>> The only input this firm buys is labor, so obviously its costs depend only
>> on how much labor it hires. Then asserting the firm will hire more labor
>> to produce the same output in response to a price change is equivalent to
>> stating the firm will incur more costs than it needs to in order to
>> produce that output.


> But the firm also borrows corn for the year. In the scenario described
> by Robert Vienneau, rising wages cause the ratio between the price of
> iron and the price of corn to rise, making it cheaper for an iron
> manufacturer to switch from a process that uses more iron to one which
> uses more corn as well as more labor per unit of iron output.


Recall there is no "price of iron" because iron is not traded.  Along an 
optimal path one could calculate what's called a "shadow price" for iron 
by economists, which may or may not be the same number as Vienneau's 
"accounting price."  Neither is needed to solve for the optimal input 
quantities.  Note again that this firm's outlays are proportional to 
labor hired per period: Vienneau's claim that labor hired per period 
*changes* (we don't even need "increases") with increases in the wage 
rate holding output constant is clearly incorrect.  That is, the solution 
to the program {min_L wf(L) s.t. g(L)=0} does not depend on w (regardless 
of whether L is a scalar or a vector).

I believe what's going on here is that Vienneau has paraphrased (without 
due credit) an archaic model of a vertically integrated *industry* and 
mistakenly applied it to a *firm*.  In the body he says he's "assuming" 
various things about the "accounting price" of iron, but in the appendix 
he solves for that price by moving along the "factor price frontier."  He 
says:

 Likewise, for iron to be produced, the third or the fourth
 constraint in the dual must be met with equality. Hence, for the
 analyzed firms to be in equilibrium, the vertically-integrated industry
 must be on the so-called factor-price frontier for that industry.
 
The factor price frontier gives zero profit combinations of input prices. 
But a firm's profits are a decreasing function of input prices: An
increase in wages will not be accompanied by a change in the "accounting
price" of iron or any other parameter that leaves profits at zero, it will
instead decrease profits (notice the "accounting price" of iron *falls* 
when the wage rate rises).  Vienneau's solution instead involves an
endogenous change in other parameters such that profits are held at zero --
even abusing the term "labor demand curve" to allow aggregation over time,
the object he's talking about is not a labor demand curve, and the
properties of the object he's talking about are not surprising.  Notice
too the use of "industry" and "firm*S*" when what we are supposed to be
considering is the optimal response of *a* firm to a change in input
prices.



>> This particular bit o' spam is
>> riddled with mathematical and conceptual errors; factor
>> demand curves cannot slope up.


> I always thought "spam" meant something broadcast much more widely.


Vienneau has a small cache his "long essays" which he regularly posts all 
over the place.  Google suggests minor variants of this particular piece 
have been posted about 70 times to a variety of groups.  I think such 
behavior is accurately described as "spamming."


> This may seem picky, but as a sci.math regular, I'd say that it seems
> pretty common for people to describe as "mathematical errors" things
> which aren't mathematical errors.


Whether one wishes to call the errors in this piece "mathematical" or
"conceptual" is a matter of semantics.  Vienneau claims to be showing
properties of a mathematical relationship which do not in fact hold, but
this is a result of misunderstood concepts rather than an arithmetic error
in the solution (not that's I've checked his ludicrous arithmetic --- for
all I know it's wrong too).


> From this remark,
> 
> Robert Vienneau:
>> So, as good economists have long recognized, the theory I am attacking
>> is incorrect, as a matter of mathematics and logic.
> 
> I was under the impression he was happily acknowledging that what he
> claims to be showing is well-known in economics.


You misunderstand Vienneau's intent.  Recall the preamble to the
arithmetic features an economist who is supposed to be "unable to explain"
the analysis Vienneau is about to present.  The "good economists" in the
quote above are the tiny band of aging political idealogues Vienneau loves
to paraphrase; the vast majority of economists are the, er, non-good
economists not in that camp.  Unfortunately Vienneau rarely gets even the
radical critiques (of economics as it stood in the late 19th century) he
paraphrases right, as this thread amply demonstrates.