idea to use a flawed critique of the conventional concept
of "capital" in order to undermine an already outdated interpretation
of marginal productivity theory.

On the grounds of the labor theory of value, we don't need the
Cambridge critique.

In standard theory, the notion of physical marginal productivity is a
*technical* relation between inputs and outputs.  There's no economics
there.  So, when standard theory speaks of the "marginal productivity
of capital," it means the marginal productivity of specific capital
inputs (means of production).  Or if you think that the term
"productivity" should be reserved to the relation between outputs and
concrete labor inputs, then call it "effectiveness of the means of
production" as Marx called it.  Same thing: physical outputs/physical
inputs.

Essentially, the capital critique says that at an aggregate level you
cannot map the technical relation from inputs to outputs, because in
aggregating MP ("capital") the weights are value notions.  In standard
theory, the input-output technical relation is conceptualized as the
"production possibilities set" (PPS).  In applications, the PPS is
usually specified as a "production function" and sometimes a
"well-behaved" one.  In some abstract analyses, you don't even need it
to be a function or to be well-behaved.

But, in any case, the PPS is the *technical* piece of the analysis. 
The economic piece of the analysis is the prices and quantities of
inputs and outputs.  Under partial equilibrium, you add the utility
function, assume exogenously all other prices and quantities, add a
supply=demand consistency condition, and use maximization in
consumption and production to pin down the equilibrium price/quantity
of the item you care about.  Under general equilibrium, to the
production functions you add utility functions,  n-1 supplies=demands
conditions plus Walras law, and use maximization in consumption and
production to simultaneously determine the equilibrium price and
quantity vectors.

Michael -- you want to keep the Cambridge critique in the drawer, but
I won't let you get away with that.  Behold the *correct* Marxist
viewpoint on the Cambridge confusion:

Input aggregation (implicit or explicit) is a necessity in ANY type of
society.  In a full-fledged communist society, with no markets
whatsoever, given needs, people would still have to allocate their
labor time ("living" and "materialized") to different uses.  To avoid
wasting labor, they would have to allocate it according to proportions
determined by the (expected marginal) productivity of labor time in
each of its different "useful, concrete" (Marx) applications.

But, what do we mean by "useful, concrete" here?  Do we mean, for
example, the labor required to produce shoes?  Shoes seem to be pretty
concrete and the labor spent producing them certainly appears concrete
at first sight.  But, in practice, we need *all sorts* of labor,
living and materialized, to produce shoes?  When you look carefully,
they all are *very* different types of labor executed by very
different concrete workers.  Even the labor of the same worker will be
different from instant to instant.  Narrow this down to "living" labor
types and keep it simple: which labor in particular is "useful,
concrete"?  The labor required to glue leather pieces together?  Then
by "useful, concrete" we really mean only the labor that produces a
particular outcome (glued leather pieces) among the many other
outcomes required to produce finished shoes.  We can apply this
reasoning recursively ad infinitum.  But, depending on the task,
communists would not want to waste much labor time splitting hairs. 
For various purposes, they would have to stop somewhere and deal with
*aggregates*, say, deal with shoe-producing labor as if all the types
of labor involved in shoe production were homogeneous.

How would they add up "useful, concrete" labors that are so dissimilar
in practice (sewing, gluing, painting, operating different machines,
etc.) into one single measure of "useful, concrete" shoe-producing
labor?  They would have to use an index, an average.  And the weights?
 The weights would have to be some measure of the "relative
importance" society assigns to each type of detailed "useful,
concrete" labor.  But under full communism (no markets here), that
"relative importance" would be dictated precisely by those "definite
proportions"!

In a market society, the "relative importance" concretely assigned to
each labor input is given by its price (ultimately, value).  But here
we must distinguish the value *form* from its *content*: the technical
factors that determine it.  I.e., definite proportions of allocated
labor, proportions that, given the concrete needs of a society,
reflect the shadow "prices" of the labor inputs (i.e., the expected
marginal productivity of labor in each concrete application).  The
Cambridge critics conflate here form and content.  They say, if you
introduce "definite proportions" (shadow "prices"), then you are
introducing values, in the sense of specific social relations.  But,
this is NOT true.

If this seems complicated when dealing with "living" labor, the
complication is greater with "past" labor "embodied" in MP.  In
aggregating different kinds of MP ("capital inputs"), the "relative
importance" of each individual input depends on its expected marginal
productivity multiplied by a measure of the "relative importance" of
the outputs it helps produce.  But, again, one thing is that every
society needs to measure the "relative importance" of different kinds
of stuff and a different thing is that in some societies this
"relative importance" takes the form of value and price.  In a market
setting, these are values indeed, but they enter here not because they
are values (forms in the context of particular social relations), but
because they are "definite proportions," shadow "prices," or measures
of "relative importance."  And these are common to all types of
society.

The neoclassicals -- it is argued -- postulate a production function
relating physical inputs to physical outputs.  So, clearly, "capital"
here means "a physical set of MP."  Yet their aggregation of the
"physical set of MP" is not merely "physical" because the weights used
are the values of specific marginal productivities (e.g., MP_inputs *
P_output), which in an ideal competitive context, equalize to the
rental rates on the capital inputs.  Then changes in "capital" can be
due to changes in the composition of the individual physical inputs,
which is okay.  But, alternatively, they may result from changes in
their marginal productivities in cash terms (i.e., marginal
productivities times the price of the output the inputs help produce),
which is not okay because the "physical" measure is then buffeted by
changes in values.  The effect on the measure of "capital" may not be
a big deal when the two types of changes concord.  But if they don't,
the neoclassicals might wind up with changes in their measure of
"physical capital" completely dominated by changes in the rental rates
of the different types of MP.  How, then, can they map one-to-one
changes in the amount of individual physical inputs and their
aggregate measure?  They can't!  In other words, they may have
"reswitching"!  (Or, as you prefer to put it, the neoclassicals assume
the profit rate here to determine the profit rate there and that's
tautological!)

But change the context to see through the argument:  Communist plans
presume that physical inputs can be mapped to physical outputs at
different levels of aggregation.  Yet their aggregation of a "physical
set of MP" is not merely "physical" because the weights used are
marginal productivities times other weights: measures of the "relative
importance" assigned to particular outputs.  But then changes in their
"physical" aggregate measure of MP can result from changes in the
composition of individual MP, which is okay.  Or from changes in the
"relative importance" of the inputs, in turn due to changes in the
"relative importance" of the use values each given MP helps produce,
which is not okay.  Why?  Because then the measure of "physical MP" is
exposed to changes in the "relative importances."  That would not be a
big deal if the two types of changes agreed.  But if they don't, the
communists might wind up with changes in their measure of "physical
MP" completely dominated by changes in the "relative importance" of
the different types of MP.  Communist planners cannot map one-to-one
changes in the amount of individual physical inputs and their
aggregate measure.  They may have "reswitching."

There you have it: reswitching plagues neoclassical economics and
communist planning alike.  In principle, reswitching affects any
conceivable economic theory that requires aggregation (of LP and/or
MP).  Since aggregation is inescapable in making economic choices in
small or large economic units under all conceivable economic
arrangements, then the possibility of reswitching is practically
inescapable.  What any reasonable decision maker would say is, "Okay,
what's the chance of reswitching and how large is the cost involved so
that I can compute an expected loss to the best of our knowledge?"  If
the expected loss is large, then she'll want to disaggregate things a
little and pose the question again.  Eventually, she'd reach a level
of disaggregation where the expected loss involved equals the
resources required to prevent it and reswitching effectively vanishes
as a practical problem.  "What do I care about reswitching if I have
bigger fish to fry? -- she'll think."

* * *

The Cambridge critique "affects" Marx's reproduction story because, in
his illustration, the departments are broken down using "use value" as
the criterion: means of production in one bucket, consumption goods in
the other bucket.  I.e., Marx assumes a (capitalist) department I that
produces quantities of an implied homogeneous "use value" called
"means of production."  And by this Marx means exactly the same "use
value" that standard economic theory conceptualizes as "capital" in
some PPS applications (e.g, the "aggregate production function"). 
General equilibrium can "escape" this problem, because it allows for
an arbitrarily large number of inputs so that aggregation is not
necessary for the analysis.  But, indeed, aggregation is not required
in the abstract!  In any concrete society, facing practical economic
choices, aggregation is inescapable.

Best,

Julio