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Wages, Employment Still Not Determined By Supply And Demand

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Robert Vienneau

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Oct 13, 2002, 6:59:58 PM10/13/02
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1.0 INTRODUCTION

Mainstream North American economists are generally socialized to be
ignorant of price theory. At least, that's what the empirical evidence
presented by Usenet suggests. But hope springs eternal. So once more I
give some posters the opportunity to acknowledge the validity of
certain aspects of price theory.

This long post presents an example in which higher wages are
associated with firms choosing to employ more workers per unit output
produced. The exact numeric values used aren't necessarily reasonable.
The example, though, is used to make a point.

I assume a reader willing to follow tedious arithmetic. Skip down
to the conclusions at the end if you're curious about my point.

2.0 DATA ON TECHNOLOGY

Consider a very simple vertically-integrated firm that produces a
single consumption good, corn, from inputs of labor, iron, and (seed)
corn. All production processes in this example require a year to
complete. Two production processes are known for producing corn. These
processes require the following inputs to be available at the beginning
of the year for each bushel corn produced and available at the end of
the year:

TABLE 1: INPUTS REQUIRED PER TON CORN PRODUCED

Process A Process B

1 Person-Year 1 Person-Year
2 Tons Iron 1/2 Tons Iron
2/5 Bushels Corn 3/5 Bushels Corn

Apparently, inputs of iron and corn can be traded off in producing
corn outputs.

Iron is also produced by this firm. Two processes are known for
producing iron:

TABLE 2: INPUTS REQUIRED PER TON IRON PRODUCED

Process C Process D

1 Person-Year 275/464 Person-Years
1/10 Tons Iron 113/232 Tons Iron
1/40 Bushels Corn 0 Bushels Corn

Inputs of corn and iron can be traded off in producing iron. The
process that uses less iron and more corn, however, also requires
a greater quantity of labor input.

2.1 PRODUCTION FUNCTIONS

The data above allow for the specification of two well-behaved
production functions, one for corn and the other for iron. For
illustration, I outline how to construct the production function
for corn.

Let L be the person-years of labor, Q1 be tons iron, and Q2 be
bushels corn available for inputs for corn-production during the
production period (a year). Let X1 be the bushels corn produced
with Process A, and X2 be the bushels corn produced with Process B.
The production function is found as the solution of an optimization
problem. The (nonvertically-integrated) firm wants to produce as
much total corn output as possible. Accordingly, the production
function for corn is found as the solution to the Linear Program
in Display 1:

Max X = X1 + X2

2*X1 + (1/2)*X2 <= Q1
(2/5)*X1 + (3/5)*X2 <= Q2 (1)
X1 + X2 <= L

X1 >= 0, X2 >= 0

Let X = f(Q1, Q2, L) be the solution of this LP, that is, the
production function for corn. (This production function is not
Leontief.) The production functions constructed in this manner
exhibit properties typically assumed in neoclassical economics. In
particular, they exhibit Constant Returns to Scale, and the marginal
product, for each input, is a non-increasing step function. The
production functions are differentiable almost everywhere.

The point of this example, that sometimes a vertically integrated
firm will want to hire more labor per unit output at higher wages,
is compatible with the existence of many more processes for producing
each commodity. As more processes are used to construct the production
functions, the closer they come to smooth, continuously-differentiable
production functions. The point of this example seems to be compatible
with smooth production functions. It also does not depend on the
circular nature of production in the example, in which corn is used
to produce more corn.

2.2 TECHNIQUES

A technique consists of a process for producing iron and a process
for producing corn. Thus, there are four techniques in this example.
They are defined in Table 3.

TABLE 3: TECHNIQUES AND PROCESSES

Technique Processes

Alpha A, C
Beta A, D
Gamma B, C
Delta B, D


3.0 QUANTITY FLOWS

I want to consider a couple of different levels at which this
firm can operate the processes comprising the techniques. First,
suppose Process A is used to produce 1 41/49 Bushels corn, and
Process C is used to produce 4 4/49 Tons iron. The quantity flows
shown in Table 4 result.

TABLE 4: THE ALPHA TECHNIQUE PRODUCING CORN NET

INPUTS Process C Process A
Labor 4 4/49 Person-Years 1 41/49 Person-Years
Iron 20/49 Tons Iron 3 33/49 Tons Iron
Corn 5/49 Bushels Corn 36/49 Bushels Corn

OUTPUTS 4 4/49 Tons Iron 1 41/49 Bushels Corn

LABOR-INTENSITY: 5 45/49 Person-Years Per Bushel

When the firm operates these processes in parallel, it requires
a total of 41/49 Bushels corn as input. The output of the
corn-producing process can replace this input, leaving a net
output of one Bushel corn. Notice that the total inputs of
iron are 20/49 + 3 33/49 = 4 4/49 Tons iron, which is exactly
replaced by the output of Process C. So Table 4 shows a technique
in which 5 45/49 Person-Years labor are used to produce a net
output of one Bushel corn. The firm, when operating this technique
can produce any desired output of corn by scaling both processes
equally.

Table 5 shows the application of the same sort of arithmetic to
the Beta technique. The labor-intensity of the Beta technique is
listed.


TABLE 5: THE BETA TECHNIQUE PRODUCING CORN NET

INPUTS Process D Process A
Labor 3 304/357 Person-Years 1 2/3 Person-Years
Iron 3 59/357 Tons Iron 3 1/3 Tons Iron
Corn 0 Bushels Corn 2/3 Bushel Corn

OUTPUTS 6 178/357 Tons Iron 1 2/3 Bushel Corn

LABOR-INTENSITY: 5 185/357 Person-Years Per Bushel

Neither the Gamma nor the Delta technique are profit-maximizing
for the prices considered below.

4.0 PRICES

Which technique will the firm adopt, if any? The answer
depends, in this analysis, on which is more profitable. So one
has to consider prices. I assume throughout that inputs of iron,
corn, and labor are charged at the start of the year. Corn is
the numeraire; its price is unity throughout. Two different
levels of wages are considered.

4.1 PRICES WITH LOW WAGE

Accordingly, assume wages are initially 3/2780 Bushels per
Person-Year. By assumption, the firm neither buys nor sells iron on
the market. The firm produces iron solely for its own use. Still,
the firm must enter a price of iron on its books. I assume an
initial price of 55/1112 Bushels per Ton.

Table 6 shows accounting with these prices. The column labeled
"cost" shows the cost of the inputs needed to produce one unit
output, a bushel corn or a ton iron, depending on the process.
Accounting profits for a unit output are the difference between
the price of a unit output and this cost. The rate of (accounting)
profits, shown in the last column, is the ratio of accounting
profits to the cost. The rate of profits is independent of
the scale at which each process is operated.

TABLE 6: COSTS, WAGE 3/2780 BUSHELS PER PERSON-YEAR,
PRICE OF IRON 55/1112 BUSHELS PER TON

INDUSTRY PROCESS COST PROFITS

Corn A 2*(55/1112) + (2/5)*1
+ 1*(3/2780) = 1/2 100%
Corn B (1/2)*(55/1112) + (3/5)*1
+ 1*(3/2780) = 6959/11120 60%
Iron C (1/10)*(55/1112) + (1/40)*1
+ 1*(3/2780) = 69/2224 59%
Iron D (113/232)*(55/1112) + 0
+ (275/464)*(3/2780) = 55/2224 100%

These prices are compatible with the use of the Beta technique
to produce a net output of corn. The Beta technique specifies that
Process A be used to produce corn and process D be used to produce
iron. Notice that Process B is more expensive than Process A, and
that process C is more expensive than Process D. These prices do
not provide signals to the firm that processes outside the Beta
technique should be adopted. The vertically-integrated firm is
making a rate of profit of 100% in producing corn with the Beta
technique. The same rate of profits are earned in producing corn
and in reproducing the used-up iron by an iron-producing process.

4.2 ONE SET OF PRICES WITH HIGHER WAGE

Suppose this firm faces a wage more than 20 times higher, namely
109/4040 Bushels per Person-Year. Consider what happens if the firm
doesn't revalue the price of iron on its books. Table 7 shows this
case. Since labor enters into each process, the rate of profits
has declined for all processes. The ratio of labor to the costs of
the other inputs is not invariant across processes. Thus, the
rate of profits has declined more in some processes than in
others. Notice especially, than the rate of profits is no longer
the same in the processes, A and D, that comprise the Beta
technique.

TABLE 7: COSTS, WAGE 109/4040 BUSHELS PER PERSON-YEAR,
PRICE OF IRON 55/1112 BUSHELS PER TON

INDUSTRY PROCESS COST PROFITS

Corn A 2*(55/1112) + (2/5)*1
+ 1*(109/4040) = 0.5259 90.1%
Corn B (1/2)*(55/1112) + (3/5)*1
+ 1*(109/4040) = 0.6517 53.4%
Iron C (1/10)*(55/1112) + (1/40)*1
+ 1*(109/4040) = 0.05693 -13.1%
Iron D (113/232)*(55/1112) + 0
+ (275/464)*(109/4040) = 0.04008 23.4%

This accounting data does not reveal the firm's rate of return
in operating the Beta technique. The firm cannot be simultaneously
making both 23% and 90% in operating that technique. Furthermore,
this data provides a signal to the firm to withdraw from iron
production and make only corn. So this data says that something
must change.

4.3 ANOTHER SET OF PRICES

Perhaps all that is needed is to re-evaluate iron on the
firm's books. Higher wages have made iron more valuable. Table
8 shows costs and the rate of profits when iron is
evaluated at an accounting price of 0.106 Bushels per Ton.


TABLE 8: COSTS, WAGE 109/4040 BUSHELS PER PERSON-YEAR,
PRICE OF IRON 0.10569123726 BUSHELS PER TON

INDUSTRY PROCESS COST PROFITS

Corn A 2*(0.106) + (2/5)*1
+ 1*(109/4040) = 0.6384 56.65%
Corn B (1/2)*(0.106) + (3/5)*1
+ 1*(109/4040) = 0.6798 47.10%
Iron C (1/10)*(0.106) + (1/40)*1
+ 1*(109/4040) = 0.06255 68.97%
Iron D (113/232)*(0.106) + 0
+ (275/464)*(109/4040) = 0.06747 56.65%

This revaluation of iron reveals that the firm makes a rate
of profits of 57% in operating the Beta technique. The firm makes
the same rate of profits in producing corn and in producing its
input of iron. But the manager of the iron-producing process would
soon notice that the cost of operating process C is cheaper.


4.4 FINAL EQUILIBRIUM PRICES

So the firm would ultimately switch to using process C
to produce iron. The price of iron the firm would enter on its
books would fall somewhat. Table 9 shows the accounting with a
price of iron of 10/101 Bushels per Ton. The firm has adopted
the cheapest process for producing iron, and the rate of profits
is the same in both corn-production and iron-production. The
accounting for this vertically-integrated firm is internally
consistent.

TABLE 9: COSTS, WAGE 109/4040 BUSHELS PER PERSON-YEAR,
PRICE OF IRON 10/101 BUSHELS PER TON

INDUSTRY PROCESS COST PROFITS

Corn A 2*(10/101) + (2/5)*1
+ 1*(109/4040) = 5/8 60%
Corn B (1/2)*(10/101) + (3/5)*1
+ 1*(109/4040) = 2553/4040 58%
Iron C (1/10)*(10/101) + (1/40)*1
+ 1*(109/4040) = 25/404 60%
Iron D (113/232)*(10/101) + 0
+ (275/464)*(109/4040) = 24,075/374,912
54%

5.0 CONCLUSIONS

Table 10 summarizes these calculations. The ultimate result of
a higher wage is the adoption of a more labor-intensive technique.
If this firm continues to produce the same level of net output
and maximizes profits, its managers will want to employ more workers
at the higher of the two wages considered.

TABLE 10: PROFIT-MAXIMIZING FIRM ADOPTS MORE LABOR-INTENSIVE
TECHNIQUE AT HIGHER WAGE

LABOR-INTENSITY OF
WAGE CORN-PRODUCING TECHNIQUE

3/2780 Bushels Per Person-Year 5 185/357 Person-Years Per Bushel
109/4040 Bushels Per Person-Year 5 45/49 Person-Years Per Bushel

So much for the theory that wages and employment are determined
by the interaction of well-behaved supply and demand curves on the
labor market.

--
Try http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Bukharin.html
To solve Linear Programs: .../LPSolver.html
r c A game: .../Keynes.html
v s a Whether strength of body or of mind, or wisdom, or
i m p virtue, are found in proportion to the power or wealth
e a e of a man is a question fit perhaps to be discussed by
n e . slaves in the hearing of their masters, but highly
@ r c m unbecoming to reasonable and free men in search of
d o the truth. -- Rousseau

Frank Altschuler

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Oct 13, 2002, 7:49:38 PM10/13/02
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> So much for the theory that wages and employment are determined
> by the interaction of well-behaved supply and demand curves on the
> labor market.

So much for the theory that RV is doing anything but amusing himself in his
off hours.

I love phrases such as "Higher wages have made iron more valuable". Silly
me, I thought that the value of iron had something to do with the uses made
of the iron (cars, waffle irons etc.). I had no idea that increasing the
wages paid for its manufacture increased its value.

But wait! There's more!

RV: "The ultimate result of a higher wage is the adoption of a more


labor-intensive technique. If this firm continues to produce the same level
of net output and maximizes profits, its managers will want to employ more
workers at the higher of the two wages considered."

In the real world when presented with wage demands in excess of market
reality, companies do hire fewer people and invest in productivity tools
(perhaps that's what he meant by the somewhat elliptical phrase
"labor-intensive technique" where he might have been fishing for a phrase
that implied greater productivity). Employers have to make up the
difference between the output they could have achieved by hiring at market
rates and the output they can afford at the new "minimum" or "living" wage.
So far, so good.

But, he then turns around and, forgetting the increased capital investment
that the employer had to make in order to make up the productivity deficit
imposed by increasing wages, assumes that they'd then go into a wild hiring
binge ("managers will want to employ more workers at the higher of the two
wages"). My guess would be that managers will want to move their operations
(and whizzy new labor saving devices) to somewhere where they can get equal
productivity at the lower of the two wages (I don't see anything indicating
that the higher wage employees are in any way more "valuable" than the lower
paid workers, just higher paid.).


David Lloyd-Jones

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Oct 13, 2002, 10:34:27 PM10/13/02
to
Frank Altschuler wrote:

> But wait! There's more!
>

Frank,

You are just frothing at the mouth and disgracing yourself.

You keep referring to "the real world," (presumably your version of it),
when Robert Vienneau's model that you pretend to attack is quite
explicitly not the real world: it is a model, crafted to show a point.

As an aside, I might comment that Vienneau, after a painful but vigorous
five years or so, seems to be showing signs of becoming an economist. I
wish him well in his continuing work -- and suggest that you, Frank,
might take him as a behavioural model.

With best wishes,

-dlj.


David Lloyd-Jones

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Oct 14, 2002, 12:25:14 AM10/14/02
to
David Lloyd-Jones wrote:

> As an aside, I might comment that Vienneau, after a painful but vigorous
> five years or so, seems to be showing signs of becoming an economist. I
> wish him well in his continuing work -- and suggest that you, Frank,
> might take him as a behavioural model.

Let me add a small thing. Robert has a tiresome mode, where he quotes
stuff you've never heard of from the Authority you thought you were
acquainted with. Bleahhhh: low grade show. He wins, but he wins small.

I think his model-making is more impressive, though not yet great. (To
titivate [look it up]: what he does now is what I and my friend Fred
Martin did when we were 14, so it's pretty good, but not yet ready for
prime time.) By "impressive" I mean he is really destructive. His long
boring corn-and-whiskey things really do knock the pins out from under
whoever he's after.

Of people who have attacked Robert, let's say there are two, Chris
whatsisname at Queens/Alberta, and everybody else. My score is Chris has
won maybe 55% to date, but only by painting Robert's areas of ignorance
as frauds. Shows Chris is learning the ways of academic politics, seems
to me. All other attacks on Vienneau have the same or lower scores.

I haven't nailed him once, and G-d knows I would swoop in if I saw the
chance.

In recent months Robert seems to have stopped being a Vulgar Marxist.
(My partner, a strong conservative active in the Sudanese war, thinks
that every bit of Marx I have ever shown her is obviously true. Vulgar
Marxism has many homes.) When I was 13 years old the only thing that
saved me from Marxism was the beauty of Bertrand Russell.... And so it
goes...

As Robert continues his determined reading I think he may grow in
confidence, become lower in antagonism, and -- here's my guess -- become
a teacher to us all.

But I don't think it's happened quite yet.

But-but I think it will.

-dlj.


Robert Vienneau

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Oct 15, 2002, 2:02:12 AM10/15/02
to
In article <mEnq9.82$1Z7.23...@newssvr30.news.prodigy.com>, "Frank
Altschuler" <falts...@sbcglobal.net> wrote:

> > So much for the theory that wages and employment are determined
> > by the interaction of well-behaved supply and demand curves on the
> > labor market.

> [Silliness deleted.]

> I love phrases such as "Higher wages have made iron more valuable".
> Silly
> me, I thought that the value of iron had something to do with the uses
> made
> of the iron (cars, waffle irons etc.). I had no idea that increasing the
> wages paid for its manufacture increased its value.

In my example, the price of "iron" has something to with the uses made
of the "iron", e.g., in the production of "corn". "Iron" in my example
is not iron; "corn" is not corn. They are names of commodities in
the example picked to suggest commodities used exclusively for producing
other commodities and for producing both themselves and for consumption.

> But wait! There's more!

And why are you using that particular phrase?



> RV: "The ultimate result of a higher wage is the adoption of a more
> labor-intensive technique. If this firm continues to produce the same
> level
> of net output and maximizes profits, its managers will want to employ
> more
> workers at the higher of the two wages considered."

> In the real world when presented with wage demands in excess of market
> reality, companies do hire fewer people and invest in productivity tools
> (perhaps that's what he meant by the somewhat elliptical phrase
> "labor-intensive technique" where he might have been fishing for a phrase
> that implied greater productivity).

No. Assertions about "reality" don't make it so. A famous study of
natural experiments a few years back came up with no such result.

My example is of a firm choosing among known processes for producing
output. It does not include R&D, which results in new technology.

I explain what I mean by "technique" and "labor intensity" in the
post to which Frank is pretending to respond. The technique
with higher labor intensity has lower (net) output per worker.
So his comment is exactly backwards.

> Employers have to make up the
> difference between the output they could have achieved by hiring at
> market
> rates and the output they can afford at the new "minimum" or "living"
> wage.

Why would the level of net output in my example be affected by the
level of wages?

> So far, so good.

> But, he then turns around and, forgetting the increased capital
> investment
> that the employer had to make in order to make up the productivity
> deficit
> imposed by increasing wages, assumes that they'd then go into a wild
> hiring
> binge ("managers will want to employ more workers at the higher of the
> two
> wages").

Nope. I assume no such thing. I derive the increased employment,
given the level of net output, from the assumptions of
profit-maximization and known technology. It's a matter of
arithmetic.

What I actually wrote was:

"If this firm continues to produce the same level of net output
and maximizes profits, its managers will want to employ more workers
at the higher of the two wages considered."

> My guess would be that managers will want to move their

> operations
> (and whizzy new labor saving devices) to somewhere where they can get
> equal
> productivity at the lower of the two wages (I don't see anything
> indicating
> that the higher wage employees are in any way more "valuable" than the
> lower
> paid workers, just higher paid.).

In my example, all workers are paid whatever the wage is. So the above
comment makes no sense.

Certainly one of my assumptions is unrealistic in Frank's case. I
assumed a reader able and willing to follow arithmetic.

Robert Vienneau

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Oct 16, 2002, 6:39:42 PM10/16/02
to
In article <aok9at$23b$1...@nntp.itservices.ubc.ca>, JT
<ji...@interchange.ubc.ca> wrote:

> : The data above allow for the specification of two well-behaved


> : production functions, one for corn and the other for iron. For
> : illustration, I outline how to construct the production function
> : for corn.

[>: Accordingly, the production ]


[>: function for corn is found as the solution to the Linear Program ]
[>: in Display 1: ]
[>: ]
[>: Max X = X1 + X2 ]
[>: ]
[>: 2*X1 + (1/2)*X2 <= Q1 ]
[>: (2/5)*X1 + (3/5)*X2 <= Q2 (1) ]
[>: X1 + X2 <= L ]
[>: ]
[>: X1 >= 0, X2 >= 0 ]

> : Let X = f(Q1, Q2, L) be the solution of this LP, that is, the
> : production function for corn. (This production function is not
> : Leontief.)

> The production function is only non-Leontief because you have forced the
> firm to start with a non-optimal input bundle.

That comment makes no sense to me. Do you deny that the production
function (for corn) is the solution to the above LP? You will notice
that the input bundle (L, Q1, Q2) can be any given triple with
non-negative elements.

> Given prices for all the
> inputs, the firm would generally only opt to use one of the two production
> technologies.

I assume you mean by a "technology" what I have been calling a "process".
I suspect you are confused on the role of prices here.

In other words, although you are correct in saying that the
production function for corn is non-Leontief, your explanation
of why seems like nonsense to me.

> Inputs would then be choosen accordingly and only one
> process would be used.

The above is certainly not true. Sometimes the solution to the above
LP consists of a linear combination of the two processes.

For example, suppose the inputs into (non-vertically) integrated
corn-production are 3 Person-Years, 3 Tons Iron, and 1 Bushel Corn.
Using the program in my sig, you can find that Process A will
be used to produce 13/10 Bushels Corn and Process B will be
used to produce 4/5 Bushels Corn. Thus, the production function
for corn, evaluated at these inputs, yields 21/10 Bushels Corn.

[>: assume wages are initially 3/2780 Bushels per ]


> : Person-Year. By assumption, the firm neither buys nor sells iron on
> : the market. The firm produces iron solely for its own use. Still,
> : the firm must enter a price of iron on its books. I assume an
> : initial price of 55/1112 Bushels per Ton.

> This is not an innocuous assumption. Why doesn't the firm outsource
> iron?

If the firm were to outsource iron, the market price of iron
would have to be as in my example for an "equilibrium" to be
established. Equilibrium, in this context, means firms engaged
in iron-production would not find that they could make more
profit by disinvesting in iron-production and investing in
corn-production. Likewise firms in corn-production would not
find they can make more by disinvesting in corn-production
and investing in iron-production. Furthermore, no firm is
operating a process in which they make a loss. And there
are no unoperated processes that are cheaper to operate
for producing a produced commodity than the processes
actually in operation.

> And what possible justification can you offer for the price of
> steel that you have picked? Your concept of profits becomes meaningless
> when the price of inputs is choosen arbitrarily by the firm.

I find your comment unclear. Either the initial price is chosen
arbitrarily by the firm, in which case they could set it to whatever
they like (e.g., 55/1112 Bushels per Ton) or the initial price is
not an innocuous choice by the analyst.

As a matter of fact, I chose the initial price of iron
so that the firm would be making the same rate of profits
in both iron and corn production when operating the
initial technique. Perhaps you might consider how Table 6
in my original post is constructed.

--------- From my initial post -----------------------

INDUSTRY PROCESS COST PROFITS

----------- End quote from my initial post --------

> We are not
> talking about transfer pricing here,

Well, I did not bring up transfer pricing.

> when multinationals attempt to pick
> the price of intermediate inputs for the purpose of tax arbitrage across
> several jurisdictions. There are real resource costs to producing
> iron...

My example shows iron being priced in a rational way.

REFERENCE:

H. D. Kurz and N. Salvadori, Theory of Production: A Long-Period
Analysis. Cambridge University Press, 1995.

JT

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Oct 16, 2002, 10:00:29 PM10/16/02
to
On Wed, 16 Oct 2002 18:39:42 -0400, Robert Vienneau
<rv...@see.sig.com> wrote:


>
>> : Let X = f(Q1, Q2, L) be the solution of this LP, that is, the
>> : production function for corn. (This production function is not
>> : Leontief.)
>
>> The production function is only non-Leontief because you have forced the
>> firm to start with a non-optimal input bundle.
>
>That comment makes no sense to me. Do you deny that the production
>function (for corn) is the solution to the above LP? You will notice
>that the input bundle (L, Q1, Q2) can be any given triple with
>non-negative elements.

You are answering the wrong question. A profit maximizing firm would
first calculate the cost of each production process given the price of
inputs. This is no different than what you have done in Table 6.
Depending on the cost, the firm chooses to produce using the cheaper
of the two. Inputs are then purchased in accordance with the ratios
defined by the process.

You instead have the firm arbitrarily buying inputs, without any
consideration of cost minimization, and then trying to maximize
output. This is nonsense.

Otherwise, you aren't really presenting an economics model here, but
rather just a series of production matrices. Without introducing
markets, this is a meaningless exercise; assumptions about market
structure will allow you to determine how prices are determined.

In any case models already exist in mainstream economics where
employment increases with the wage rate. One such model is the
monopsony/minimum wage model which is frequently presented in
introductory economics texts...

Robert Vienneau

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Oct 17, 2002, 5:13:04 AM10/17/02
to
In article <695squk7ec3467crb...@4ax.com>, JT
<ji...@nospam.interchange.ubc.ca> wrote:

> On Wed, 16 Oct 2002 18:39:42 -0400, Robert Vienneau
> <rv...@see.sig.com> wrote:

The data... allow for the specification of two well-behaved


production functions, one for corn and the other for iron. For

illustration, I outline how to construct the production function
for corn.

The production


function for corn is found as the solution to the Linear Program
in Display 1:

Max X = X1 + X2

2*X1 + (1/2)*X2 <= Q1
(2/5)*X1 + (3/5)*X2 <= Q2 (1)
X1 + X2 <= L

X1 >= 0, X2 >= 0

> >> : Let X = f(Q1, Q2, L) be the solution of this LP, that is, the


> >> : production function for corn. (This production function is not
> >> : Leontief.)

> >> The production function is only non-Leontief because you have forced
> >> the
> >> firm to start with a non-optimal input bundle.

> >That comment makes no sense to me. Do you deny that the production
> >function (for corn) is the solution to the above LP? You will notice
> >that the input bundle (L, Q1, Q2) can be any given triple with
> >non-negative elements.

> You are answering the wrong question.

No. You are babbling non-responsive balderdash.

Do you deny that the production function (for corn) is the
solution to the above LP? You will notice that the input bundle
(L, Q1, Q2) can be any given triple with non-negative elements.

You will notice that the arguments to a production function
are not prices.

An answer to the above question would start off with either "No"
or "Yes"...

> A profit maximizing firm would
> first calculate the cost of each production process given the price of
> inputs. This is no different than what you have done in Table 6.
> Depending on the cost, the firm chooses to produce using the cheaper
> of the two. Inputs are then purchased in accordance with the ratios
> defined by the process.

At this point, I am not concerned with (economic) profit maximization.
I am concerned with how the production function is constructed from
the data in my example.

> You instead have the firm arbitrarily buying inputs, without any
> consideration of cost minimization, and then trying to maximize
> output. This is nonsense.

The production function for corn, f(L, Q1, Q2), shows how much
corn can be produced with the given inputs. That is what the above
LP shows.

If you think that the production function for corn is something
else, perhaps you can outline how to construct it. It would be
nice if your outline did not yield the nonsensical conclusion that
all production functions are "only non-Leontief because [I] have


forced the firm to start with a non-optimal input bundle".

You might also show some appreciation of duality theory.



> Otherwise, you aren't really presenting an economics model here, but
> rather just a series of production matrices.

I am illustrating models long since established.

> Without introducing
> markets,

My example contains markets. But that is irrelevant to how the
production function is constructed.

> this is a meaningless exercise; assumptions about market
> structure will allow you to determine how prices are determined.

The assumption is that the markets in my example are competitive.



> In any case models already exist in mainstream economics where
> employment increases with the wage rate. One such model is the
> monopsony/minimum wage model which is frequently presented in
> introductory economics texts...

Why should I care?

Many introductory economics textbooks present nonsense for the
case of perfect competition. My example makes that point.

I am not concerned here with overlays to that nonsense, where
those overlays involve elements of market imperfections, information
assymmetries, income effects, etc. On the other hand, you seem
to want to change the subject.

Is the example with which I started this thread correct?

JT

unread,
Oct 17, 2002, 9:56:23 AM10/17/02
to
On Thu, 17 Oct 2002 05:13:04 -0400, Robert Vienneau
<rv...@see.sig.com> wrote:

>> You are answering the wrong question.
>
>No. You are babbling non-responsive balderdash.
>
>Do you deny that the production function (for corn) is the
>solution to the above LP? You will notice that the input bundle
>(L, Q1, Q2) can be any given triple with non-negative elements.
>You will notice that the arguments to a production function
>are not prices.
>
>An answer to the above question would start off with either "No"
>or "Yes"...

Yes, I am. The firm picks the lowest cost process. The production
function is then either

C=min(L,10C,40I)

or

C=min(464/275L,232/113I)

which are both Leotief processes...

>You might also show some appreciation of duality theory.

You might want to learn something about the theory of the firm. A
cost minimizing firm will generally use only one of the two processes.


>
>My example contains markets. But that is irrelevant to how the
>production function is constructed.

Not at all. As I said before, firms will choose the lower cost
process.


>The assumption is that the markets in my example are competitive.

Which, with fully stipulated markets and factor supplies, would drive
profits to zero. So your profit rates are drivel. I think your are
either a troll or someone who wants to attack the mainstream with a
little understanding of linear programming and not even the slightest
grasp of basic microeconomic thoery.

PLONK!

Dan Parker

unread,
Oct 17, 2002, 1:51:36 PM10/17/02
to
"David Lloyd-Jones" <dlloy...@rogers.com> wrote in message
news:T2qq9.239767$8b1.1...@news01.bloor.is.net.cable.rogers.com...

What if Frank prefers investigating and problem solving in
the real world? Even as a matter of efficiency, it would seem
far more utile, and maybe more fun, to indulge in massive
amounts of mind altering drugs than to study the details
of mainstream economics. The end result, as far as engaging
in productive behaviour, would be similar.

dp
>
> With best wishes,
>
> -dlj.
>
>


David Lloyd-Jones

unread,
Oct 17, 2002, 3:18:13 PM10/17/02
to
Dan Parker asks:

> What if Frank prefers investigating and problem solving in
> the real world?

He might want to stay away from a discussion of models. Then again he
might want to use models as a way of understanding the real world.
Either way, I think it might be a good idea to keep straight in his
mind, and in his writing, which is supposed to be which.

> Even as a matter of efficiency, it would seem
> far more utile, and maybe more fun, to indulge in massive
> amounts of mind altering drugs than to study the details
> of mainstream economics. The end result, as far as engaging
> in productive behaviour, would be similar.

A frequent and rather dopey sort of remark made in disparagement of
economics. Funny thing is, most people who disparage "mainstream
economics" are themselves followers of various ululating cults:
protectionism, subsidies to the useless, training of the inapt, and so on.

-dlj.

James A. Donald

unread,
Oct 17, 2002, 6:07:56 PM10/17/02
to
Robert Vienneau

> Do you deny that the production function (for corn) is the
> solution to the above LP?

If each producer is himself free to use the lowest cost technology for
roduction of corn, he is not going to produce corn according to your
LP, so absent men with batons and guns standing over the kulaks, the
production function for corn, as Lenin found, is not going to follow
your LP.

Your model does not depict a free market economy, since the production
costs are never in equilibrium.

I make the same comment as I always make about your calculations.
Your argument is merely the standard totalitarian argument that
capitalism is already a centrally planned economy, and you can plan
the kulaks lives
as well as the next guy, and will be more benevolent in doing so.

Robert Vienneau

unread,
Oct 17, 2002, 6:57:35 PM10/17/02
to
In article <qrftqu8mpffmpdjq8...@4ax.com>, JT
<ji...@nospam.interchange.ubc.ca> wrote:

I answer this nonsense even though JimT indicates he's stopped
reading. Maybe somebody will be amused.

--- Begin Extract From Original Post ----------------------

The data... allow for the specification of two well-behaved
production functions, one for corn and the other for iron. For
illustration, I outline how to construct the production function
for corn.

The production function for corn is found as the solution to the
Linear Program in Display 1:

Max X = X1 + X2

2*X1 + (1/2)*X2 <= Q1
(2/5)*X1 + (3/5)*X2 <= Q2 (1)
X1 + X2 <= L

X1 >= 0, X2 >= 0

---------------- End Extract ---------------------------------------

> >Do you deny that the production function (for corn) is the
> >solution to the above LP? You will notice that the input bundle
> >(L, Q1, Q2) can be any given triple with non-negative elements.
> >You will notice that the arguments to a production function
> >are not prices.

> >An answer to the above question would start off with either "No"
> >or "Yes"...

> Yes, I am. The firm picks the lowest cost process. The production
> function is then either
>
> C=min(L,10C,40I)
>
> or
>
> C=min(464/275L,232/113I)
>
> which are both Leotief processes...

The above is silly. First, it does not specify a production funtion.
Second, it is using the coefficients from the iron-producing processes,
not the corn-producing processes. Third, it presents an assertion
about Leontief PROCESSES as if it is contradicting a correct assertion
I made about how the production FUNCTION was not Leontief.

I'll go through a specific example that shows my respondent to
be simply incorrect.

First, from my original post, the coefficients for the processes
for producing corn are:


TABLE 1: INPUTS REQUIRED PER TON CORN PRODUCED

Process A Process B

1 Person-Year 1 Person-Year
2 Tons Iron 1/2 Tons Iron
2/5 Bushels Corn 3/5 Bushels Corn

So by JimT's "logic"

> The production function [for corn] is then either

X = min(L, (1/2) Q1, (5/2) Q2)

> or

X = min(L, 2 Q1, (5/3) Q2 )

> which are both Leotief processes...

where X is the Bushels Corn produced, L is the (direct) labor
input, Q1 is the iron input, and Q2 is the corn input.

Next, again consider inputs of 3 Person-Years, 3 Tons Iron, and 1
Bushel Corn. What is output? JimT's logic says, it is either 3/2
Bushels Corn or 5/3 Bushels Corn. Which answer is correct? JimT
gives no way of deciding.

Well, both are wrong, as I have previously pointed out. Suppose
Process A is used to produce 13/10 Bushels Corn and Process B
is used to produce 4/5 Bushels Corn. Readers, if any, can check
that these outputs will not require more inputs of any good
than are available (some labor will not be used). So I say
that output is 4/5 + 13/10 = 21/10 Bushels Corn. This exceeds
either of JimT's non-answers.

So JimT is claiming that firms will not produce as much as they
can, that profit-maximizing firms will willingly and knowingly
leave 100 dollar bills on the pavement.



> >You might also show some appreciation of duality theory.

> You might want to learn something about the theory of the firm. A
> cost minimizing firm will generally use only one of the two processes.

Who knows what JimT means by "generally"? He's probably
simply wrong. It is not the case that the firm will choose
a linear combination of the two processes only for a set
of measure zero in the set of factor prices.

Anyway, let me display that the cost-minimizing firm can choose
the linear combination of processes that I specified above. (This
requires knowledge of Linear Programming to follow.)

I here use a different concept of prices and cost-minimization
than in my original post. (I could explain how these two
different concepts are related, but that would take more time
than I would expect my readers, if any, would want to see in this
post.)

One should no longer think of iron and corn inputs as having been
previously produced. The corn output is a completely different
commodity than the corn input. The inputs are now just
given in quantity; they are like given natural resources. We
are not considering a vertically-integrated firm that has
adapted its produced inputs to be in the proper proportions
(e.g., as in Marshall's long run equilibrium).

Recall, the LP I was considering, where I have reordered
the constraints and substituted in the specific numeric
values for inputs:

Max X = X1 + X2

X1 + X2 <= 3
2*X1 + (1/2)*X2 <= 3
(2/5)*X1 + (3/5)*X2 <= 1

X1 >= 0, X2 >= 0

It's a standard result in Linear Programming that the dual
problem is:

Min C = 3 w1 + 3 w2 + w3

w1 + (1/2) w2 + (3/5) w3 >= 1
w1 + 2 w2 + (2/5) w3 >= 1

w1 >= 0, w2 >= 0, w3 >= 0

where C is the total cost and w1, w2, and w3 are shadow
prices for labor, iron-input, and corn-input, respectively.
The solution shadow prices are:

w1 = 0 Bushels per Person-Year
w2 = 1/5 Bushels Per Ton
w3 = 3/2 Produced Bushels Per Input Bushel

Notice that the minimized cost here is 21/10 Produced Bushels Corn,
which matches the quantity output. So this solution shows the
total output allocated to economic rents for the "factors".

Put aside that this is a model of central planning; pretend it
is about competitive markets. Notice that both constraints are
met with equality. This implies, contrary to JimT's assertion,
that both processes will be used by a cost-minimizing competitive
firm facing these factor prices.

Furthermore, note that my original LP for constructing the
production function for corn is indeed a correct way of
constructing the production function for corn; it is
dual to this way of thinking about cost-minimization, where
this is different than in my original post and contrary to
the characteristics of corn and iron.

> >My example contains markets. But that is irrelevant to how the
> >production function is constructed.

> Not at all. As I said before, firms will choose the lower cost
> process.

Which, in the price structure I originally presented, has nothing
to do with the construction of the production functions.

> >The assumption is that the markets in my example are competitive.

> Which, with fully stipulated markets and factor supplies, would drive
> profits to zero. So your profit rates are drivel.

As usual, the above is, at least, based on a misrepresentation
of my posts. In the theory, PURE ECONOMIC profits are zero. I
specifically stated in my original post that my table was talking
about ACCOUNTING profits. Accounting profits need not be zero in
the theory of perfect competition.

--- Begin Another Extract From Original Post ----------------------

Table 6 shows accounting with these prices. The column labeled
"cost" shows the cost of the inputs needed to produce one unit
output, a bushel corn or a ton iron, depending on the process.
Accounting profits for a unit output are the difference between
the price of a unit output and this cost. The rate of (accounting)
profits, shown in the last column, is the ratio of accounting
profits to the cost. The rate of profits is independent of
the scale at which each process is operated.

TABLE 6: COSTS, WAGE 3/2780 BUSHELS PER PERSON-YEAR,
PRICE OF IRON 55/1112 BUSHELS PER TON

INDUSTRY PROCESS COST PROFITS

Corn A 2*(55/1112) + (2/5)*1
+ 1*(3/2780) = 1/2 100%
Corn B (1/2)*(55/1112) + (3/5)*1
+ 1*(3/2780) = 6959/11120 60%
Iron C (1/10)*(55/1112) + (1/40)*1
+ 1*(3/2780) = 69/2224 59%
Iron D (113/232)*(55/1112) + 0
+ (275/464)*(3/2780) = 55/2224 100%

---------------- End Extract ---------------------------------------

> I think your are
> either a troll or someone who wants to attack the mainstream with a
> little understanding of linear programming and not even the slightest
> grasp of basic microeconomic thoery.

> PLONK!

Actually, what I am saying is standard theory among those
(apparently few) economists who are well-educated in price
theory.

But hey, you might as well killfile those who don't share your
conceptual confusion and inability or unwillingness to do
arithmetic.

Robert Vienneau

unread,
Oct 17, 2002, 7:04:35 PM10/17/02
to
In article <96dc81b9.02101...@posting.google.com>,
jam...@echeque.com (James A. Donald) wrote:

> Robert Vienneau
> > Do you deny that the production function (for corn) is the
> > solution to the above LP?

> If each producer is himself free to use the lowest cost technology for
> roduction of corn, he is not going to produce corn according to your
> LP, so absent men with batons and guns standing over the kulaks, the
> production function for corn, as Lenin found, is not going to follow
> your LP.

The bit about the LP defining the production function was an aside
in my original post. The analysis of prices in my original post
was a description of producers free to use (and using) the
lowest cost method(s) for production of corn. The remainder of
James' comment above also bears no rational relation to anything
I posted in this thread, at least in the spatial-temporal
dimension the rest of us inhabit.



> Your model does not depict a free market economy, since the production
> costs are never in equilibrium.

I made no claim that anything would ever be in equilbrium in any
"free market" economy.

> I make the same comment as I always make about your calculations.
> Your argument is merely the standard totalitarian argument that
> capitalism is already a centrally planned economy, and you can plan
> the kulaks lives
> as well as the next guy, and will be more benevolent in doing so

But the posts I posted, at least in the spatial-temporal everybody
other than James inhabits, did not argue that capitalism is
already a centrally planned economy.

Dan Parker

unread,
Oct 17, 2002, 9:02:14 PM10/17/02
to

"David Lloyd-Jones" <dlloy...@rogers.com> wrote in message
news:3DAF0CD2...@rogers.com...

>
> > Even as a matter of efficiency, it would seem
> > far more utile, and maybe more fun, to indulge in massive
> > amounts of mind altering drugs than to study the details
> > of mainstream economics. The end result, as far as engaging
> > in productive behaviour, would be similar.
>
> A frequent and rather dopey sort of remark made in disparagement of
> economics.

Can you direct me to the sources of this frequent remark?
And yes dope would be involved.

>Funny thing is, most people who disparage "mainstream
> economics" are themselves followers of various ululating cults:

This reads like those who believe in mainstream economics are
followers of one of the various ululating cults. Which would be
the truth.

In any case, what you have remarked on is a dynamic
that is obvious in any time of change when the old system
is wearing out. There are many who flail about for other
ways, once the corruption of the current system becomes
obvious. There are also many, including people with the
highest professional credentials, who present thoughtful
alternatives.

> protectionism, subsidies to the useless, training of the inapt, and so on.

Like mainstream economics again. Which leaves the thoughtful
alternative analyses the way of the future. If you ever want to make
yourself useful, you'd give up the guard dog routine for some
work in this field :-).

About 95% of money is created as debt, at compound interest.
Even bankers now will admit that they create the money, and
that yes, the loans are at compound interest. Compound interest
is positive feedback. That is, it graphs exponentially. So according
to the most basic math, what can be proven by the official figures,
and which the bankers will admit to, the system must be one of
lunatic instability.

I'm sorry I don't have as much time to spend on newsgroups as
I would like, so I'll post a link here for others seeking some
answers about how to develop viable alternatives.

http://www.socialcredit.com/links.htm

dp


>
> -dlj.
>


JT

unread,
Oct 18, 2002, 1:03:14 AM10/18/02
to
On Thu, 17 Oct 2002 18:57:35 -0400, Robert Vienneau
<rv...@see.sig.com> wrote:

You should have presented the dual in the first place. I can finally
guess at what you are trying to do.

>Recall, the LP I was considering, where I have reordered
>the constraints and substituted in the specific numeric
>values for inputs:
>
> Max X = X1 + X2
>
> X1 + X2 <= 3
> 2*X1 + (1/2)*X2 <= 3
> (2/5)*X1 + (3/5)*X2 <= 1
>
> X1 >= 0, X2 >= 0
>
>It's a standard result in Linear Programming that the dual
>problem is:
>
> Min C = 3 w1 + 3 w2 + w3
>
> w1 + (1/2) w2 + (3/5) w3 >= 1
> w1 + 2 w2 + (2/5) w3 >= 1
>
> w1 >= 0, w2 >= 0, w3 >= 0
>

This is *not* the dual for a competitive firm. By assumption, the
competitive firm takes prices as *given* and chooses outputs
accordingly to minimize costs. You are taking the inputs as given and
letting the firm choose the prices to minimize the cost. I'll let you
figure out what the right linear programming function is. One hint;
the correct function to minimize is

min c= w1C+w2I + w3L

where w1 is the price of corn, etc.
One constraint involves specifying the amount of output; typically
this is set to one. The firm can alway scale inputs accordingly later
to increase/decrease output. The solution involves finding the
correct ratio of inputs (C,I,L). This is not inconsistent with the
program you have set out above. However, for most price combinations,
the firm will only pick a vector of inputs (C,I,L) such that the
solution to the problem that you have written down will involve either
X1=0 or X2=0. As the firm chooses the inputs optimally, there will be
none of the waste that you demonstrate in your counter example.

My guess is that you are using the First Welfare Theorem, which states
that under a certain set of conditions, the solution to the social
planner's problem is the same as the outcome of a decentralized
economy. In this case, if the economy-wide beginning of period
endowments of inputs were the values you gave, then I guess that the
market clearing prices could indeed be the same as the shadow prices
that you present. For this set of prices, a linear combination of the
two techniques would indeed be used (or at least I am guessing,
without further consideration.).

What I fail to see is how your example in any way supports your
grandiose claim

>So much for the theory that wages and employment are determined
>by the interaction of well-behaved supply and demand curves on the
>labor market.

By your own assessment, the wage rate (shadow price) of labour will
only change when the initial vector (supply) of available inputs
changes (see your linear program above). In a dynamic context, the
beginning of period inputs are not random. You may want to think
about the Marshallian steady state.


JT

unread,
Oct 18, 2002, 1:43:51 AM10/18/02
to
On Fri, 18 Oct 2002 00:03:14 -0500, JT
<ji...@nospam.interchange.ubc.ca> wrote:


>This is *not* the dual for a competitive firm. By assumption, the
>competitive firm takes prices as *given* and chooses outputs
>accordingly to minimize costs.

Sorry, that should have read "chooses inputs"...

Christopher Auld

unread,
Oct 18, 2002, 12:28:14 PM10/18/02
to
Robert Vienneau <rv...@see.sig.com> wrote:


>Who knows what JimT means by "generally"? He's probably
>simply wrong. It is not the case that the firm will choose
>a linear combination of the two processes only for a set
>of measure zero in the set of factor prices.

>The solution shadow prices are:


>
> w1 = 0 Bushels per Person-Year
> w2 = 1/5 Bushels Per Ton
> w3 = 3/2 Produced Bushels Per Input Bushel

>Notice that the minimized cost here is 21/10 Produced Bushels Corn,
>which matches the quantity output. So this solution shows the
>total output allocated to economic rents for the "factors".

>Put aside that this is a model of central planning; pretend it
>is about competitive markets. Notice that both constraints are
>met with equality. This implies, contrary to JimT's assertion,
>that both processes will be used by a cost-minimizing competitive
>firm facing these factor prices.

In RV's notation, the cost to produce one unit of corn using
process 1 is

C1 = w1 + 2w2 + (2/5)w3,

and using process 2,

C2 = w1 + (1/2)w2 + (3/5)w3.

Since everything is linear, the firm will either choose process
1, process 2, or a be indifferent over which process to use,
contrary to RV's wild-eyed and lamentably incorrect assertions.
Equating C1 and C2 shows the firm will be indifferent iff

w2 (2/5 - 3/5) 2
-- = ----------- = --.
w3 (2 - 1/2) 15

Notice that the ratio of the shadow prices in the solution to
RV's (pointless) programming problem is 2/15.

Isoquants in (iron, corn) space with this technology are kinked
straight lines. The reason RV is able to show that there are
bundles of inputs such that the firm prefers to use a linear
combination of the processes is simply that he's chosen a bundle
of inputs that isn't "on" either process, ie, it would be wasting
inputs if the firm were forced to use only one of the two Leontief
technologies it has available. But of course the incorrectly
maligned JimT is quite correct when he notes that such a bundle
will generally never be chosen by a competitive cost-minimizing
firm, and if it is the case that such a bundle is optimal (which
only happens for a set of measure zero of factor prices), then it
is also the case that there exists a continuum of other input
bundles which produce the same output for the same cost. The
firm never strictly prefers to use both processes.


>But hey, you might as well killfile those who don't share your
>conceptual confusion and inability or unwillingness to do
>arithmetic.

Oh my, RV should probably not make such remarks, given his
ongoing inability to get freshman-level maths (we won't even
discuss freshman level economics) correct. Possibly RV wouldn't
make such mistakes if he would just copy the algebra of the
models he's for some reason been spamming the net with o' these
many years rather than insisting on turning them into tedious
numerical examples.

Incidentally, wages and employment in RV's model are determined
by... supply and demand (although perfect competition + constant
returns to scale make the model pretty much pointless). The
positive relation between wages and employment RV shows can obtain
does not constitute an example of an upward-sloping labor demand
schedule. Many people have explained this to RV over many years.

--
Chris Auld
Department of Economics
University of Calgary
au...@ucalgary.ca

James A. Donald

unread,
Oct 18, 2002, 5:44:00 PM10/18/02
to
--

On Thu, 17 Oct 2002 19:04:35 -0400, Robert Vienneau
<rv...@see.sig.com> wrote:
> The bit about the LP defining the production function was an
> aside in my original post. The analysis of prices in my
> original post was a description of producers free to use (and
> using) the lowest cost method(s) for production of corn.

No it is not. You call it that, but your model describes a
planned economy in which individual producers do not get to
choose.

--digsig
James A. Donald
6YeGpsZR+nOTh/cGwvITnSR3TdzclVpR0+pr3YYQdkG
YQG3IbRIpL0JxJAIR+DogeVUv9WdUOejq3RvT30K
4t/2AJNC2Q3dPvixBjKcqsR5zIyEhbHm9TYhxbDOl


Robert Vienneau

unread,
Oct 18, 2002, 5:42:33 PM10/18/02
to
In article <gt2vqusgeqigo6go5...@4ax.com>, JT
<ji...@nospam.interchange.ubc.ca> wrote:

> On Thu, 17 Oct 2002 18:57:35 -0400, Robert Vienneau
> <rv...@see.sig.com> wrote:

> You should have presented the dual in the first place. I can finally
> guess at what you are trying to do.

I doubt it.



> >Recall, the LP I was considering, where I have reordered
> >the constraints and substituted in the specific numeric
> >values for inputs:
> >
> > Max X = X1 + X2
> >
> > X1 + X2 <= 3
> > 2*X1 + (1/2)*X2 <= 3
> > (2/5)*X1 + (3/5)*X2 <= 1
> >
> > X1 >= 0, X2 >= 0
> >
> >It's a standard result in Linear Programming that the dual
> >problem is:

I have changed the notation:

> > Min C = 3 w0 + 3 w1 + w2
> >
> > w0 + (1/2) w1 + (3/5) w2 >= 1
> > w0 + 2 w1 + (2/5) w2 >= 1
> >
> > w0 >= 0, w1 >= 0, w2 >= 0

where C is the total cost and w0, w1, and w2 are shadow


prices for labor, iron-input, and corn-input, respectively.

> This is *not* the dual for a competitive firm.

The above comment is silly. It is a mathematical fact that the
above two LPs are duals. This has nothing to do with the
semantics, that is, with what sort of model(s) these problems
are used to describe.

> By assumption, the
> competitive firm takes prices as *given* and chooses outputs
> accordingly to minimize costs. You are taking the inputs as given and
> letting the firm choose the prices to minimize the cost.

No. I have outlined a Linear Program whose solution is the production
function for corn. Since the arguments of production functions are
inputs, the quantities of inputs are taken as given in the statement
of this production function. I have noted, correctly, that the
decision variables in the dual problem are shadow prices of
factor inputs. As I explain below, the economy, in the theory, solves
for these prices. It is as if the economy is a giant computer, to use
a well-established metaphor.

I never asserted that a firm would solve the dual LP.

> I'll let you
> figure out what the right linear programming function is. One hint;
> the correct function to minimize is

> min c= w1C+w2I + w3L

In my notation, the objective function for the dual is

Minimize w0 L + w1 * Q1 + w2 * Q2

I can only wonder if JimT has been reading my posts, since he
presents his repetition of what I argued as if it is in contrast
to my posts. And since I had already established the notation
(L, Q1, Q2), why doesn't he use it?

I am quite aware of how to formulate other LPs relevant to my
example, thank you very much.

> One constraint involves specifying the amount of output; typically
> this is set to one. The firm can alway scale inputs accordingly later
> to increase/decrease output. The solution involves finding the
> correct ratio of inputs (C,I,L). This is not inconsistent with the
> program you have set out above. However, for most price combinations,
> the firm will only pick a vector of inputs (C,I,L) such that the
> solution to the problem that you have written down will involve either
> X1=0 or X2=0.

What prices the firm faces is not random, given endowments, in the
theory.

> As the firm chooses the inputs optimally, there will be
> none of the waste that you demonstrate in your counter example.

The only "waste" I demonstrate is in JimT's unargued assertion that
"generally" the production function for corn is formed from only
one of the corn-producing processes, not a linear combination
of them. It would be wasteful to use only one production process
for producing corn when the inputs into corn production are

3 Person-Years, 3 Tons Iron, and 1 Bushel Corn.

Naturally, JimT has yet to clarify what he means by "generally"
or this muddled statement:

"The production function is only non-Leontief because you have
forced the firm to start with a non-optimal input bundle."

The arguments to a production function are input quantities.

About the only sense I could see in arguing that the production
functions in my example are Leontief is to say that one doesn't
call production functions only of this form "Leontief":

X = min ( Q0/a0j, Q1/a1j, ..., Qn/anj )

Rather one might be willing to call "Leontief" the production
functions in my example. A better name might be something like
"generalized Leontief" production functions.



> My guess is that you are using the First Welfare Theorem, which states
> that under a certain set of conditions, the solution to the social
> planner's problem is the same as the outcome of a decentralized
> economy. In this case, if the economy-wide beginning of period
> endowments of inputs were the values you gave, then I guess that the
> market clearing prices could indeed be the same as the shadow prices
> that you present. For this set of prices, a linear combination of the
> two techniques would indeed be used (or at least I am guessing,
> without further consideration.).

It is a matter of fairly basic ideas in microeconomics, I thought.

Consider a simple economy in which all outputs are produced
directly from various natural resources. Call these resources,
counter-intuitively, labor, iron, and seed corn. There are no
capital goods. Suppose that consumers have no desire to consume
resources directly. (This assumption allows one to abstract from
reservation demand.)

Suppose the economy produces one consumption good. Then
competitively maximizing firms, supposedly, would result in
the solution of the LPs that I gave. That is, an equilibrium
of the firms would result in each process being operated at
the level found as a solution of the primal LP. The equilibrium
rental rates for the factor inputs would be the shadow prices
found as a solution of the dual LP.

If there were more than one consumption good, the output
prices would appear in the objective function for the prime
and in the right-hand-side of the dual. These output prices
are parameters in this model of production.

Here's a nice theorem about this sort of model:

If a constraint is met with inequality in the solution of the
primal LP (i.e., a factor is in excess supply), the
corresponding shadow price will be zero in the solution to
the dual LP. If a constraint is met with inequality in the
solution of the dual LP (i.e., a process costs more to operate
than the value of its output), it will not be operated in the
solution to the primal LP.

Thus, the shadow price for labor is zero in the specific solution
I calculated, since labor turned out to be in excess supply in the
vector of input quantities I gave.

Now in this sort of model, input quantities are whatever they
are. It would be ad hoc to impose any sort of constraints on
ratios for inputs. If you think about isoquants in quantity
space, I think you can see that the solution will generally
involve operating linear combinations of processes. If you
have some sort of probability distribution for the quantities
of inputs, the probability measure for the corresponding
distribution in the space of factor prices will be positive
for those price ratios in which profit-maximizing firms
adopt a linear combination of processes. At least I think
that's true.

So I don't know why one would say "generally" only one process
is adopted.

By the way, arguably, it is a mistake to see this as a model
of a market-economy. It is a model of central planning. But,
of course, as I noted, the concept of prices I used in the
solution to my numeric example in my original post was a
different concept of prices.

> What I fail to see is how your example in any way supports your
> grandiose claim

JimT misspelled "well-established".



> >So much for the theory that wages and employment are determined
> >by the interaction of well-behaved supply and demand curves on the
> >labor market.

I agree. JimT fails to see how.

Is the example with which I started this thread correct?

An answer to the above question would start off with either "Yes"
or "No"...



> By your own assessment, the wage rate (shadow price) of labour will
> only change when the initial vector (supply) of available inputs
> changes (see your linear program above).

I stated, explicitly, that the concept of prices relevant for my
dual LP above was a different concept than that used in my example
in my original post:

[>> Anyway, let me display that the cost-minimizing firm can choose ]


[>> the linear combination of processes that I specified above. (This ]
[>> requires knowledge of Linear Programming to follow.) ]
[>> ]
[>> I here use a different concept of prices and cost-minimization ]

[>> than in my original post. ]

> In a dynamic context, the
> beginning of period inputs are not random. You may want to think
> about the Marshallian steady state.

First, JimT is changing the subject here. He is no longer attempting
to defend his incorrect assertion that one must consider a
non-vertically integrated corn-producing firm's profit-maximizing
(or cost-minimizing) problem to construct the production function
for corn.

Second, JimT presents his comments about a dynamic context as if
they are in contrast to my exposition of my example. Suppose the
numeric example in my original post was an entire economy. Then
my example can be read as an example of a generalized von Neumann
ray in which both (accounting) profits and wages are consumed.
There's a large literature relating von Neumann rays to "dynamic"
models.

Third, I thought I explained in my original post that
beginning-of-period inputs are endogeneous, not given,
in my example:

------- Begin extract from original post ----------------------


I want to consider a couple of different levels at which this
firm can operate the processes comprising the techniques. First,
suppose Process A is used to produce 1 41/49 Bushels corn, and
Process C is used to produce 4 4/49 Tons iron. The quantity flows
shown in Table 4 result.

TABLE 4: THE ALPHA TECHNIQUE PRODUCING CORN NET

INPUTS Process C Process A
Labor 4 4/49 Person-Years 1 41/49 Person-Years
Iron 20/49 Tons Iron 3 33/49 Tons Iron
Corn 5/49 Bushels Corn 36/49 Bushels Corn

OUTPUTS 4 4/49 Tons Iron 1 41/49 Bushels Corn

LABOR-INTENSITY: 5 45/49 Person-Years Per Bushel

When the firm operates these processes in parallel, it requires
a total of 41/49 Bushels corn as input. The output of the
corn-producing process can replace this input, leaving a net
output of one Bushel corn. Notice that the total inputs of
iron are 20/49 + 3 33/49 = 4 4/49 Tons iron, which is exactly
replaced by the output of Process C. So Table 4 shows a technique
in which 5 45/49 Person-Years labor are used to produce a net
output of one Bushel corn. The firm, when operating this technique
can produce any desired output of corn by scaling both processes
equally.

------- End extract from original post -----------------------

Notice that in the above I have calculated the outputs of the
processes comprising a given techniques required to ensure
net output is a Bushel Corn. Notice that the inputs are
found as a result of these calculations; I did not take
them as givens.

By the way, how much corn can firms produce in my example if
the total inputs available for the corn-producing process
are L Person-Years, Q1 Tons Iron, and Q2 Bushels (Seed) Corn?
How would you find the answer to this question?

Robert Vienneau

unread,
Oct 19, 2002, 2:39:18 PM10/19/02
to
Poor Chris Auld:

> [ Comments, including stupidities. ]

A prediction: No economist will post here a derivation of a
long-period non-upward-sloping labor demand schedule and of
a labor supply schedule for my example, possibly with additional
assumptions.

"But, as economic theory has learned since the 1930s, the
pattern of activities adopted in the face of long-run
factor-price changes can be complicated and counterintuitive.
Consequently, the long-run demand for factors can be badly
behaved functions of factor prices... The principle of
variation works as an argument for long-run determinancy insofar
as the set of zero-profit activities shift in response to factor
price changes; it is not necessary that newly adopted activities
use cheaper factors more intensively or that production is more
capital intensive when r falls."
-- Michael Mandler, 1999.

James A. Donald

unread,
Oct 19, 2002, 9:29:22 PM10/19/02
to
--

On Sat, 19 Oct 2002 14:39:18 -0400, Robert Vienneau
<rv...@see.sig.com> wrote:

> Poor Chris Auld:
>
> > [ Comments, including stupidities. ]
>
> A prediction: No economist will post here a derivation of a
> long-period non-upward-sloping labor demand schedule and of
> a labor supply schedule for my example, possibly with
> additional assumptions.

Your models, if interpreted as models of a market economy, are
incoherent. From a contradiction, one can prove anything.


--digsig
James A. Donald
6YeGpsZR+nOTh/cGwvITnSR3TdzclVpR0+pr3YYQdkG

mti1JB0vl5P/Wera9chCQI6x1pf+gcjdWiTihM99
4XRBB70uluh3yeA1XcUiXDQ0wQpFwaqus+zACIYbh


Christopher Auld

unread,
Oct 20, 2002, 11:44:51 AM10/20/02
to
Robert Vienneau <rv...@see.sig.com> wrote:
>Poor Chris Auld:
>
>> [ Comments, including stupidities. ]

This is sad even by Robert Vienneau's abysmal, kooky
standards. Perhaps Robert shouldn't post on usenet
if he's going to get so touchy when it's pointed out
that he's wrong.


>A prediction: No economist will post here a derivation of a
>long-period non-upward-sloping labor demand schedule and of
>a labor supply schedule for my example, possibly with additional
>assumptions.

A prediction: Robert Vienneau will never understand what
the technical term "labor demand schedule" means.

Robert Vienneau

unread,
Oct 22, 2002, 2:59:21 AM10/22/02
to
James A. Donald goes on:

> On Thu, 17 Oct 2002 19:04:35 -0400, Robert Vienneau
> <rv...@see.sig.com> wrote:
> > The analysis of prices in my
> > original post was a description of producers free to use (and
> > using) the lowest cost method(s) for production of corn.

> No it is not. You call it that, but your model describes a
> planned economy in which individual producers do not get to
> choose.

On the other hand, from my original post:

-----------------------------------------------------------------

TABLE 8: COSTS, WAGE 109/4040 BUSHELS PER PERSON-YEAR,
PRICE OF IRON 0.10569123726 BUSHELS PER TON

INDUSTRY PROCESS COST PROFITS

Corn A 2*(0.106) + (2/5)*1


+ 1*(109/4040) = 0.6384 56.65%
Corn B (1/2)*(0.106) + (3/5)*1
+ 1*(109/4040) = 0.6798 47.10%
Iron C (1/10)*(0.106) + (1/40)*1
+ 1*(109/4040) = 0.06255 68.97%
Iron D (113/232)*(0.106) + 0
+ (275/464)*(109/4040) = 0.06747 56.65%

This revaluation of iron reveals that the firm makes a rate
of profits of 57% in operating the Beta technique. The firm makes
the same rate of profits in producing corn and in producing its
input of iron. But the manager of the iron-producing process would
soon notice that the cost of operating process C is cheaper.

--------------------------------------------------------------------

This argues that, in the model, the managers of a
vertically-integrated firm will choose which processes they want
to adopt on the basis of cost.

Apparently, on James' planet nobody ever develops a rational
argument.

Robert Vienneau

unread,
Oct 22, 2002, 2:58:05 AM10/22/02
to
In article <aouj1j$6t...@acs4.acs.ucalgary.ca>, au...@acs.ucalgary.ca
(Christopher Auld) wrote:

> Robert Vienneau <rv...@see.sig.com> wrote:
> >Poor Chris Auld:

> >> [ Comments, including stupidities. ]

> [ Stupidity deleted ]

> >A prediction: No economist will post here a derivation of a
> >long-period non-upward-sloping labor demand schedule and of
> >a labor supply schedule for my example, possibly with additional
> >assumptions.

> A prediction: Robert Vienneau will never understand what
> the technical term "labor demand schedule" means.

Chris Auld behaves consistently with my prediction. And poor
Chris Auld's comment is typically off-kilter, misconceived, and
directed to no cognitive values. Directing his silly whining
at Michael Mandler would be more appropriate, if his
silliness were ever appropriate.

Robert Vienneau

unread,
Oct 22, 2002, 2:57:04 AM10/22/02
to
Consider a model of a very simple economy in which two goods
that can be consumed are produced. These goods are called,
confusingly, produced corn and produced iron. Produced corn is
the numeraire in this model. The price of produced iron is
a given parameter in this model, p Bushels per Ton.

Produced goods are produced directly from natural resources
in this model; there are no capital goods. Somewhat confusingly,
these natural resources are called labor, unproduced iron, and
unproduced corn. Factor endowments - L Person Years, Q1 Tons
Iron, and Q2 Bushels Corn - are given parameters in this model.

The technology is also given. Technology is specifed by two
Constant-Returns-to-Scale fixed-coefficient processes for
producing corn and two CRS fixed-coefficient processes for
producing iron.

The equilibrium levels of operation of each process, for
the technology I specified in my first post on this thread,
are the decision variables that solve the following Linear
Program:

Max Z = Z1 + Z2 + p Z3 + p Z4

Z1 + Z2 + Z3 + (275/464) Z4 <= L
2*Z1 + (1/2)*Z2 + (1/10) Z3 + (113/232) Z4 <= Q1
(2/5)*Z1 + (3/5)*Z2 + (1/40) Z3 <= Q2

Z1 >= 0, Z2 >= 0, Z3 >= 0, Z4 >= 0

where

Z is the value of output,
Z1 is the amount of corn produced with the first
corn-producing process,
Z2 is the amount of corn produced with the second
corn-producing process,
Z3 is the amount of iron produced with the first
iron-producing process,
Z4 is the amount of iron produced with the second
iron-producing process.

Suppose both corn-producing processes are operated, and one
of the iron-producing processes is operated. Or suppose both
iron-producing processes are operated, and one of the corn
producing processes is operated. In either case, all three of
the constraints are met with equality, and three of the
(non-slack) decision variables would appear on the left-hand
side of the constraints if the coefficients were confined
to those variables with positive values. In other words,
one would get a system of three equations with three unknowns.
I have not solved the LP, but I believe that the solution in
these cases would define a region in quantity space with
positive volume.

This conclusion does not depend on the number of process
at all. Suppose there were a lot more processes for producing
iron and corn each, but less than an uncountably infinite
number. It is still the case, I think, that the region in
quantity space where a non-trivial linear combination of
processes is used in one or the other industry would have
a positive volume. If one focuses one's attention on internal
solutions, in some sense, the region in which only one process
is adopted in each industry has a set of Lebesque measure
zero.

Endowments cannot be assumed to exhibit any restricted
relationship. Generally, a linear combination of processes
will be adopted in some industry. Two properties of the
example drive this result in a model with this sort of
structure. Factors are not specialized, in some sense. And
the number of factors exceeds the number of produced goods.

Equilibrium factor prices are the shadow prices that solve
the dual of the above linear program. There are three prices,
one for each factor. Each process specified in the technology
provides a constraint in the dual problem. The number of
constraints met with equality is equal to the number of
processes adopted in the solution to the primal LP. If only
one process is adopted for each industry, the dual LP will
not pin down factor prices; they will be indeterminate. But
generally, that will not happen. A linear combination of
processes will be adopted in one industry, and the factor
shadow prices will be determinate. For reasonable probability
distributions over the space of endowments, shadow prices
with this characteristic of determinates have a positive
probability.

This conclusion, that generally factor prices will be such
that a cost-minimizing firm will want to adopt a non-trivial
linear combination of processes in equilibrium in some industry
or another, does not necessarily apply to models with another
structure.

I don't claim anything in the above argument as original with me.
Quite the contrary.

I emphasize, again, that the concept of prices used above differs
from that used in my numerical example of competitive profit-maximizing
firms employing more labor per (net) unit output at higher wages.

Poor Chris Auld.

James A. Donald

unread,
Oct 22, 2002, 11:37:40 AM10/22/02
to
--

On Tue, 22 Oct 2002 02:57:04 -0400, Robert Vienneau
<rv...@see.sig.com> wrote:
> The equilibrium levels of operation of each process, for
> the technology I specified in my first post on this thread,
> are the decision variables that solve the following Linear

The trouble is that you, the central planner, declare these to
be "equilibrium" levels, rather than show that it is in the
interests of producers and consumers to act in a way that would
bring production to these levels. In other words, these are
planned levels, not equilibrium levels.

In short, you are yet again making the old familiar argument,
that capitalism is central planning, and you, being a nice guy,
would plan better results than those selfish capitalists.

--digsig
James A. Donald
6YeGpsZR+nOTh/cGwvITnSR3TdzclVpR0+pr3YYQdkG

TBMOqrfbSUy/32ZwVrWKbXFJUvvSxxdY+OUjq4sv
4yA56qJeEGEeOIOXVklKuu8HbI2h3ecBhR5IjY2CS


Christopher Auld

unread,
Oct 22, 2002, 12:20:16 PM10/22/02
to
Robert Vienneau <rv...@see.sig.com> wrote:

[ blather ]

> Poor Chris Auld.

In the model RV posted, individual firms can use one
of two Leontief processes to produce corn. Since
RV assumes constant returns to scale, zero profits,
and that firms take prices as parametric, the output
of any firm is undetermined, which is why RV considers
only the firm's problem of cost-minimization in
producing, without loss of generality, one unit of
output. Under these assumptions, if the firm produces
that one unit by producing (a) units using process 1
and (1-a) units using process 2, its costs are

C(a) = aC1 + (1-a)C2

where Ci is the cost of producing one unit using process
i and Ci do not depend on a. Even RV should be able to
see that cost minimization is trivial here: a=0 if C1>C2,
a=1 if C1<C2, or any a yields the same cost if C1=C2. In
words, if and only if the price ratio is such that costs
are equal, the firm is indifferent over processes. This is
the only case in which the firm would ever use both
processes, and IT ONLY HAPPENS FOR A SET OF MEASURE ZERO
OF FACTOR PRICES, and either trivial combination works just
as well as the non-trivial solutions in this case.

In the bungled post I've deleted, RV tries to paraphrase
whatever he's Googled up on more complex versions of his
toy model. For example, he wants to talk about endowments,
which don't exist in his original version. Perhaps he
doesn't want to close the model because then it becomes
clear that both supply and demand generally shift to
produce apparently counterintuitive factor price/quantity
movements, more likely he simply doesn't understand the
issues (one of RV's many elementary misunderstandings
concerns the conceptual difference between a firm's
equilibrium and an economy's equilibrium, which is at play
here).

Robert Vienneau regularly makes a complete hash of
elementary economic concepts and mathematics, yet he
desperately wants to be taken seriously on advanced topics
in economic theory (more accurately, he firmly believes he
understands these topics better than the vast majority of
professional economists, not unlike Archimedes Plutonium's
beliefs about number theory and mathematicians). Perhaps
one day he will realize that one must learn the basics
before lecturing on sophisticated issues -- and here the
sophisticated issue is a largely uninteresting class of
models considered some forty years ago and only still
considered in certain branches of the history of economic
thought. But probably not, because Robert Vienneau is truly
one of the net's most prolific kooks, and he becomes more
tiresome as the shrillness of his oft-spammed "long essays"
increases.

Christopher Auld

unread,
Oct 22, 2002, 12:27:57 PM10/22/02
to
Robert Vienneau <rv...@see.sig.com> wrote:

>> A prediction: Robert Vienneau will never understand what
>> the technical term "labor demand schedule" means.

>Chris Auld behaves consistently with my prediction. And poor
>Chris Auld's comment is typically off-kilter, misconceived, and
>directed to no cognitive values.

Boring. Period-by-period, in RV's model wages and employment
are determined by supply and demand. Technically, this is
the only time frame in which one can use those terms. If one
abuses terminology and uses the phrase "long-run factor demand"
to refer to a total relationship between factors and factor
prices as other prices or quantities change over time, then
of course a seemingly counterintutive relationship could obtain,
as any good undergraduate could explain. Perhaps if RV tried to
understand the intuition behind his "long essays" he wouldn't
so regularly be revealed as a kook.

Robert Vienneau

unread,
Oct 23, 2002, 3:30:30 AM10/23/02
to
James Donald:

> On Sat, 19 Oct 2002 14:39:18 -0400, Robert Vienneau
> <rv...@see.sig.com> wrote:

> > A prediction: No economist will post here a derivation of a
> > long-period non-upward-sloping labor demand schedule and of
> > a labor supply schedule for my example, possibly with
> > additional assumptions.

> Your models, if interpreted as models of a market economy, are
> incoherent. From a contradiction, one can prove anything.

I guess James finds arguments like so incoherent:

If 2 Ton Irons are needed per Bushel Corn produced by Process
A, and 1 41/49 Bushels Corn are produced by this process,
then 3 33/49 Tons Iron will be needed for input into this
process.

If it costs $0.06255 Per Ton for Iron produced by Process C
and it costs $0.06747 Per Ton for Iron produced by Process D,
then firms will have a tendency to adopt Process C (the
cheaper one).

They probably don't have arithmetic on James' planet.

Robert Vienneau

unread,
Oct 23, 2002, 3:37:21 AM10/23/02
to
In article <ap3uad$73...@acs4.acs.ucalgary.ca>, au...@acs.ucalgary.ca
(Christopher Auld) wrote:

> Robert Vienneau <rv...@see.sig.com> wrote:

[> A prediction: No economist will post here a derivation of a ]


[> long-period non-upward-sloping labor demand schedule and of ]
[> a labor supply schedule for my example, possibly with ]

[> additional assumptions. ]

> [ Silliness deleted. ]

> Period-by-period, in RV's model wages and employment
> are determined by supply and demand. Technically, this is
> the only time frame in which one can use those terms.

I cannot decide if Chris Auld realizes he is changing the
subject and intends to implicitly concede supply and demand
do not explain prices and quantities in long run models. If
he wants to seem intellectually honest, he will explicitly state
that supply and demand do NOT explain prices and quantities
in long run models.

Consider an entire economy in which iron and corn are produced
with the technology I specified in my original post.

There are at least three models at play here.

(1) Static Equilibrium. This is the model, possibly extended,
I presented yesterday. Endowments and technology are part of
the data, as I described yesterday. The natural extension, for
those who believe in utility theory, is to take the distribution
of ownership of factors among consumers as given. The data
would then include the preferences of consumers over produced
goods. This extension makes the price of produced iron, in
terms of the numeraire (produced corn), endogeneous. Notice
there's no necessity for the prices of produced corn and
produced iron to equal the prices of iron and corn inputs.

(2) (Short-run) Temporary Equilibrium. Endowments at the
initial time are still given. Extend the model such that
produced iron and corn can be used as inputs into the
next period. Utility theory would be invoked to explain
how much iron and corn would be consumed between periods
and how much would be carried over into the next period
as input into further production. This extends to as
many periods as you like.

(3) Long-run equilibria. Long-run equilibria could be
conceived as a limit point of the dynamics outlined for
a model of temporary equilibria. These would be an
extension of my original example to an entire economy.
Endowments are endogeneous in such models; there ratios
are not constrained by period zero endowments since
there is no period zero in this model.

Chris is stating, correctly, that supply and demand functions
appear in short run models of temporary equilibria. Supply
and demand functions, as Chris describes them, do NOT appear
in models of long-run equilibria. Some literature does
refer to examples like mine as of an upward-sloping labor
demand schedule. I think understanding the effect is more
important than the label.

Sequences of temporary equilibria have many fundamental
problems that still remain open, even more than 60 years after
J. R. Hicks introduced them. It is even debated if this
is the appropriate dynamics to use. My long-run equilibria
have also been described as the result of other dynamics,
such as cross-dual dynamics.

One objection to sequences of temporary equilibria is that
they are essentially models of centrally planned economies.
However well-taken this objection is, economists have
not applied this objection to some other dynamics that
have my long-run equilibria as limit points. In fact, some
economists have argued that these other formulations do
not suffer from that objection.

Another objection involves issues of (in)stability. The literature,
I think, is still open on whether the sort of effect that I
illustrated, reswitching, and so on, are manifested in sequences
of temporary equilibria by effects on the stability of such
paths. Frank Hahn has hinted that they are, but not in any argument
that he has fully developed. P. Garegnani has claimed that the
argument about how long-run prices do not reflect relative
scarcity extends to sequences of temporary equilibria. One sees
the effect there by shifts between periods in supply and demand
curves. Bertram Schefold has outlined how to construct examples
of wages and employment increasing together. Garegnani's and
Schefold's arguments have been criticized.

Another economist who has considered how temporary equilibria and
long run models hang together is Michael Mandler. From what I
understand, Mandler is at Harvard.

"But, as economic theory has learned since the 1930s, the
pattern of activities adopted in the face of long-run
factor-price changes can be complicated and counterintuitive.
Consequently, the long-run demand for factors can be badly
behaved functions of factor prices... The principle of
variation works as an argument for long-run determinancy insofar
as the set of zero-profit activities shift in response to factor
price changes; it is not necessary that newly adopted activities
use cheaper factors more intensively or that production is more
capital intensive when r falls."
-- Michael Mandler, 1999.

Consider the intro textbook story about how minimum wages result
in unemployment. I believe some earlier poster on this thread
implicitly referred to that story. I don't know of any textbook
that explicitly presents this story in a context where no
produced capital goods arise. So it cannot be about (1) Static
Equilibria. I don't know of any intro textbook that presents labor
as a dated input and notes that an equality of demand and
supply in one period is consistent with endogeneous forces
that result in changed wages and employment in subsequent
periods. So this story cannot be about (2) Temporary Equilibria.
Frank Hahn has criticized this story on these grounds, if
I understand right. And, since supply and demand do not arise
in (3) Long Run Models, this story cannot be about the
long-run. So what is this story about?

(Notice that long-run Marshallian equilibrium is a non-starter.
My objection based on long-run models shows that Marshall's
principle of substitution does not apply to long run models.
And my objection does not require a full-blown long-run
equilibrium model; it only requires consideration of changed
wages in a vertically-integrated sector.)

> If one
> abuses terminology and uses the phrase "long-run factor demand"
> to refer to a total relationship between factors and factor
> prices as other prices or quantities change over time,

The bit about "changing over time" doesn't belong in this long-run
context. Notice Chris Auld offers no suggestion whatsoever what
the firm's accounting price for iron should be in my original
example at different levels of wages.

> then
> of course a seemingly counterintutive relationship could obtain,

> [ Stupidity deleted. ]

Chris Auld presents his comments about "abus[ing] terminology"
as if it is in response to something I posted on this thread. But,
of course, I never described here the relationship between
labor-input-per-unit-output and wages I derived in my example
initiating this thread as a "long-run factor demand" schedule.

I'm quite willing to quote the literature, though:

"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.

By the way, what should I conclude about JimT vanishing from the
scene? It seems to me he is being intellectual cowardly.

Robert Vienneau

unread,
Oct 23, 2002, 3:40:45 AM10/23/02
to
In article <ap3ts0$5r...@acs4.acs.ucalgary.ca>, au...@acs.ucalgary.ca
(Christopher Auld) wrote:

> Robert Vienneau <rv...@see.sig.com> wrote:

> [Repetition of an argument that Chris already gave. ]

> In
> words, if and only if the price ratio is such that costs
> are equal, the firm is indifferent over processes. This is
> the only case in which the firm would ever use both
> processes, and IT ONLY HAPPENS FOR A SET OF MEASURE ZERO
> OF FACTOR PRICES,

That's ambiguous, and Chris should know it.

A Lebesque measure is only one kind of measure.

I think my intutition was correct in the context in
which JimT was raising his point, as I understood it. If
one takes as given a probability distribution over
endowments, the corresponding probability distribution
over equilibrium prices (which are found by solving
the model) generally has a positive probability of prices
being such that a non-trivial linear combination of
processes will be adopted in equilibrium.

That is, IT HAPPENS FOR A SET WITH A POSITIVE
MEASURE, where that measure defines the derived
probability distribution in the space of factor
prices.

It any case, the production functions are non-Leontief,
not "only non-Leontief because ..." in JimT's muddled
formulation.

> and either trivial combination works just
> as well as the non-trivial solutions in this case.

> [ Stupidities - deleted. ]

> he wants to talk about endowments,
> which don't exist in his original version.

JimT's raised a mistaken point about how one needed to
consider the firm's profit-maximizing/cost-minimizing
problem to construct production functions. This was
in the context of my aside about how to construct
production functions. Given inputs certainly
appeared in my original formulation of a certain
LP.

Furthermore, JimT appeared to me to be talking about
the shadow prices that appear in the dual to that LP.

I have always explicitly stated that this concept
of prices is different than I used in my original
post.

So I don't take Chris' point, if he has any.

In my long-run model, as I understand it, in the
solution, generally only one process will be adopted
for each produced commodity.

Generalized Leontief production functions, as in
my example, differ in important ways from
Leontief production functions. Furthermore, the
effect I illustrated is NOT driven by the existence
of "kinks" in the production functions.

In other words, JimT's objection seemed misdirected
to me, however he might try to put it.

> Perhaps he
> doesn't want to close the model because then it becomes
> clear that both supply and demand generally shift to
> produce apparently counterintuitive factor price/quantity
> movements,

> [ Stupidity - deleted. ]

Chris' comment makes no sense to me. Closing my
original model does NOT include the specification of
given endowments of iron and steel. Perhaps he will think
about my 2nd and 3rd models in my previous post.

I do not close my model, extended to be an entire
economy, because I recognize:

(1) My point about long-run models does not
require such closure.

(2) I recognize that there are a variety of
ways of closing it, and I find more
intriquing certain heterodox closures.

(I've explained this many times in this newsgroup.)

Furthermore, if he is talking about endogeneous shifts
in supply and demand in (short-run) temporary equilibria
models, he is echoing a point of the Sraffian
literature.

> (one of RV's many elementary misunderstandings
> concerns the conceptual difference between a firm's
> equilibrium and an economy's equilibrium, which is at play
> here).

If Chris were very familiar with the literature on which I
drew in constructing my argument, he would know:

(1) The effect illustrated has been claimed to apply
to a vertically-integrated industry. One does
not need to consider an entire economy.

(2) In an article published in the last decade in the
Cambridge Journal of Economics, the concept of
prices have been claimed to be accounting prices,
as in my example.

I have come to understand the latter (cutting-edge) point
by constructing such arguments as I presented here. I'm
thinking of reviewing the article I have in mind, now
that I've done the work to understand its point, to be
sure my memory is correct.

> [ Stupidities and denials of the existence of some ]
> [ contemporary literature in economics - deleted. ]

I don't think Chris looks good with all these stupidities
directed at personalities. (And, Chris, the phrase
"stupidities directed at personalities" is redundant
with the way I have been using "stupidities".) It would seem
he is trying to discredit me to avoid admitting that the
literature upon which I draw gives perfectly valid reasons
for thinking many introductory textbooks are misleading.

I continually point out that this line of reasoning that
I present is hardly original to me. There are whole
communities of contemporary economists that I am agreeing
with.

Christopher Auld

unread,
Oct 23, 2002, 1:02:41 PM10/23/02
to
Robert Vienneau <rv...@see.sig.com> wrote:

>Chris is stating, correctly, that supply and demand functions
>appear in short run models of temporary equilibria.

This is, of course, complete capitulation, even if Robert does not
understand why. As I already clearly stated, referring to total
relationships between factor prices and factors demanded as multiple
prices or quantities change as "factor demand schedules" is an
abuse of terminology.


>Consider the intro textbook story about how minimum wages result
>in unemployment.

Which is a partial equilibrium argument. Robert might as well
stop spamming his "long essay" and post the single sentence, "You
know, that doesn't necessarily hold if we consider feedback from
other markets." Again, any good undergraduate is aware of all
this, contra the hilarious insult Robert which now opens his "long
essay" (hint: insisting education makes you ignorant is possibly
the least persuasive _ad hominem_ argument in existence).

Robert's semi-relevant comments on dynamic economic models are
poorly informed. He is not aware of modern dynamic models, and
he does not appear to be interested in learning. As usual, he
is more interested in confusing history of economic thought with
current theory:

>(Notice that long-run Marshallian equilibrium is a non-starter.

Who cares? Is Robert ever going to grasp the quite obvious
fact that the literature has progressed in the last century?


>Chris Auld presents his comments about "abus[ing] terminology"
>as if it is in response to something I posted on this thread. But,
>of course, I never described here the relationship between
>labor-input-per-unit-output and wages I derived in my example
>initiating this thread as a "long-run factor demand" schedule.

Robert has posted literally hundreds of times that this schedule
is a labor demand schedule, including in this very post. And
he ended his essay with the ridiculous conclusion that his toy
model invalidates supply and demand. Simply because one can write
down models of labor market phenomena in which supply and demand
do not determine wages and employment does not imply supply and
demand is a useless framework, indeed, the mainstream literature
is full of such models, and at least one appears in every
introductory economics textbook.

And, why did Robert post this thread to alt.fan.noam-chomsky?
Is he confusing mathematics with his radical politics again?

Christopher Auld

unread,
Oct 23, 2002, 1:25:30 PM10/23/02
to
Robert Vienneau <rv...@see.sig.com> wrote:

>I think my intutition was correct in the context in
>which JimT was raising his point, as I understood it. If
>one takes as given a probability distribution over
>endowments, the corresponding probability distribution
>over equilibrium prices (which are found by solving
>the model) generally has a positive probability of prices
>being such that a non-trivial linear combination of
>processes will be adopted in equilibrium.
>
>That is, IT HAPPENS FOR A SET WITH A POSITIVE
>MEASURE, where that measure defines the derived
>probability distribution in the space of factor
>prices.

This is ridiculous. Robert picked a point not on one
of the two processes available to firms. JimT correctly
pointed out that such an input bundle would generally not
be chosen. Robert frothed at the mouth, misunderstood
the programming problem he cribbed from some third source,
and insisted that it is not the case that only a lower-
dimensional subspace of price vectors could induce the
firm to find it optimal to hire such a bundle.

There is nothing stochastic in Robert's model so I don't
know where the stuff above probability distributions comes
from, but it isn't relevant and it doesn't salvage
Robert's faulty arithmetic: An individual firm in this
model either uses one and only one process, or it is
indifferent over processes. It is only indifferent for
one price ratio in a continuum of possible price ratios,
ie, for a set of measure zero. This ain't rocket science.

Now, of course trying to construct a model with perfect
competition and constant returns to scale leads to
indeterminant outcomes. If the economy has endowments
such that all firms using one process does not exhaust
the endowments, that isn't an equilibrium, and some
fudge like an ad hoc probability distribution over
inputs hired when firms are indifferent could be used
to acheive an equilibrium. But Robert again confuses
an equilibrium for the economy with an equilibrium for
the firm: Once again, contra Robert, there is only one
price ratio for which the firm would ever use both
processes.


>Furthermore, if he is talking about endogeneous shifts
>in supply and demand in (short-run) temporary equilibria
>models, he is echoing a point of the Sraffian
>literature.

And in the perfectly mainstream literature, including most
introductory economics textbooks. Robert talks as if he
firmly believes the alpha and omega of mainstream economic
thought is partial equilibrium models as they were understood
circa 1910.


>I don't think Chris looks good with all these stupidities
>directed at personalities.

Again, Robert now opens his "long essay" with a personal
attack, and a silly personal attack it is, a sort of
reverse credentialism in which he insists people who
disagree with him are ignorant not because of a lack
of education, but because they are far more educated than
he himself is. He then has the lack of self-awareness to
whine when, oddly, these people fail to treat the 973th
repost of this essay, replete with a shiny new insult,
with the utmost respect and careful consideration.


>he is trying to discredit me to avoid admitting that the
>literature upon which I draw gives perfectly valid reasons
>for thinking many introductory textbooks are misleading.

Does Robert really believe the professional literature
and the professionals who he sneers at never get beyond
"introductory textbooks?" What on earth is his point?


>I continually point out that this line of reasoning that
>I present is hardly original to me. There are whole
>communities of contemporary economists that I am agreeing
>with.

Another of Robert's issues is he likes to restate arguments,
he restates them incorrectly, he then interprets "Robert
Vienneau is mistaken" as "the literature on which I draw is
mistaken." Sometimes both quoted remarks are true, more
often just the first one holds.