>> resulting from solving the maximization problem.  The factor demand
>> curve for any of those inputs is the schedule x_i (w_i | w_{-i} ).
>> Sum these schedules across firms to get the aggregate labor demand
>> schedule.


> The above is handwaving that assumes what is to be proved - that
> the (vertically integrated) firm can be in long-run equilibrium
> for some interesting range of p and w.


This is nonresponsive.  How precisely does your problem not fit into
the general framework given, Rob?  Yet again, one does not impose a
zero profit condition nor vary any other parameter than the factor
price of interest when deriving the schedule.  Let's make it even
more general, Rob: the write the firm's profit function as
P(x | w_i ; \Omega), where x is the set of choice variables, w_i is 
the factor price we are intersted in deriving a factor demand curve 
for and \Omega is every other parameter affecting the firm's 
decisions.  Maximize with respect to x.  The resulting schedule 
x_i(w_i | \Omega) is the factor demand function for factor i.  It 
does not slope up, as a simple axiomatic argument shows, and it 
does exist.  

Simply, in Rob's context, the demand curve for unskilled labor at time
t is the responses to the query "how much unskilled labor would the 
firm hire at t" as the wage of unskilled labor at t varies, ALL ELSE
EQUAL.  It is permissible for the answer to be zero, unbounded, or
not unique.

Consider again a simpler presentation of the basic ideas in Rob's
posts.  Let z(w,r)=0 denote an aggregate zero profit condition.
Suppose it is monotone such that we can write r=r(w) in equilibrium.  
Let L(w,r) denote a labor demand schedule. L(w|r) is the factor 
demand schedule, EVEN THOUGH it is generally the case that 
z(w,r) != 0 along that schedule.



>> Rob will object that in the "long period" there is a functional 
>> relationship between the elements of w.


> Chris doesn't seem to understand the relationship between the
> factor price frontier and profit-maximizing.


Really?  How exactly did Rob draw that conclusion in response to
my remark?



>> Rob will fail, again, to
>> understand that that fact does not alter anything in the preceding
>> paragraph.  If he wants to keep declaring his "challenge has not
>> been met," he must show why the problem he presents is not a 
>> special case of the above.


> This is to disguise that Chris has not met my challenge.
> He is relying on popular non-formal understandings of "prices"
> and "inputs" to disguise that he has not shown how to formulate
> my example in his terms.


Actually, Rob, I presented a very general and very common (and
formal) statement of the problem.


> In particular, I don't know how many
> inputs he sees in my example,


It doesn't matter.  The simple framework I gave is applicable for
an arbitrary number of inputs.


> whether he sees more
> than one variable denoting unskilled labor in his formulation
> (perhaps at different dates), whether he considers the rate
> of interest a price, and, if so, the price of what input.


Yet again, it doesn't matter.  The rate of interest is held constant
while deriving a factor demand schedule.  Yet again, it doesn't matter
if that fact places the economy in disequilibrium or violates a zero
profit condition.


> In short, Chris has not met any reasonable standard of the burden
> of proof. He has not shown how to construct long period labor
> demand curves for *this* example. His claim that I "must show
> why the problem he presents is not a special case of the
> above" is an implicit admission, as I read it, that he has
> not met the challenge.


As I've said repeatedly, I am NOT going to drag out a calculator and
work through Rob's pointlessly tedious and cumbersome presentation.
Yet again, Rob's claims are based on his faultly understanding of
elementary microeconomic theory, namely, his abject failure to
acknowledge that when many prices change, the resulting locus of
equilibria is not a labor demand curve, "long period" or otherwise.


> Chris is being silly. It would help his claim that economists
> such as himself understood my point if he would show some grasp
> of the analytical tools that I think useful for the analysis
> of the choice of technique in long period positions. I don't
> think he understands them.


Oh, he got me!  Turns out junior high school algrebra is far 
beyond me (don't tell, 'k?  I'd get fired -- lucky I've been able
to bluff thus far).  Why Rob thinks that using cumbersome assumptions 
such as discontinuous technologies form an "analytical tool" which is 
mysterious or difficult to understand is quite an enigma.


> It should be clear that one part of my motivation is finding
> certain analytical tools elegant.


Elegant!?  Good grief, Rob, you have failed.  Miserably.



>> Exactly what result that's well-known do you imagine I'm disputing,
>> Rob?


> I suppose Chris cannot be said to be disputing the use of the factor
> price frontier to analyze the choice of technique. He is merely
> not demonstrating any command of this tool. In fact, I honestly
> think he is still ignorant of this tool.


Damnit, Rob, when many parameters vary (along a factor price frontier)
the resulting locus of... oh, why bother?



>> I do dispute your insistence, over the span of years, that
>> your result shows that factor demand curves can slope up -- that 
>> interpretation is not "well known," however, because it is dead
>> wrong.


>  "However, as was argued in Section 3 with regard to 'perversely'
>  shaped, that is, upward sloping, factor-demand functions, this
>  possibility would question the validity of the entire economic
>  analysis in terms of demand and supply."
>    -- H. D. Kurz and N. Salvadori, _Theory of Production: A Long
>       Period Analysis_, Cambridge University Press, 1995.
>
> I find Kurz and Salvadori quite credible. The above is near the
> end of a long textbook. The analysis in that textbook, as should
> be true of most textbooks, was built up over decades. Important
> economists in developing this analysis include such obscure nonentities
> as Paul Samuelson, Robert Solow, Franco Modigliani - not that
> they would necessarily agree with Kurz and Salvadori's
> conclusions.


We have discussed this quote before.  Either (1) Rob is quoting out
of context or (2) Kurz and Salvadori are abusing standard terminology.
Rob's argument from authority when he thinks authority is on his side
noted (if he can find Samuelson, Solow, or Modigliani talking about
upward sloping labor demand curves, _that_ would be interesting).


> Despite Chris' insistence that this interpretation is dead wrong,
> I have yet to see him grapple much with the arguments I
> report. His demonstrated resistance to such serious intellectual
> work I find to be of most interest for psychology or the
> sociology of knowledge.


Yeah, I know Rob, I'm a dunce.  Not unlike every other professional
economist who's ever posted here, and many other notable economists
who Rob has deigned to give his opinions on.  Of course, it seems to
me that the "serious intellectual work" the eminent Rob Vienneau
"reports" on is mostly simplistic, archaic, and often hilariously
misinterpreted.  Perhaps worthy of a solid A- and a gentle lecture 
from the professor on style in an undergraduate history of thought
class.  But what do I know?  I'm not as clever as Rob.

I guess, given the self-aggrandization Rob indulges in above, he 
needs to rebuked again for taking himself and this forum far, far too
seriously.  This is entertainment, Rob, if you want to contribute to
the "serious" intellectual conversation of economists, a peer-
reviewed journal is the appropriate venue.


> I think he has a point that talking about upward sloping,
> factor-demand functions in this context is metaphoric. That is
> why I have moved to thinking it better to saying supply and
> demand is not applicable to long period analysis.


Define, "not applicable."  Economists tend to use supply and demand
to think about gross price and quantity changes, mostly in markets
which are small relative to the economy.  Under such conditions, 
the feedback effects Rob has been preaching about for years are
vanishing relative to own-price effects, and supply and demand can
be a very useful tool.  More complex models are employed to analyze
deviations from competive assumptions in many markets (notably, the
labor market) and when general equilibrium considerations 
are important (and, of course, in the common situation when outcomes
other than prices and quantities are of interest).  So, again, 
exactly what do you mean by "not applicable," Rob?  And _exactly_ 
what are you saying that any second year economics major isn't 
already aware of?


>>> Anyway, the demonstration, on one of several possible grounds, that 
>>> neoliberal advocates do not have a theory to support their remaking of 
>>> the world seems to be of contemporary interest.


>> And here Rob's political motivations are laid bare.  Rob's posts
>> would be more honest and more interesting if he would simply argue about
>> his political beliefs rather than pretending to be talking about 
>> microeconomic theory.


> But many economists think the stuff taught in "mainstream" intermediate
> microeconomics classes is ideology, incoherent as theory. I am indeed
> arguing about those incoherences.


When Rob is railing against "neoliberal advocates," he is not, of course,
talking about microeconomic theory.  I would be interested if he could
name one economist who would label "the stuff" in intermediate micro
"incoherent ideology."  I seem to recall learning about basic tools and
concepts such as: demand, supply, cost, equilibrium, utility, the envelope
theorem, the Slutsky equation, the core, moral hazard, adverse selection,
externalities, public goods, market structure, Nash and subgame perfect 
equilibrium, rent seeking behavior, Pareto criteria, dynamic games, a 
little dynamic optimization, and many others in undergraduate 
microeconomics.  All nonsense; the lot is neoliberal, incoherent ideology.
Right Rob?  Question: can one understand neo-Marxist, or neo-Institutional,
or any other "school" of economic thought absent any understanding of the
concepts presented in mainstream undergraduate microeconomics?

Rob also seems to think that support for neoliberal politics begins and
ends with a demonstration that (consumer surplus + producer surplus) is
at a maximum where supply and demand curves intersect.  While I would not
classify my own political beliefs as consistently "neoliberal," I will
point out that Rob's charge is just, well, silly (to use his favorite term).