>   This essay demonstrates that the existence of "price Wicksell effects"
> can lead to the inequality of the marginal product of capital and the
> interest rate. The inequality being challenged here should be understood
> as it is used in macroeconomic models with aggregate production functions.
> That is, macroeconomic modeling with aggregate production functions is
> inadequately grounded in microeconomic theory. I conclude with some
> rather far-reaching possibilitis.

Wait, wait, you mean to tell us there are *aggregation problems* in
macroeconomics!? Oh my god, stop the presses! Thank you, thank you,
Rob for bringing this startling new fact to the attention of the
economics profession!

>   I have explaind this before. Several economists have mistakenly
> asserted this argument has a simple technical flaw, althought they don't 
> all agree where that flaw lies. In fact, the length of my exposition
> here results from my attempting to clarify several points of confusion
> exhibited by economists responding to previous versions.

To be clear here: no one has ever denied that there are problems aggregating
capital.  The issue is whether Rob's little model demonstrates that fact.
Anyone who wishes can look up my post of June 7, 1996 (Rob has been feverishly
working on this for a little while) demonstrating that the original version
of this essay showed that, under the assumptions Rob claimed, the interest
rate equaled the value of the marginal product of capital in the model Rob
posted. Shall we press on and see if, in three years, Rob has managed to
come up with a correct exposition of some elementary economics first
expounded when my grandfather was a lad?

> I claim this argument is not about index number problems or the
> aggregation of capital [3]. I also do not see how it relates to the
> aggregation of production functions. Those who believe otherwise are

Since the argument (when given correctly) only holds in economies with
more than one capital good, it is indeed about aggregation problems
in certain macroeconomic models. Since this paragraph hangs alone and Rob
everywhere else discusses the issue as an aggregation problem, perhaps
it is he should be more clear.

Rob goes on to consider an economy with the technology:

>      a01 person years  &  a11 tons steel   PRODUCE  1 ton steel
>      a02 person years  &  a12 tons steel   PRODUCE  1 bushel wheat

and explicitly says:

> capital good might be used at a different set of prices. We certainly
> haven't assumed a Leontief fixed-coefficients technology.

And derives an implication of perfect competition:

>     w  =  [ 1 - a11 (1 + r) ] / d(r)                                 (19)

He then goes on:

> interest rate [6]. The factor price frontier is thus formed from
> the outer-envelope curve of the factor price curves corresponding to
> each individual technique. Points on this frontier that lie on two or
> more curves for individual techniques are known as "switch points."
> The optimal cost-minimizing technique is unique at interest rates
> for non-switching points.


And here is where the problems begin For smooth production functions,
*every* point in price space is a "switch point". Generally, the proportion
of inputs varies continuously with ratios of input prices. So when Rob
goes on and assumes:

> Assume the observed technique is a non switching point.

In other words, assume we are at a point on the production function with
a "kink:" a small change in factor prices will produce no substitution
effect. Also note that at such a point the production function is not
differentiable.

So when Rob goes on with:

         dw/dr =  - a12 a01 / [ d( r ) d( r ) ]                           (20)

His result obtains because only because of the special assumptions on
technology. Generally, one couldn't treat factor ratios as parametric
with respect to factor prices, as Rob does above.

So, despite the fact the some of Rob's exposition gets the ideas right, he's
yet again blown the math, since his math doesn't, in fact, apply under the
assumptions typical in neoclassical theory. Now, Rob, being Rob, goes on
to make a lovely sequence of political implications and a whole heap of
snide, sneering jabs at professional economists:

> Neoclassical theory [17]. In particular, it was shown, I think, that
> Neoclassical economists cannot consistently maintain in their equilibrium
> framework that owners of capital goods make any contribution to production.

Since one can demonstrate the same aggregation problems exist if labor is
actually heterogeneous, does that mean we can also conclude that labor makes
no contribution to the production process?     (For god's sake, Rob, trying
to claim capital "makes no contribution to production" is just so silly
and so transparently a desperate attempt to maintain a certain political
ideology, it's just pathetic.)

>   Finally, it is curious that economists continue to use aggregate
> production functions despite the clear warnings of this traditional

[ Yadda yadda yadda ]

Well, Rob, you're always welcome to relax that modeling assumption, produce
new models that outperform the old ones, and gain publishing success.

>   What explains this apparent continuation of the miseducation of
> economists that Joan Robinson decried over forty years ago [19]? My
> hypothesis is partly ideological. Any advanced treatment of capital
> theory and the appropriate analytical tools [20] would expost the student to
> the Cambridge Capital Controversy. The student would then learn of about some
> serious questioning of the internal consistency of many claims of
> neoclassical economists. There are obviously normative overtones to this
> controversy, for example, over the exploitative nature of profits and the
> capitalist system as a whole. Neoclassical economics might be claimed to
> currently fill the social role of "hired prize fighters" for capital, what
> Marx characterized as "vulgar economics" [21]. This social role is
> threatened by the CCC.

Yeah, more advice on advanced training in economics from Rob Vienneau. For
one thing, aggregation problems are a key issue in micro and macro theory
at the first year level.  For another, I guess I'll just ask Rob once again
why he thinks he's qualified to comment on what should or shouldn't be taught
to graduate students.  Correct me if I'm wrong, Rob, but it seems to me that
at least some of the following criteria should hold if someone wishes to
make comments about the content of graduate training in economics:

  - person has some graduate training in economics
  - person holds BA in economics
  - person holds MA in economics
  - person holds Ph.D in economics
  - person has graduate training in another relevant discipline
  - person has taught course at the graduate level in economics
  - person does research in economics
  - person understands basic economic tools and theories

None apply to Rob Vienneau.  Rob, it's a big, big world of economics out there,
and wasting time in a grad theory course discussing ancient debates over capital
theory just has an opportunity cost that exceeds whatever benefits the students
would receive.  I hate to shatter your Evil Conspiracy Theory (you and Jay have
been comparing notes, haven't you?), but the reason this stuff isn't taught to
graduate students are that mundane: it's just not that important, relative to
all the other stuff they must learn.