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Some comments on Robert Vienneau's LTV document

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Darren

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Apr 30, 2003, 10:46:20 PM4/30/03
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http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/LTV-FAQ.html

Hi, I looked this over and just thought I'd share a few thoughts. I'm
just an undergraduate Econ student with no serious credentials or
knowledge of Marxism, just curiosity.

1. I was very, very surprised that one of the Frequently Asked
Questions about the LTV wasn't "what about supply and demand"? Millions
of people have shambled through Econ 101 and heard the little story
about Supply and Demand. Some of those people, if they grow curious
about Marxism and the LTV, are going to check out your LTV document, and
that question will be the first one out of their mouths. It will
certainly be "Frequently Asked"!

It seems to me, with my lofty wisdom from two Micro courses, that the
Supply curve incorporates the cost of labour, and so supply and demand
explains prices of commodities just as well as LTV (better, in fact, as
it explains fluctuations in price as well) while *also* explaining why
a Van Gogh painting (few weeks of work by the artist, few dabs of paint)
is worth millions of dollars. I've seen a few posts by various people
critiquing the LTV, and they all said some variant of what I just said.
(I am not asserting absolutely that this is a sound objection, just a
very, very common one). I would think that if you were seriously
interested in singing the praises of the LTV, you would take great pains
to counter such a common objection in a list of "Frequently" asked
questions. Yet you don't. I find that very weird.

2. Numerical examples are always great learning tools, but why on earth
did you pick such preposterous numbers for your example in section 3.2?
73 and 9/17 quarters of wheat! What the hell???? I'm not afraid of
fractions, but what's wrong with round numbers? Get the point across a
little better, don't they? I actually tried to figure out that example,
but I gave up, as I couldn't immediately eyeball the relationship
between 39 11/51 tons of iron and 8 40/51 tons of iron, and I wasn't
sure why I should bother trying. (I have NO idea what those
"subsystems" are about). You do want to be understood, don't you?

3. Use-value: it seems to me that "use-value" does not reside in the
thing itself, but in the relationship between the thing and the
evaluator. So, a single apple has many use-values, one for each person
who might use it. My use-value for the apple is very high, I love
apples. Your use value is very low, because you absolutely can't stand
apples, you wouldn't eat one unless you were starving to death. I
realize this is a pretty off-the-cuff criticism, but I've seen it, and I
don't really see this idea discussed or addressed anywhere in your
document. I think the document should make this idea clear, and be
clear as to why it doesn't matter to Marxism.

So, with those problems, I wasn't sure what to make of the whole
"exploitation" thing. If your goal was to turn me into a Marxist, you
have not, as of yet, succeeded.

Cheers,
Darren

Ron Peterson

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May 1, 2003, 12:55:12 PM5/1/03
to
Darren <no.e...@thank.you> wrote:
> http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/LTV-FAQ.html

> 1. I was very, very surprised that one of the Frequently Asked
> Questions about the LTV wasn't "what about supply and demand"? Millions
> of people have shambled through Econ 101 and heard the little story
> about Supply and Demand. Some of those people, if they grow curious
> about Marxism and the LTV, are going to check out your LTV document, and
> that question will be the first one out of their mouths. It will
> certainly be "Frequently Asked"!

It seems that the LTV isn't about predicting the prices of products,
instead it's about macro-economic concerns, AFAIK.

> It seems to me, with my lofty wisdom from two Micro courses, that the
> Supply curve incorporates the cost of labour, and so supply and demand
> explains prices of commodities just as well as LTV (better, in fact, as
> it explains fluctuations in price as well) while *also* explaining why
> a Van Gogh painting (few weeks of work by the artist, few dabs of paint)
> is worth millions of dollars. I've seen a few posts by various people
> critiquing the LTV, and they all said some variant of what I just said.
> (I am not asserting absolutely that this is a sound objection, just a
> very, very common one). I would think that if you were seriously
> interested in singing the praises of the LTV, you would take great pains
> to counter such a common objection in a list of "Frequently" asked
> questions. Yet you don't. I find that very weird.

A Van Gogh painting isn't a commodity. And, you are back to describing
prices.

> 3. Use-value: it seems to me that "use-value" does not reside in the
> thing itself, but in the relationship between the thing and the
> evaluator. So, a single apple has many use-values, one for each person
> who might use it. My use-value for the apple is very high, I love
> apples. Your use value is very low, because you absolutely can't stand
> apples, you wouldn't eat one unless you were starving to death. I
> realize this is a pretty off-the-cuff criticism, but I've seen it, and I
> don't really see this idea discussed or addressed anywhere in your
> document. I think the document should make this idea clear, and be
> clear as to why it doesn't matter to Marxism.

Robert does discuss use-value. Use-value does matter in that if a
commodity has no use-value to anyone, its exchange-value will be nil.

> So, with those problems, I wasn't sure what to make of the whole
> "exploitation" thing. If your goal was to turn me into a Marxist, you
> have not, as of yet, succeeded.

You can define value in terms of other things besides labor, but its the
one thing that most people have. So, all that the LTV is saying is that
labor (actually labor-time) can be associated with all commodities. I
don't think that the view is that of Marx alone, since Robert does
mention Ricardo.

Robert has mentioned the term "exploitation" shouldn't be looked at as a
moral judgement.

--
Ron

Darren

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May 1, 2003, 2:36:56 PM5/1/03
to

Ron Peterson wrote:

> Darren <no.e...@thank.you> wrote:
> > http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/LTV-FAQ.html
>
> > 1. I was very, very surprised that one of the Frequently Asked
> > Questions about the LTV wasn't "what about supply and demand"? Millions
> > of people have shambled through Econ 101 and heard the little story
> > about Supply and Demand. Some of those people, if they grow curious
> > about Marxism and the LTV, are going to check out your LTV document, and
> > that question will be the first one out of their mouths. It will
> > certainly be "Frequently Asked"!
>
> It seems that the LTV isn't about predicting the prices of products,
> instead it's about macro-economic concerns, AFAIK.

Robert has taken great pains to hide that. The *first sentence* of Robert's
document: "The LTV is the theory that market prices are attracted by prices
proportional to the labor time embodied in commodities."

But "A theory that market prices are attracted by _________" is exactly about
predicting market prices. That's what a theory is.


> > It seems to me, with my lofty wisdom from two Micro courses, that the
> > Supply curve incorporates the cost of labour, and so supply and demand
> > explains prices of commodities just as well as LTV (better, in fact, as
> > it explains fluctuations in price as well) while *also* explaining why
> > a Van Gogh painting (few weeks of work by the artist, few dabs of paint)
> > is worth millions of dollars. I've seen a few posts by various people
> > critiquing the LTV, and they all said some variant of what I just said.
> > (I am not asserting absolutely that this is a sound objection, just a
> > very, very common one). I would think that if you were seriously
> > interested in singing the praises of the LTV, you would take great pains
> > to counter such a common objection in a list of "Frequently" asked
> > questions. Yet you don't. I find that very weird.
>
> A Van Gogh painting isn't a commodity. And, you are back to describing
> prices.

LTV explains the price of a can of beans (sort of), but not a Van Gogh.
S and D explains the price of a can of beans AND the price of a Van Gogh.

So why do I need the LTV?

And again, if the LTV is not about prices, it is not immediately clear to me
from Robert's document what it is about.

> > 3. Use-value: it seems to me that "use-value" does not reside in the
> > thing itself, but in the relationship between the thing and the
> > evaluator. So, a single apple has many use-values, one for each person
> > who might use it. My use-value for the apple is very high, I love
> > apples. Your use value is very low, because you absolutely can't stand
> > apples, you wouldn't eat one unless you were starving to death. I
> > realize this is a pretty off-the-cuff criticism, but I've seen it, and I
> > don't really see this idea discussed or addressed anywhere in your
> > document. I think the document should make this idea clear, and be
> > clear as to why it doesn't matter to Marxism.
>
> Robert does discuss use-value. Use-value does matter in that if a
> commodity has no use-value to anyone, its exchange-value will be nil.

Yes, I just didn't see it made clear that a commodity does not and cannot have
a single, innate "use-value". I've seen people get hung up on this point
before, so it is worthy of FAQ inclusion. (The F stands for "frequently").

> > So, with those problems, I wasn't sure what to make of the whole
> > "exploitation" thing. If your goal was to turn me into a Marxist, you
> > have not, as of yet, succeeded.
>
> You can define value in terms of other things besides labor, but its the
> one thing that most people have. So, all that the LTV is saying is that
> labor (actually labor-time) can be associated with all commodities.

OK, but this statement isn't really a "theory" anymore, it's a mundane
truism. This is exactly what corporate accountants do all day, associate
labour time with commodities produced. (I used to write software for some of
them).

But so what? Their prices will still be determined by many other things in
addition to the labour time embodied in them. Demand, for one. Ah, but the
LTV isn't about prices, OK, OK. Where is the "Value" part of the LTV then?

> Robert has mentioned the term "exploitation" shouldn't be looked at as a
> moral judgement.

If so, that seems like a very elementary point to put in the FAQ as well. In
my experience, people who use the word "exploitation" w.r.t. labour seem to
relish its moral overtones. It means something very much like "ripped off" to
most people.

My bottom line: I'm surprised that a prolific and obviously smart guy like
Robert has left such obvious (to me) questions out of his *Frequently Asked*
Questions document, and I'm shocked at the poor quality of his examples. It's
as though he doesn't really want to be understood clearly.

Cheers,
Darren

Robert Vienneau

unread,
May 1, 2003, 4:35:43 PM5/1/03
to
In article <3EB0879A...@thank.you>, Darren <no.e...@thank.you>
wrote:

> http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/LTV-FAQ.html
>
> Hi, I looked this over and just thought I'd share a few thoughts. I'm
> just an undergraduate Econ student with no serious credentials or
> knowledge of Marxism, just curiosity.

> 1. I was very, very surprised that one of the Frequently Asked
> Questions about the LTV wasn't "what about supply and demand"? Millions
> of people have shambled through Econ 101 and heard the little story
> about Supply and Demand. Some of those people, if they grow curious
> about Marxism and the LTV, are going to check out your LTV document, and
> that question will be the first one out of their mouths. It will
> certainly be "Frequently Asked"!

Look at:

"5.7 How has an analysis of prices of production been used to
construct a critique of bourgeois economics?"

Maybe expecting readers to associate "bourgeois economics" with
"Supply and Demand" is too much. I could have expanded that
question to lots of points. But I didn't want the FAQ to be
overbalanced there. I wanted it more to be an examination of
the LTV from a viewpoint internal to traditions in which the LTV
was developed.



> It seems to me, with my lofty wisdom from two Micro courses, that the
> Supply curve incorporates the cost of labour, and so supply and demand
> explains prices of commodities just as well as LTV

Non sequitur. See first paragraph in the answer to 3.10.

> (better, in fact, as
> it explains fluctuations in price as well)

See 5.5 and 6.7.

> while *also* explaining why
> a Van Gogh painting (few weeks of work by the artist, few dabs of paint)
> is worth millions of dollars.

A non-reproducible commodity. Note the second sentence in the first
paragraph to Question 1.0.

> I've seen a few posts by various people
> critiquing the LTV, and they all said some variant of what I just said.
> (I am not asserting absolutely that this is a sound objection, just a
> very, very common one). I would think that if you were seriously
> interested in singing the praises of the LTV,

That already seems to reflect to me a reaction more to be explained
by sociology than rational thought. My FAQ is not unalloyed praise
of the LTV, as the last sentence to the first paragraph of the
answer to Question 1.0 might suggest.

> you would take great pains
> to counter such a common objection in a list of "Frequently" asked
> questions. Yet you don't. I find that very weird.

From my perspective, it's obvious that what your teachers are
probably teaching you in intro economics is clearly crap. But
I am not writing a FAQ about that.

> 2. Numerical examples are always great learning tools, but why on earth
> did you pick such preposterous numbers for your example in section 3.2?
> 73 and 9/17 quarters of wheat!

The numbers I picked were in the table above. 73 9/17 is derived. I
suppose I could multiply everything by, I guess, 51. I don't see
that that makes everything too much clearer. There's no way of
explaining this that I can see that doesn't use ratios.

I explain that the numbers in the subsystems tables are derived:

"These quantity flows can be broken down into two subsystems, one for
wheat and another for iron, as shown in the following tables:"

Look at the last column of these three tables:

QUANTITY FLOWS

592 quarters wheat
48 tons iron

WHEAT SUBSYSTEM
588 3/17 quarters wheat
39 11/51 tons iron

IRON SUBSYSTEM
3 13/17 quarters wheat
8 40/51 tons iron

I know enough to focus on this and see that 588 + 3 ~ 592 and
39 + 8 ~ 48. So I don't see it as hard to see what it means to
says these subsystems break down the quantity flows. Why this
breakdown, and not some other, is not immediately obvious. But
I explain.

> What the hell???? I'm not afraid of
> fractions, but what's wrong with round numbers? Get the point across a
> little better, don't they? I actually tried to figure out that example,
> but I gave up, as I couldn't immediately eyeball the relationship
> between 39 11/51 tons of iron and 8 40/51 tons of iron, and I wasn't
> sure why I should bother trying. (I have NO idea what those
> "subsystems" are about). You do want to be understood, don't you?

Question 3.2 comes after 3.1. Two ways are explained for calculating
labor values in 3.1. Notice that Question 3.2 ends with:

"One could also calculate labor values for this example by a
reduction of all inputs to dated labor flows."

I expected the reader to associate that statement with the second
method explained in 3.1. So the remainder of 3.2 should be associated
with the first method in 3.1.

But I explain the important points about these subsystems. Did you
try and check the claims in the text? What do you find unclear about
this text:

"The proportions of inputs and outputs in the wheat industry [are]
the same in each subsystem and the overall economy. These
proportions identify the production process used in the wheat
industry. The proportions of inputs and outputs in the iron
industry are also unchanged between the subsystems and the
overall economy. The subsystems show a conceptual division of
the given quantity flows across subsystems.

39 11/51 tons iron are produced and productively consumed in the
wheat subsystem. The net output of the wheat subsystem consists of
500 quarters wheat alone. In effect, the wheat subsystem is a
vertically-integrated industry for producing wheat. 627 23/51
person-years labor is the only non-reproduced input in the wheat
subsystem. Hence 627 23/51 person-years are embodied in 500
quarters wheat, or the labor value of wheat is 1 13/51 person-years
per quarter.

The iron subsystem shows a vertically-integrated industry for
producing a net output of 8 tons iron with inputs of 12 28/51
person years. The labor value of iron is 1 29/51 person-years per
ton. Notice that the ratio of the labor value of iron to the
labor value of wheat, 1 1/4 quarters per ton, has the dimensions
of a relative price.


> 3. Use-value: it seems to me that "use-value" does not reside in the
> thing itself, but in the relationship between the thing and the
> evaluator. So, a single apple has many use-values, one for each person
> who might use it. My use-value for the apple is very high, I love
> apples. Your use value is very low, because you absolutely can't stand
> apples, you wouldn't eat one unless you were starving to death. I
> realize this is a pretty off-the-cuff criticism, but I've seen it, and I
> don't really see this idea discussed or addressed anywhere in your
> document. I think the document should make this idea clear, and be
> clear as to why it doesn't matter to Marxism.

As you doubtless know, utility underlies the bourgeois theory of
the demand for consumer goods. Note:

"2.2 What are 'use values?'"

I don't see the answer denying that a use-value is in the
relationship between a thing and an evaluator. I do note that
Ricardo and Marx don't seem to think use-value can be reduced
to a single dimension.

Also notice Question 4.3. I think I make it clear that Marx
considered this objection. I'm not too happy with my lapse
into Hegelese at the end there.



> So, with those problems, I wasn't sure what to make of the whole
> "exploitation" thing. If your goal was to turn me into a Marxist, you
> have not, as of yet, succeeded.

It certainly wasn't my goal. I'm not a Marxist.

My FAQ has been actually used by professors trying to explain things.
Maybe it needs some accompanying lecture. Quite a few Yahoo-like
Internet directories link to my FAQ.

I recently asked a younger colleage of mine about activism on his
campus. He said the artist-types seemed to have a weekly protest.
I was like, "They wouldn't get along with me. I explain Marxism
with matrices."

Many seem to find the existence of this whole math-and-Marx bit
astonishing.

--
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

Ron Peterson

unread,
May 1, 2003, 5:13:05 PM5/1/03
to
Darren <no.e...@thank.you> wrote:

> Ron Peterson wrote:

>> It seems that the LTV isn't about predicting the prices of products,
>> instead it's about macro-economic concerns, AFAIK.

> Robert has taken great pains to hide that. The *first sentence* of Robert's
> document: "The LTV is the theory that market prices are attracted by prices
> proportional to the labor time embodied in commodities."

That would be a conclusion of the theory.

> But "A theory that market prices are attracted by _________" is exactly about
> predicting market prices. That's what a theory is.

An economic theory is a model of economic processes. I think that the
purpose of studying economics is to make decisions that will give the
greatest benefit for the least cost(labor time).

>> A Van Gogh painting isn't a commodity. And, you are back to describing
>> prices.

> LTV explains the price of a can of beans (sort of), but not a Van Gogh.
> S and D explains the price of a can of beans AND the price of a Van Gogh.

> So why do I need the LTV?

So we can determine the best way to maximize economic benefit.

> And again, if the LTV is not about prices, it is not immediately clear to me
> from Robert's document what it is about.

I think that economics is like an elephant being viewed by a number of
blind men.

>> Robert does discuss use-value. Use-value does matter in that if a
>> commodity has no use-value to anyone, its exchange-value will be nil.

> Yes, I just didn't see it made clear that a commodity does not and cannot have
> a single, innate "use-value". I've seen people get hung up on this point
> before, so it is worthy of FAQ inclusion. (The F stands for "frequently").

Maybe, Robert will expand the Web page to include other questions.

>> You can define value in terms of other things besides labor, but its the
>> one thing that most people have. So, all that the LTV is saying is that
>> labor (actually labor-time) can be associated with all commodities.

> OK, but this statement isn't really a "theory" anymore, it's a mundane
> truism. This is exactly what corporate accountants do all day, associate
> labour time with commodities produced. (I used to write software for some of
> them).

I don't see how the LTV is a mundane truism. It's not obvious to me.

> But so what? Their prices will still be determined by many other things in
> addition to the labour time embodied in them. Demand, for one. Ah, but the
> LTV isn't about prices, OK, OK. Where is the "Value" part of the LTV then?

It's assigning a labor-time value to items much as we can associate a
weight or volume to items.

>> Robert has mentioned the term "exploitation" shouldn't be looked at as a
>> moral judgement.

> If so, that seems like a very elementary point to put in the FAQ as well. In
> my experience, people who use the word "exploitation" w.r.t. labour seem to
> relish its moral overtones. It means something very much like "ripped off" to
> most people.

Sure.

> My bottom line: I'm surprised that a prolific and obviously smart guy like
> Robert has left such obvious (to me) questions out of his *Frequently Asked*
> Questions document, and I'm shocked at the poor quality of his examples. It's
> as though he doesn't really want to be understood clearly.

Since, I haven't prepared a web site on the topic, I am not going to
cast stones.

--
Ron

Darren

unread,
May 1, 2003, 7:21:58 PM5/1/03
to

Ron Peterson wrote:

> Darren <no.e...@thank.you> wrote:
>
> > Ron Peterson wrote:
>
> >> It seems that the LTV isn't about predicting the prices of products,
> >> instead it's about macro-economic concerns, AFAIK.
>
> > Robert has taken great pains to hide that. The *first sentence* of Robert's
> > document: "The LTV is the theory that market prices are attracted by prices
> > proportional to the labor time embodied in commodities."
>
> That would be a conclusion of the theory.

It's not clear to me how this sentence:


"It seems that the LTV isn't about predicting the prices of products, instead it's

about macro-economic concerns."
and this:


"The LTV is the theory that market prices are attracted by prices proportional to
the labor time embodied in commodities."

Can be reconciled.

If the LTV is a theory about market prices, then it can be used to predict market
prices. If the LTV isn't such a theory, then it can't be used to predict market
prices.... and I'm back at square one wondering what the LTV is.

> > But "A theory that market prices are attracted by _________" is exactly about
> > predicting market prices. That's what a theory is.
>
> An economic theory is a model of economic processes.

...That makes testable predictions.

> I think that the
> purpose of studying economics is to make decisions that will give the
> greatest benefit for the least cost(labor time).

I agree with your statement of purpose for economics.... and the idea of quantifying
"economic cost" as labour *time* is interesting and intriguing as a *normative*
concept. So *that's* what the LTV is trying to get at. This could even be compared
and contrasted to "mainstream" concepts like Consumer Surplus and all that....
interesting.

> >> A Van Gogh painting isn't a commodity. And, you are back to describing
> >> prices.
>
> > LTV explains the price of a can of beans (sort of), but not a Van Gogh.
> > S and D explains the price of a can of beans AND the price of a Van Gogh.
>
> > So why do I need the LTV?
>
> So we can determine the best way to maximize economic benefit.

So it seems to me that the LTV is not really a *theory* (ie it is utterly
untestable), it is a normative statement about 'value' and 'cost' (ie that they
*should* be based on labour). Nothing wrong with normative statements at all, let's
just be clear about what we are saying.

> > And again, if the LTV is not about prices, it is not immediately clear to me
> > from Robert's document what it is about.
>
> I think that economics is like an elephant being viewed by a number of
> blind men.

Well, we are trying to take off our blindfolds, you know ;)

> >> Robert does discuss use-value. Use-value does matter in that if a
> >> commodity has no use-value to anyone, its exchange-value will be nil.
>
> > Yes, I just didn't see it made clear that a commodity does not and cannot have
> > a single, innate "use-value". I've seen people get hung up on this point
> > before, so it is worthy of FAQ inclusion. (The F stands for "frequently").
>
> Maybe, Robert will expand the Web page to include other questions.
>
> >> You can define value in terms of other things besides labor, but its the
> >> one thing that most people have. So, all that the LTV is saying is that
> >> labor (actually labor-time) can be associated with all commodities.
>
> > OK, but this statement isn't really a "theory" anymore, it's a mundane
> > truism. This is exactly what corporate accountants do all day, associate
> > labour time with commodities produced. (I used to write software for some of
> > them).
>
> I don't see how the LTV is a mundane truism. It's not obvious to me.

If LTV is merely saying " labor-time can be associated with all commodities.", I can
assure you that nothing could be more mundane. That is exactly what armies of cost
accountants around the world do all day long, Monday to Friday, with two 15 minute
coffee breaks daily and three weeks of vacation per year. They count the number of
widgets produced, they count the labour hours dedicated to widget production and
overhead (ie sweeping the floors around the widget machines) and they "allocate" (ie
decide how many) labour hours in total went into each widget. I wrote computer
software to help people do this, and that software produced vast stacks of reports
on the labour-time per widget (along with some stuff about wages and total labour
costs per widget and whatnot), which executives read while sipping their morning
coffee.

HOWEVER, if LTV merely says " labor-time can be associated with all commodities."
then I don't see where the V in the LTV is. Merely "associating labour time with
commodities" says nothing about the VALUE of the commodity.

> > But so what? Their prices will still be determined by many other things in
> > addition to the labour time embodied in them. Demand, for one. Ah, but the
> > LTV isn't about prices, OK, OK. Where is the "Value" part of the LTV then?
>
> It's assigning a labor-time value to items much as we can associate a
> weight or volume to items.

No, we cannot do this, because "weight" (mass actually) and "volume" are properties
that are intrinsic to the object, and "value" is not. (Exchange or use value,
doesn't matter). If we say "the value of that widget is seven labour hours"
(because it took the worker seven hours to make it), one might respond "value to
who? Widget A took two hours to produce, and Widget B took seven hours to produce,
but that says nothing about what their *value* will be *to me* (or to Bob, or Joe,
or Sue, or you)."

You might say "widget B *ought* to be worth more to you than widget A (ie higher use
value) because it took more labour hours to produce", that's a normative statement
to which I will reply "so what? I like widget A better".

And if you say "widget B *will* have a higher exchange value (ie market price) than
widget A", well that's a positive statement about market prices and we can go test
it.

Cheers,
Darren

Darren

unread,
May 1, 2003, 7:48:43 PM5/1/03
to

Darren wrote:

> Ron Peterson wrote:
>
> > Darren <no.e...@thank.you> wrote:
>

> > > DM: But so what? Their prices will still be determined by many other things in


> > > addition to the labour time embodied in them. Demand, for one. Ah, but the
> > > LTV isn't about prices, OK, OK. Where is the "Value" part of the LTV then?
> >

> > RP: It's ***assigning a labor-time value*** to items much as we can associate a


> > weight or volume to items.

Actually, I've had another thought. The problem is that the idea of "assigning value"
is ambiguous. "Assigning cost" is easy enough, the accountants do it, the executives
nod in approval and make decisions for the firm based on those costs, and life goes on.

But what does "assigning value" actually mean? Are we assigning "exchange value" based
on labour time (in other words, making predictions about market prices based on labour
time)? Or we assigning "use value" based on labour time? (ie whether you actually want
the damn thing or not, this widget *ought* to be useful to you because I put ten hours
of my labour into it).

Robert Vienneau

unread,
May 1, 2003, 9:18:32 PM5/1/03
to
In article <3EB1A910...@thank.you>, Darren <no.e...@thank.you>
wrote:

> Ron Peterson wrote:

> > Darren <no.e...@thank.you> wrote:

> > > Ron Peterson wrote:

> > >> It seems that the LTV isn't about predicting the prices of products,
> > >> instead it's about macro-economic concerns, AFAIK.

> > > Robert has taken great pains to hide that. The *first sentence* of
> > > Robert's
> > > document: "The LTV is the theory that market prices are attracted by
> > > prices
> > > proportional to the labor time embodied in commodities."

> > That would be a conclusion of the theory.

> It's not clear to me how this sentence:
> "It seems that the LTV isn't about predicting the prices of products,
> instead it's
> about macro-economic concerns."
> and this:
> "The LTV is the theory that market prices are attracted by prices
> proportional to
> the labor time embodied in commodities."
> Can be reconciled.

The focus of the first volume of Marx's Capital isn't about predicting


the prices of products, instead it's about macro-economic concerns.

The LTV is the theory that market prices are attracted by prices


proportional to the labor time embodied in commodities.

Marx used the LTV. Marx's theory of value isn't quite the same
as the LTV.

Ron Peterson

unread,
May 3, 2003, 7:32:21 PM5/3/03
to
Darren <no.e...@thank.you> wrote:

> It's not clear to me how this sentence:
> "It seems that the LTV isn't about predicting the prices of products, instead it's
> about macro-economic concerns."
> and this:
> "The LTV is the theory that market prices are attracted by prices
> proportional to the labor time embodied in commodities."
> Can be reconciled.

The "attracted by" simply means what would happen in a steady state
economy (i.e. no new technologies or products).

>Ron wrote:
>> I think that the
>> purpose of studying economics is to make decisions that will give the
>> greatest benefit for the least cost(labor time).

> I agree with your statement of purpose for economics.... and the idea
> of quantifying "economic cost" as labour *time* is interesting and
> intriguing as a *normative* concept. So *that's* what the LTV is
> trying to get at. This could even be compared and contrasted to
> "mainstream" concepts like Consumer Surplus and all that....
> interesting.

> So it seems to me that the LTV is not really a *theory* (ie it is

> utterly untestable), it is a normative statement about 'value' and
> 'cost' (ie that they *should* be based on labour). Nothing wrong with
> normative statements at all, let's just be clear about what we are
> saying.

>> I don't see how the LTV is a mundane truism. It's not obvious to me.

> If LTV is merely saying " labor-time can be associated with all
> commodities.", I can assure you that nothing could be more mundane.

Then how do you handle depreciation? Why is there a return to capital?

>> It's assigning a labor-time value to items much as we can associate a
>> weight or volume to items.

> No, we cannot do this, because "weight" (mass actually) and "volume"
> are properties that are intrinsic to the object, and "value" is not.

What is the weight and volume of a glass? There is nothing intrinsic
about those measures.

--
Ron

Darren

unread,
May 4, 2003, 2:13:43 PM5/4/03
to

Ron Peterson wrote:

> Darren <no.e...@thank.you> wrote:
>
> > It's not clear to me how this sentence:
> > "It seems that the LTV isn't about predicting the prices of products, instead it's
> > about macro-economic concerns."
> > and this:
> > "The LTV is the theory that market prices are attracted by prices
> > proportional to the labor time embodied in commodities."
> > Can be reconciled.
>
> The "attracted by" simply means what would happen in a steady state
> economy (i.e. no new technologies or products).

You missed the problem. 2nd sentence says LTV is a theory of prices (in other words: is
about predicting prices), first sentence directly contradicts this. Please advise.

> >Ron wrote:
> >> I think that the
> >> purpose of studying economics is to make decisions that will give the
> >> greatest benefit for the least cost(labor time).
>
> > I agree with your statement of purpose for economics.... and the idea
> > of quantifying "economic cost" as labour *time* is interesting and
> > intriguing as a *normative* concept. So *that's* what the LTV is
> > trying to get at. This could even be compared and contrasted to
> > "mainstream" concepts like Consumer Surplus and all that....
> > interesting.
>
> > So it seems to me that the LTV is not really a *theory* (ie it is
> > utterly untestable), it is a normative statement about 'value' and
> > 'cost' (ie that they *should* be based on labour). Nothing wrong with
> > normative statements at all, let's just be clear about what we are
> > saying.
>
> >> I don't see how the LTV is a mundane truism. It's not obvious to me.
>
> > If LTV is merely saying " labor-time can be associated with all
> > commodities.", I can assure you that nothing could be more mundane.
>
> Then how do you handle depreciation? Why is there a return to capital?

Why shouldn't there be? I think you are missing my point. The statement " labor-time


can be associated with all

commodities." alone is not an adequate theory of VALUE. Where is the reference to VALUE
in that statement?

> >> It's assigning a labor-time value to items much as we can associate a
> >> weight or volume to items.
>
> > No, we cannot do this, because "weight" (mass actually) and "volume"
> > are properties that are intrinsic to the object, and "value" is not.
>
> What is the weight and volume of a glass? There is nothing intrinsic
> about those measures.

Huh? Put a glass on a scale. Weigh it. That's the weight. If I put the glass on a
scale, I'll get the same reading as if you do it. Seems intrinsic to the glass to me.
(actually "weight", strictly speaking, is not intrinsic: it's the force of earth's
gravity, if you took the glass to the Moon, the "weight" would be something else. MASS
is actually the intrinsic quality... and the MASS can be deduced from the weight. But I
don't think that's what you were getting at.... however I'm not sure what you *were*
getting at.) If every single human on earth drops dead tomorrow, the weight of the glass
does not change, but the idea of "the value of the glass" suddenly becomes meaningless.
The glass is unchanged, but there is no one to value it.

You might think I'm nit-picky, fussing over definitions and whatnot, but I find that
asking people to clearly say what they mean settles a lot of discussions before they even
start. The definitions of the LTV that I'm being given are persistently and maddeningly
unclear, as though the people who write about LTV are allergic to plain English, and that
tells me something right there.

Darren


Darren

unread,
May 5, 2003, 1:37:46 AM5/5/03
to

Robert Vienneau wrote:

> In article <3EB0879A...@thank.you>, Darren <no.e...@thank.you>
> wrote:
>
> > http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/LTV-FAQ.html
> >
> > Hi, I looked this over and just thought I'd share a few thoughts. I'm
> > just an undergraduate Econ student with no serious credentials or
> > knowledge of Marxism, just curiosity.
>
> > 1. I was very, very surprised that one of the Frequently Asked
> > Questions about the LTV wasn't "what about supply and demand"? Millions
> > of people have shambled through Econ 101 and heard the little story
> > about Supply and Demand. Some of those people, if they grow curious
> > about Marxism and the LTV, are going to check out your LTV document, and
> > that question will be the first one out of their mouths. It will
> > certainly be "Frequently Asked"!
>
> Look at:
>
> "5.7 How has an analysis of prices of production been used to
> construct a critique of bourgeois economics?"
>
> Maybe expecting readers to associate "bourgeois economics" with
> "Supply and Demand" is too much.

It was too much for me to pick up on, anyway. I think you should change the title
to "What about Supply and Demand"? Also, 5.6 seems a relevant section. Will
review when time permits... although to be honest I'm detecting some
unsubstantiated assertions about neo-classical economics and axe-grinding in your
document, IMHO.

> I could have expanded that
> question to lots of points. But I didn't want the FAQ to be
> overbalanced there. I wanted it more to be an examination of
> the LTV from a viewpoint internal to traditions in which the LTV
> was developed.

I'm suspicious of "viewpoints"... why not write for an intelligent and curious
reader? Surely you don't have to rely so heavily on Marxese to get your points
across.

> > 2. Numerical examples are always great learning tools, but why on earth
> > did you pick such preposterous numbers for your example in section 3.2?
> > 73 and 9/17 quarters of wheat!
>
> The numbers I picked were in the table above. 73 9/17 is derived. I
> suppose I could multiply everything by, I guess, 51. I don't see
> that that makes everything too much clearer. There's no way of
> explaining this that I can see that doesn't use ratios.

I'm actually going to try to convert your example algebraically and see if it
makes more sense. I'm not sure I believe you when you say that 73 and 9/17 was the
simplest number to come up with. I can't believe you couldn't massage the numbers
a bit to illumiate the concepts better while preserving the same relationships.
12/4 and (214 1/7) / (71 8/21) is the same ratio, but one is much clearer than
the other.

> As you doubtless know, utility underlies the bourgeois theory of
> the demand for consumer goods. Note:
>
> "2.2 What are 'use values?'"

So use value is just the "utility" that my evil neo-classical economics instructor
taught me? If it isn't, I don't see the difference (except in the idea that
use-value would have to have multiple dimensions - that is different kinds of
"utility" A and B in an object that a person wouldn't know how to trade off from...
I suppose if use-value couldn't be reduced to a single dimension, and a person was
offered bundle X with use value 2A + 3B or bundle Y with use value 3A + 2B, he
would simply explode from indecision).

> I don't see the answer denying that a use-value is in the
> relationship between a thing and an evaluator. I do note that
> Ricardo and Marx don't seem to think use-value can be reduced
> to a single dimension.

Though I don't see much of this "use value is relative" point being made in the
document much, either. Perhaps it is irrelevant? If so, it's not clear to me how
use-value fits into "exploitation".

I cannot shake the feeling that this material has been made deliberately confusing.

> Many seem to find the existence of this whole math-and-Marx bit
> astonishing.

Well, to be blunt, considering how easily I sailed through the neo-classical stuff
with straight As, I'm finding the Marxist math suspiciously daunting. Will try to
give it more time.

Darren


Ron Peterson

unread,
May 5, 2003, 9:25:50 AM5/5/03
to
Darren <no.e...@thank.you> wrote:

> Why shouldn't there be? I think you are missing my point. The
> statement " labor-time can be associated with all commodities." alone
> is not an adequate theory of VALUE. Where is the reference to VALUE
> in that statement?

Note: Please set your line wrap to something less than 80 characters.

I think I see the cause of your confusion. There is a labor-time-value
that can be associated with commodities, just like there can be
associated a weight-value with an object. Value without a qualifier is
meaningless.

>> What is the weight and volume of a glass? There is nothing intrinsic
>> about those measures.

> Huh? Put a glass on a scale. Weigh it. That's the weight. If I
> put the glass on a scale, I'll get the same reading as if you do it.

No, I think we're likely to get different weights. Drinking glasses can
be made of different material and have different capacities.

> You might think I'm nit-picky, fussing over definitions and whatnot,
> but I find that asking people to clearly say what they mean settles a
> lot of discussions before they even start. The definitions of the LTV
> that I'm being given are persistently and maddeningly unclear, as
> though the people who write about LTV are allergic to plain English,
> and that tells me something right there.

I think that its very important to be fussy over definitions. If the
definitions aren't consistent, the theory won't make sense. And if the
definitions don't match up with the real world, there isn't going to be
any way to test the theory.

LTV originated in the 18th and 19th centuries. Well, maybe the Greeks
had it first. Economists like to maintain continuity with the past and
that is why some of the terminology is archaic.

LTV only establishes a measuring device. To have a full economic theory
there needs to be a model of the economy which may vary with the
structure of society and technological developments.

--
Ron

Darren

unread,
May 5, 2003, 2:04:15 PM5/5/03
to

Ron Peterson wrote:

> Darren <no.e...@thank.you> wrote:
>
> > Why shouldn't there be? I think you are missing my point. The
> > statement " labor-time can be associated with all commodities." alone
> > is not an adequate theory of VALUE. Where is the reference to VALUE
> > in that statement?
>
> Note: Please set your line wrap to something less than 80 characters.

Sorry. My news program does that sometimes, I don't know why. I am always
set to 72 but sometimes it doesn't work.

>
>
> I think I see the cause of your confusion. There is a labor-time-value
> that can be associated with commodities, just like there can be
> associated a weight-value with an object. Value without a qualifier is
> meaningless.

Actually, *you* are the cause of my confusion :).

"Weight-value" is redundant at best, and an oxymoron at worst. If you
mean "weight", say "weight". "Weight value" is faux-precision.

You are confusing the issue, I think, by using the word "value"
interchangably as
- a synonym for "quantity" or "number", ie "weight value" - this sort of
value does not need a "valuer", it is an objective reality. I would argue
that this is a faulty use of the word "value", I think careful people try to
avoid implying that any sort of "value" is something that exists in
objective reality.
- Worth in usefulness or importance to the possessor; utility or merit: (ie:
"use value" and DOES need a valuer). It is a subjective opinion about an
object that can vary from person to person

So, back to the beginning. Is "labor-time-value" a positive or normative
concept? Is it objective or subjective? There is no "value" without a
"valuer", so does "associating a labor-time-value with a commodity" mean
"forcing every single valuer to value something the same way" or is it
merely an accounting technique that people are free to use or disregard as
they see fit? If the latter, you shouldn't say "labour time value" at all,
it implies something about the value of the object.

I agree that we can associate a labor-time (notice I dropped the word
"value") with commodities. The cost accountants do it all the time as I
said ("that widget took 7.63 hours of labour time when you factor in all the
machine maintenance labour, etc").

But the question is: what is the *significance* of that figure? Value to
*who*. For the cost accountants, their answer is "well, we are measuring
that to calculate the monetary cost of labour TO US, so we can make our
profit maximization business decisions". Hey, at least they're honest.

>
>
> >> What is the weight and volume of a glass? There is nothing intrinsic
> >> about those measures.
>
> > Huh? Put a glass on a scale. Weigh it. That's the weight. If I
> > put the glass on a scale, I'll get the same reading as if you do it.
>
> No, I think we're likely to get different weights. Drinking glasses can
> be made of different material and have different capacities.

I was talking about us measuring the same glass. You could think a 152-gram
glass is very useful and I could think it is an ugly piece of kitsch.... it
still weighs 152 grams no matter what *any* of us *think*. Weight is an
objective fact, "value" is a subjective opinion.

>
>
> > You might think I'm nit-picky, fussing over definitions and whatnot,
> > but I find that asking people to clearly say what they mean settles a
> > lot of discussions before they even start. The definitions of the LTV
> > that I'm being given are persistently and maddeningly unclear, as
> > though the people who write about LTV are allergic to plain English,
> > and that tells me something right there.
>
> I think that its very important to be fussy over definitions.

We agree there.

> If the
> definitions aren't consistent, the theory won't make sense. And if the
> definitions don't match up with the real world, there isn't going to be
> any way to test the theory.
>
> LTV originated in the 18th and 19th centuries. Well, maybe the Greeks
> had it first. Economists like to maintain continuity with the past and
> that is why some of the terminology is archaic.
>
> LTV only establishes a measuring device.

What is it measuring? And I have a second problem with the statement
(perhaps related to your archaic terminology observation): "theories" are
not "measuring devices".

Theories make falsifiable predictions. Measuring devices don't.

Robert Vienneau

unread,
May 5, 2003, 4:14:31 PM5/5/03
to
In article <3EB5EFB5...@thank.you>, Darren <no.e...@thank.you>
wrote:

> Robert Vienneau wrote:

> > In article <3EB0879A...@thank.you>, Darren <no.e...@thank.you>
> > wrote:

> > > http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/LTV-FAQ.html

> > Look at:

> > "5.7 How has an analysis of prices of production been used to
> > construct a critique of bourgeois economics?"

> > Maybe expecting readers to associate "bourgeois economics" with
> > "Supply and Demand" is too much.

> It was too much for me to pick up on, anyway. I think you should change
> the title
> to "What about Supply and Demand"?

The wording I chose is more focused and indicates why 5.7 is under
5.0. The words "Supply" and "Demand" are used by the Classical
economists in a different sense. I don't go into that. (Your
knowledge of the Neoclassical sense might actually be a hinderance
if you try to make sense out of Adam Smith in the context of his
times.)

I'm not in any hurry to change the wording.

> Also, 5.6 seems a relevant section.

It is.



> Will
> review when time permits... although to be honest I'm detecting some
> unsubstantiated assertions about neo-classical economics and axe-grinding
> in your
> document, IMHO.

I could have expanded the answer to Question 5.7. But I didn't want
the FAQ to be overbalanced there. My FAQ is mostly NOT about how
Supply and Demand are wrong, which they are.

Two centuries of work underly my FAQ. Naturally it is not long
enough to adequately explore all that work. So why shouldn't some
assertions be not completely substantiated?



> > I could have expanded that
> > question to lots of points. But I didn't want the FAQ to be
> > overbalanced there. I wanted it more to be an examination of
> > the LTV from a viewpoint internal to traditions in which the LTV
> > was developed.

> I'm suspicious of "viewpoints"... why not write for an intelligent and
> curious
> reader? Surely you don't have to rely so heavily on Marxese to get your
> points across.

The above seems almost content-free to me. I would be doing the reader
of my FAQ a disservice if I did not explain such terms as "labor
value", "organic composition of capital", and "transformation
problem". A theory as comprehensive as the LTV or Marx's naturally
has a language of technical terms to go along with it. And part of
the point of my FAQ is to help the reader understand some key terms
in that language.



> > > 2. Numerical examples are always great learning tools, but why on
> > > earth
> > > did you pick such preposterous numbers for your example in section
> > > 3.2?
> > > 73 and 9/17 quarters of wheat!

> > The numbers I picked were in the table above. 73 9/17 is derived. I
> > suppose I could multiply everything by, I guess, 51. I don't see
> > that that makes everything too much clearer. There's no way of
> > explaining this that I can see that doesn't use ratios.

> I'm actually going to try to convert your example algebraically and see
> if it
> makes more sense.

It would not surprise me that you don't have math advanced enough
to express that in a way that I find convenient. The concepts of
eigenvectors and eigenvalues run through the answers to several
questions (e.g., 6.5).

> I'm not sure I believe you when you say that 73 and
> 9/17 was the
> simplest number to come up with.

Did I say that? No, I did not.

The quantity flows in the answer to Question 3.2 are:

74 qr. wheat & 37 t. iron & 592 workers -> 592 qr. wheat
18 qr. wheat & 3 t. iron & 48 workers -> 48 t. iron

Divide the first row by 592 and the second by 48:

(1/8) qr. wheat & (1/16) t. iron & 1 worker -> 1 qr. wheat
(3/8) qr. wheat & (1/16) t. iron & 1 worker -> 1 t. iron

Notice that in the answer to Question 3.2, the net output of the
wheat subsystem is 500 quarters. The net output of the iron subsystem
is 8 tons.

Evidently, I picked nice fractions out of the air. I then did some
manipulation to ensure whole numbers appear in the starting data
and some of the results.

Some of the intermediate numbers are fractions.

I notice you did not answer my direct question about what you
found unclear about the text in the answer to Question 3.2.

> > As you doubtless know, utility underlies the bourgeois theory of
> > the demand for consumer goods. Note:

> > "2.2 What are 'use values?'"

> So use value is just the "utility" that my evil neo-classical economics
> instructor taught me?

What are you on about? No, it is not.

> If it isn't, I don't see the difference (except in the idea
> that
> use-value would have to have multiple dimensions - that is different
> kinds of
> "utility" A and B in an object that a person wouldn't know how to trade
> off from...

Not "utility" A and B. The chemical composition of a loaf of
bread has something to do with why it provides nutrition to us.
(What is nutrious varies among the fauna on this planet; it is
not intrinsic in the bread, but is relative to the creature
eating it.) The nutrition of bread is a use-value.

A brick, for example, is not nutritious. But it has other use
values.

> I suppose if use-value couldn't be reduced to a single dimension, and a
> person was
> offered bundle X with use value 2A + 3B or bundle Y with use value 3A +
> 2B, he
> would simply explode from indecision).

I am not interested in whatever handwaving your professor may
have used to get you to accept the preconceptions of utility
theory, which he probably did not make explicit.

> > I don't see the answer denying that a use-value is in the
> > relationship between a thing and an evaluator. I do note that
> > Ricardo and Marx don't seem to think use-value can be reduced
> > to a single dimension.

> Though I don't see much of this "use value is relative" point being made
> in the
> document much, either. Perhaps it is irrelevant? If so, it's not clear
> to me how
> use-value fits into "exploitation".

I don't think the use value of consumer goods has much to do with
the notion of exploitation explicated in my FAQ. And I don't
understand why you raise the question.



> I cannot shake the feeling that this material has been made deliberately
> confusing.

Do you find continually accusing somebody of having nefarious motives
encourages them to help you out?



> > Many seem to find the existence of this whole math-and-Marx bit
> > astonishing.

> Well, to be blunt, considering how easily I sailed through the
> neo-classical stuff
> with straight As, I'm finding the Marxist math suspiciously daunting.
> Will try to
> give it more time.

I would think an adult would realize how rarely anybody cares about
one's grades.

Ron Peterson

unread,
May 5, 2003, 7:35:04 PM5/5/03
to
Darren <no.e...@thank.you> wrote:

> I agree that we can associate a labor-time (notice I dropped the word
> "value") with commodities. The cost accountants do it all the time as I
> said ("that widget took 7.63 hours of labour time when you factor in all the
> machine maintenance labour, etc").

So then you agree as far as I am concerned.

> But the question is: what is the *significance* of that figure? Value to
> *who*. For the cost accountants, their answer is "well, we are measuring
> that to calculate the monetary cost of labour TO US, so we can make our
> profit maximization business decisions". Hey, at least they're honest.

It looks like businesses also agree.

> What is it measuring? And I have a second problem with the statement
> (perhaps related to your archaic terminology observation): "theories" are
> not "measuring devices".

Take the theory of thermodynamics. Proposition 0 is that there is
something called temperature. It is introducing the idea of a measure
and it is a part of a theory.

--
Ron

Robert Vienneau

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May 7, 2003, 5:21:41 AM5/7/03
to
Consider Question 5.2 in:

<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/LTV-FAQ.html>

The answer consider a simple model economy in which the following
quantity flows are observed:

74 qr. wheat & 37 t. iron & 592 workers -> 592 qr. wheat
18 qr. wheat & 3 t. iron & 48 workers -> 48 t. iron

The right hand side shows produced outputs in the wheat and iron
sectors, respectively. The left hand side shows inputs.

This post provides an algebraic representation of prices for
this example. Divide the first row above by 592 and the second by 48:



(1/8) qr. wheat & (1/16) t. iron & 1 worker -> 1 qr. wheat
(3/8) qr. wheat & (1/16) t. iron & 1 worker -> 1 t. iron

The Leontief input-output matrix is:

A = 1/8 3/8
1/16 1/16

The (row) vector of direct labor coefficients is:

a0 = [ 1 1 ]

Each column represents an industry. These are inputs for a unit
level of gross outputs.

Notice that quantity flows shown at the start have a net output of

c' = [ 500 qr. wheat 8 t. iron ]

(x' represents the tranpose of x.) So c is a column vector. Let c
represent the numeraire. Let w be the wage. Then w c represents
quantities that workers can consume. Consider the augmented
Leontief input-output matrix:

A(w) = A + c a0 w = (20 + 125 w)/160 (60 + 125 w)/160
(10 + 2 w)/160 (10 + 2 w)/160

The augmented Leontief matrix shows inputs per unit-level outputs,
including inputs that the workers purchase from their wages.

Let p = [ pw pi ] be a (row) vector representing the price of
wheat and iron, respectively. The assumption on the numeraire
yields the equation:

p c = 1 (*)

Assume the same rate of (accounting) profits, r, is earned in
both sectors. This gives the matrix equation:

p A(w) (1 + r) = p (**)

Obviously equations (*) and (**) could be generalized to an n-sector
model.

Rewrite (**):

p A(w) = 1/(1 + r) p

The desired price vector is an eigenvector of the augmented Leontief
input-output matrix corresponding to the eigenvalue 1/(1 + r). An
eigenvector with all positive elements is desired. This is ensured
by taking the Frobenius root of the augmented Leontief input-output
matrix.

Rewriting,

p [ (1/(1 + r)) I - A(w) ] = 0

For there to be a non-trivial solution, the determinate must be
zero:

determinate [ (1/(1 + r)) I - A(w) ] = 0

(That is, the two equations are linearly dependent.) This condition
on the determinate is the characteristic equation, used for finding
the eigenvalues of the augmented Leontief input-output matrix. Some
algebraic manipulation of the characteristic equation provides the
wage in terms of an exogeneously specified profit rate:

w = 5 (17 + r)(3 - r)/[(255 + r)(1 + r)]

The eigenvector of interest is:

p = [ pw pi ] = [ 320/(255 + r) 80 (5 + r)/(255 + r) ]

This solution holds for r in the range [0, 300%].

Under an old reading, Marx thought, incorrectly, that he could
plug in a value for the rate of profits as determined in the
system of labor values. Even so, the above model of prices is
not a marginalist theory. And labor values have some use in
applications of this sort of model.

Obviously, I do not present things this way in my FAQ. I did
not want to limit my audience to those who know advanced mathematics.
(I consider Perron-Frobenius theorems to be advanced mathematics.)

Darren

unread,
May 7, 2003, 11:26:31 AM5/7/03
to
Thanks Robert. I've had a rather insinuating tone in my questions, and your
replies, by contrast, have been quite courteous. Will have a look at this as time
permits. I know some Linear Algebra from long ago...

Darren

Robert Vienneau wrote:

snip...

Keith Ramsay

unread,
May 7, 2003, 11:44:04 PM5/7/03
to
Robert Vienneau <rv...@see.sig.com> wrote in message news:<rvien-8C5431....@news.dreamscape.com>...

| For there to be a non-trivial solution, the determinate must be
| zero:

DeterminANT.

Robert Vienneau

unread,
May 9, 2003, 5:38:40 AM5/9/03
to

> DeterminANT

Thanks. I've probably been consistently wrong for years.

Did you enjoy seeing that there was such an application of the
Perron-Frobenius theorems (assuming you haven't seen it before)?

The economists who participate on sci.econ will not comment. sci.econ
over a number of years provides empirical evidence that most
mainstream North American economists are ignorant of price theory.
Lately, they seem to have tired of continually demonstrating this
claim.

Keith Ramsay

unread,
May 10, 2003, 1:17:40 AM5/10/03
to
Robert Vienneau <rv...@see.sig.com> wrote in message news:<rvien-384FA4....@news.dreamscape.com>...

| > Robert Vienneau <rv...@see.sig.com> wrote in message
| > news:<rvien-8C5431....@news.dreamscape.com>...
| > | For there to be a non-trivial solution, the determinate must be
| > | zero:
|
| > DeterminANT
|
| Thanks. I've probably been consistently wrong for years.

Perhaps one reason why people abbreviate it to "det" in formulas. :-)

The determinant is the thing by which one determines, just as the
discriminant is the thing by which one discriminates, the resolvant is
the thing by which one resolves, and so on. As far as I know
determinate is just an adjective.

| Did you enjoy seeing that there was such an application of the
| Perron-Frobenius theorems (assuming you haven't seen it before)?

I haven't seen the Perron-Frobenius theorems, at least not by that
name. I'm not surprised that eigenvectors and eigenvalues appear in
economic theory at some point. It didn't look like you were using
anything too mysterious to be quoted without proof.

I'm a little more intruiged by the claim that "Econ 101" presents a
misleading picture of how prices are set. I've seen the criticism that
the "supply versus demand" story you get there treats the supply and
demand as though they were more well defined and definite functions of
price than is realistic, but I haven't taken the time to find out
about alternative theories.

I asked a Russian immigrant who said he'd been made to study Marx in
school if he could explain how Marx differed from more familiar
economists like Smith. He didn't answer directly, but said they'd had
official sessions devoted to criticizing the others-- finding that
they were wrong was a foregone conclusion-- and perhaps this kind of
study was not quite as informative as one might want!

Keith Ramsay

Robert Vienneau

unread,
May 10, 2003, 4:57:44 PM5/10/03
to
In article <17a4a089.03050...@posting.google.com>,
kra...@aol.com (Keith Ramsay) wrote:

> Robert Vienneau <rv...@see.sig.com> wrote in message
> news:<rvien-384FA4....@news.dreamscape.com>...

> | Did you enjoy seeing that there was such an application of the


> | Perron-Frobenius theorems (assuming you haven't seen it before)?

> I haven't seen the Perron-Frobenius theorems, at least not by that
> name. I'm not surprised that eigenvectors and eigenvalues appear in
> economic theory at some point. It didn't look like you were using
> anything too mysterious to be quoted without proof.

There was a thread in sci.math within the last week about Frobenius
theorems.

For the economic solution to make sense, the eigenvalue 1/(1 + r)
must be less than unity. And all the elements of the corresponding
eigenvector must be nonnegative. How can I know this is so?

Consider a Markov chain with time-invariant state-transition
probabilities. Let M be a matrix representing the state transition
probabilities. Steady-state probabilities satisfy the condition:

p = M p

Here, one of the eigenvalues must be unity. And all the elements of
the corresponding eigenvector must be non-negative. (That they sum
up to one is just a normalization condition; since eigenvectors
are only defined up to a scalar multiple, this is no big deal.)
How can one be be sure that unity is an eigenvalue?

In both cases, one might say the physical setting of the problem
ensures that the desired solution exists. But that's handwaving.
Can you provide a mathematical proof? That's what the Perron-
Frobenius theorems are about - how to get from conditions on
M or A(w) to these properties of the solution.

I have to look up the theorems myself (which I'm not doing today).
In the case of a Markov chain, you can see that all the elements of
M are non-negative and the columns add up to unity. Furthermore, for
all the elements of p to be strictly positive it would seem that M
would have to be irreducible; otherwise there would be transient
states.

This seems to be analogous to the augmented Leontief input-output
matrix, A(w), being irreducible and the workers consuming the
entire net output. So 1/(1 + r) = 1 in this case. Which means, in
the notation of my previous post:

p A(w) = p (A + c a0 w) = p

So I've already used a Perron-Frobenius theorem. By the condition on
the numeraire:

p A + a0 w = p

Or

a0 = (1/w) p (I - A)

Or

(1/w) p = a0 inv( I - A )

where a Perron-Frobenius theorem guarantees the inverse exists.

Let y be a column vector of net outputs and q be a column vector
of gross outputs. They are related as:

y = q - A q = (I - A) q

That is, the net outputs do not include the material inputs needed
for their production. The labor time required to produce the given
net output is

a0 inv( I - A ) y

Now, suppose net output consists of a single unit of the jth good.
That is, y is e(j), where e(j) is the jth column of the identity
matrix. The labor time, v(j), required to produce this net output
is defined to be the labor value of the jth commodity:

v(j) = a0 inv(I - A) e(j)

You can see that the row vector of labor values is:

v = a0 inv( I - A )

which implies

v = (1/w) p

And so we've proven that if the entire surplus is paid out in
wages, the rate of profits, r, will be zero and the associated
prices will be proportional to labor values. Do you see that
the Perron-Frobenius theorems enter in an essential way to make
everything work out nice?

> I'm a little more intruiged by the claim that "Econ 101" presents a
> misleading picture of how prices are set. I've seen the criticism that
> the "supply versus demand" story you get there treats the supply and
> demand as though they were more well defined and definite functions of
> price than is realistic, but I haven't taken the time to find out
> about alternative theories.

The criticism I refer to is not about realism of assumptions. It is
about logical consistency. I here append a numerical example that I
presented before. This example is consistent with neoclassical
assumptions. The question is how can this be consistent with a
labor market with a downward-sloping labor demand function in
quantity-price space, as in Econ 101. Nobody who posts here has
ever addressed this question with a clear answer.

I have more discussion of this on my Web site, including some
(relatively) more advanced math that I don't bring out in my
numerical example.



> I asked a Russian immigrant who said he'd been made to study Marx in
> school if he could explain how Marx differed from more familiar
> economists like Smith.

I've seen a little bit about what they've had to say about others.
It's lots of abuse. Marx drew heavily on Ricardo and Smith. You
can see that in my LTV FAQ.

> He didn't answer directly, but said they'd had
> official sessions devoted to criticizing the others-- finding that
> they were wrong was a foregone conclusion-- and perhaps this kind of
> study was not quite as informative as one might want!

Marx wrote a three part long tome - Theories of Surplus Value -
about his predecessors. There's lots of points of detail he said
they were wrong about. But I think his main criticism of his
predecessors is that they take institutions like wage-labor as
given and natural. There was history, but now that bourgeois
society exists, there is no more. Marx takes his problem as to
explain how these institutions came to be and how they are supposedly
to be transcended.

There's also a Marxist critique of J. S. Mill - though I forget
whether this is in Marx or his followers. Mill examined distribution
after production. He seems to say that the surplus can be distributed
any way we choose, independently of production. He does not notice
that the institutions and mechanisms by which the surplus is
distributed have an impact on how much there is.

1.0 INTRODUCTION

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 are obviously unreasonable. 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 for corn is the solution of an optimization
problem in which as much corn as possible is produced from the
given inputs. Accordingly, the production function for corn is
found as the solution to the Linear Program in Display 1:

Max X = X1 + X2

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

X1 >= 0, X2 >= 0

Let f(L, Q1, Q2) 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.

APPENDIX A: A FORMAL MODEL

Let
Xa = Bushels corn produced (gross) by process A
Xb = Bushels corn produced by process B
Xc = Tons iron produced by process C
Xd = Tons iron produced by process D
p = the accounting price of iron (corn is numeraire)
w = wage
r = rate of (accounting) profits
Q1 = Tons iron in firm's inventory at start of period
Q2 = Bushels corn in firm's inventory at start of period

The profit-maximizing firm solves the following program:

Given p, w, Q1, and Q2
Choose Xa, Xb, Xc, and Xd
To Maximize (1 - w - 2 p - (2/5)) Xa
+ (1 - w - (1/2) p - (3/5)) Xb
+ (p - w - (1/10) p - (1/40)) Xc
+ (p - (275/464) w - (113/232) p) Xd
Such that
(w + 2 p + (2/5)) Xa
+ (w + (1/2) p + (3/5)) Xb
+ (w + (1/10) p + (1/40)) Xc
+ ((275/464) w + (113/232) p) Xd <= Q1 p + Q2
Xa, Xb, Xc, Xd >= 0

The dual Linear Program is:

Given p, w, Q1, and Q2
Choose r
To Minimize (Q1 p + Q2) r
Such That
(w + 2 p + (2/5)) r >= 1 - w - 2 p - (2/5)
(w + (1/2) p + (3/5)) r >= 1 - w - (1/2) p - (3/5)
(w + (1/10) p + (1/40)) r >= p - w - (1/10) p - (1/40)
((275/464) w + (113/232) p) r >= p - (275/464) w - (113/232) p
r >= 0

Or:

Given p, w, Q1, and Q2
Choose r
To Minimize (Q1 p + Q2) r
Such That
(w + 2 p + (2/5))(1 + r) >= 1
(w + (1/2) p + (3/5))(1 + r) >= 1
(w + (1/10) p + (1/40))(1 + r) >= p
((275/464) w + (113/232) p)(1 + r) >= p
r >= 0

If a constraint in the dual is met with inequality in the solution, the
corresponding process in the primal will be operated at a level of zero.

For firms to continue production unaltered from period to period, both
corn and iron must be produced each period. For corn to be produced,
either the first or the second constraint in the dual must be met with
equality. Likewise, for iron to be produced, the third or the fourth
constraint in the dual must be met with equality. Hence, for the
analyzed firms to be in equilibrium, the vertically-integrated industry
must be on the so-called factor-price frontier for that industry.

Nothing guarantees that the firms will be able to sell their output
at any given location on the factor-price frontier. Whether prices that
allow firms to be in equilibrium are realized is a question that is
not addressed by this formal model.

Robert Vienneau

unread,
May 13, 2003, 5:10:40 PM5/13/03
to
Consider Question 4.1 in:

<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/LTV-FAQ.html>

This post provides an algebraic presentation of the mentioned theorem
for a simple case. Let A be a (square) Leontief input-output matrix and
a0 be the corresponding (row) vector of direct labor inputs. That is,
the ith element of the jth column of A is the material input of the
ith commodity required per unit produced of the jth commodity. The jth
element of a0 is the direct labor time required to produce a unit of
the jth commodity. Assume A is irreducible and that the maximum
eigenvalue of A is less than unity.

Let c be a column vector denoting a unit level of the commodities
which the workers purchase out of their wages. Let w be the wage,
using c as numeraire. The augmented Leontief input-output matrix
is

A(w) = A + c a0 w

Let q be a column vector denoting the gross outputs of each
industry, and let y be a column vector denoting the net outputs.
Gross and net ouputs are related as follows:

y = (I - A) q

Or:

q = inv( I - A ) y

where the inverse exists by a Perron-Frobenius theorem.

The labor force employed is given by

L = a0 q = a0 inv( I - A ) y

The goods purchased by the workers consist of

c w L = = c a0 q w = c a0 inv( I - A ) y w

The remainder of net output is purchased out of (accounting) profits.

Let v( j ) be the additional amount of labor that would be
performed in a stationary-state with the same technique, but a net
output that differs from y in containing one more unit of the jth
commodity. Then:

v( j ) = a0 inv( I - A ) e( j )

where e( j ) is the jth column of the identity matrix. Let v be
the row vector whose jth element is v( j ). Then:

v = a0 inv( I - A)

v is the vector of labor-values. Consider the ratio

e = v ( I - A - c a0 w ) q / ( v c a0 q w )

The numerator represents the labor embodied in the commodities
purchased out of profits. The denominator represents the labor
embodied in the commodities purchased out of wages.

Now consider prices. Let p be a row vector denoting prices. One has

p A(w) = (1/(1 + r)) p

and

p c = 1

The rate of profits, r, is:

r = 1/lambda( A(w) ) - 1

where lambda( X ) is the Frobenius root of the matrix X. The
assumptions on the Leontief input-output matrix imply that positive
prices and rate of profits exist for nonnegative r less than or equal
to some nonnegative value.

Notice that often there does not exist a k > 0 such that

p = k v

Definition: Labor is exploited if and only if

e > 0

Theorem: r > 0 if and only if e > 0.

In other words, the rate of profits is positive if and only if
labor is exploited.

ro...@telus.net

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May 14, 2003, 1:06:17 AM5/14/03
to
On Tue, 13 May 2003 17:10:40 -0400, Robert Vienneau
<rv...@see.sig.com> wrote:

> Definition: Labor is exploited if and only if
>
> e > 0
>
> Theorem: r > 0 if and only if e > 0.
>
> In other words, the rate of profits is positive if and only if
>labor is exploited.

All that, just to redefine profit as exploitation?

-- Roy L

Robert Vienneau

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May 15, 2003, 5:20:54 AM5/15/03
to

What utter and complete bollocks.

ro...@telus.net

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May 15, 2003, 5:08:27 PM5/15/03
to
On Thu, 15 May 2003 05:20:54 -0400, Robert Vienneau
<rv...@see.sig.com> wrote:

>In article <3ec1ce88...@news.telus.net>, ro...@telus.net wrote:
>
>> On Tue, 13 May 2003 17:10:40 -0400, Robert Vienneau
>> <rv...@see.sig.com> wrote:
>>
>> > Definition: Labor is exploited if and only if
>> >
>> > e > 0
>> >
>> > Theorem: r > 0 if and only if e > 0.
>> >
>> > In other words, the rate of profits is positive if and only if
>> >labor is exploited.
>
>> All that, just to redefine profit as exploitation?
>
>What utter and complete bollocks.

It is simple fact, Robert. All you have done is define _any_ profit
as exploitation. There is no other possible interpretation for

>> > In other words, the rate of profits is positive if and only if
>> >labor is exploited.

Deal with it.

-- Roy L

Darren

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May 16, 2003, 5:55:54 PM5/16/03
to
ro...@telus.net wrote:

> >> Roy: All that, just to redefine profit as exploitation?
> >
> >Robert: What utter and complete bollocks.
>
> Roy: It is simple fact, Robert. All you have done is define _any_


> profit
> as exploitation. There is no other possible interpretation for
>

> >> > Robert: In other words, the rate of profits is positive if and


> only if
> >> >labor is exploited.

I would have to agree with Roy on this one, and FWIW "what utter and
complete bollocks" is not a very convincing refutation by itself.

Darren

Josh Dougherty

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May 16, 2003, 9:03:34 PM5/16/03
to
<ro...@telus.net> wrote in message news:3ec40148...@news.telus.net...

It seems like he was constructing a mathematical proof of that, not
"defining" it as such. After all, I could "define" an apple as a frog, but
I haven't attempted to construct any kind of proof for it.

But you're right. It was quite a lot of effort to prove something that's so
obviously correct already.

Josh


Robert Vienneau

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May 17, 2003, 4:07:13 AM5/17/03
to

> On Thu, 15 May 2003 05:20:54 -0400, Robert Vienneau
> <rv...@see.sig.com> wrote:

> >In article <3ec1ce88...@news.telus.net>, ro...@telus.net wrote:

> >> On Tue, 13 May 2003 17:10:40 -0400, Robert Vienneau
> >> <rv...@see.sig.com> wrote:

> > > > Consider Question 4.1 in:

<http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/LTV-FAQ.html>

> >> > This post provides an algebraic presentation of the mentioned
> >> > theorem

> >> > for a simple case...


> >> > Definition: Labor is exploited if and only if
> >> >
> >> > e > 0
> >> >
> >> > Theorem: r > 0 if and only if e > 0.
> >> >
> >> > In other words, the rate of profits is positive if and only if
> >> >labor is exploited.

> >> All that, just to redefine profit as exploitation?

> >What utter and complete bollocks.

> It is simple fact, Robert. All you have done is define _any_ profit
> as exploitation.

Balderdash. I have defined exploitation as arising when e > 0. And
"all that" has other uses. John Opie could say so, but he won't.

> There is no other possible interpretation for

> >> > In other words, the rate of profits is positive if and only if
> >> >labor is exploited.

> Deal with it.

One none-too-bright fellow once described an earlier exposition
of the same ideas as:

"A slew of mathematical economics which is readily accessible to,
perhaps, 100 people in the world, and which seems likely to be
accessible to an unusually well-trained and mathematically-minded
economist after perhaps several days of continuous effort."

I didn't quite see how saying I had the understanding of one of
the top 100 mathematical economists in the world amounted to a
refutation.

Tim Worstall

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May 17, 2003, 7:55:04 AM5/17/03
to
"Josh Dougherty" <jdoc1...@earthlink.net> wrote in message news:<GTfxa.943$rO.1...@newsread1.prod.itd.earthlink.net>...

I惻l admit that I did not follow Robert愀 math. Sorry, just
gobbledygook to me, no doubt that being my not Robert愀 fault.
Yet a thought occurs to me. It sounds like a proof of the Labout
Theory of Value, that the " value " of an item is equal to the labour
that went into it愀 production, and that therefore any value received
for the itme which does not go to the labourers is exploitation.

Just as an exercise, what if we turn this assumption on its head ?
I make a number of assumptions first.
1) Labour is free to move to where it wishes. No monopsonist employers
therefore.
2) By becoming employed, the labour has access to greater capital than
if working alone. This seems logical, as it is the capitalist employer
who has the capital that they can use.
3) By being employed, the labour is receiving greater wages than by
working alone. This would seem to follow from 1), as of course if they
recieved lower incomes by being employed, then they would be working
independently.

This seems to correspond fairly closely to the real world.
And it occurs to me that as labour is receiving higher wages by use of
the capitalist愀 capital, can we not equally say that labour is
exploiting the capitalist ?

Tim Worstall

Robert Vienneau

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May 17, 2003, 7:33:32 PM5/17/03
to
In article <3EC541FC...@thank.you>, Darren <no.e...@thank.you>

There's nothing to refute.

Just to see if you are paying attention, what does the following
comment from my original post assert?



Notice that often there does not exist a k > 0 such that

p = k v

(Recall:

v = a0 inv( I - A)

A(w) = A + c a0 w

p A(w) = (1/(1 + r)) p

p c = 1
)

Robert Vienneau

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May 17, 2003, 7:35:26 PM5/17/03
to
In article <825e2890.03051...@posting.google.com>,
t...@2xtreme.net (Tim Worstall) wrote:

> I惻l admit that I did not follow Robert愀 math. Sorry, just
> gobbledygook to me, no doubt that being my not Robert愀 fault.
> Yet a thought occurs to me. It sounds like a proof of the Labout
> Theory of Value, that the " value " of an item is equal to the labour
> that went into it愀 production, and that therefore any value received
> for the itme which does not go to the labourers is exploitation.
>
> Just as an exercise, what if we turn this assumption on its head ?
> I make a number of assumptions first.
> 1) Labour is free to move to where it wishes. No monopsonist employers
> therefore.
> 2) By becoming employed, the labour has access to greater capital than
> if working alone. This seems logical, as it is the capitalist employer
> who has the capital that they can use.
> 3) By being employed, the labour is receiving greater wages than by
> working alone. This would seem to follow from 1), as of course if they
> recieved lower incomes by being employed, then they would be working
> independently.
>
> This seems to correspond fairly closely to the real world.
> And it occurs to me that as labour is receiving higher wages by use of
> the capitalist愀 capital, can we not equally say that labour is
> exploiting the capitalist ?

One can be as clueless as one likes, refuse to make sense of what
others are saying, and say anything that one likes. As you demonstrate.

ro...@telus.net

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May 17, 2003, 8:13:33 PM5/17/03
to

Uh-oh. Watch out below, Darren. You're probably about to be hit by
Robert's patented Mathematical Snowstorm.

-- Roy L

ro...@telus.net

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May 17, 2003, 8:18:14 PM5/17/03
to
On Sat, 17 May 2003 01:03:34 GMT, "Josh Dougherty"
<jdoc1...@earthlink.net> wrote:

><ro...@telus.net> wrote in message news:3ec40148...@news.telus.net...
>> On Thu, 15 May 2003 05:20:54 -0400, Robert Vienneau
>> <rv...@see.sig.com> wrote:
>>
>> >In article <3ec1ce88...@news.telus.net>, ro...@telus.net wrote:
>> >
>> >> On Tue, 13 May 2003 17:10:40 -0400, Robert Vienneau
>> >> <rv...@see.sig.com> wrote:
>> >>
>> >> > Definition: Labor is exploited if and only if
>> >> >
>> >> > e > 0
>> >> >
>> >> > Theorem: r > 0 if and only if e > 0.
>> >> >
>> >> > In other words, the rate of profits is positive if and only if
>> >> >labor is exploited.
>> >
>> >> All that, just to redefine profit as exploitation?
>> >
>> >What utter and complete bollocks.
>>
>> It is simple fact, Robert. All you have done is define _any_ profit
>> as exploitation. There is no other possible interpretation for
>>
>> >> > In other words, the rate of profits is positive if and only if
>> >> >labor is exploited.
>>
>> Deal with it.
>
>It seems like he was constructing a mathematical proof of that, not
>"defining" it as such.

No. See the end of his original post where he defines "exploitation."

>After all, I could "define" an apple as a frog, but
>I haven't attempted to construct any kind of proof for it.

Right. But you're not Robert.

>But you're right. It was quite a lot of effort to prove something that's so
>obviously correct already.

Only if you define it that way.

-- Roy L

ro...@telus.net

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May 17, 2003, 8:24:38 PM5/17/03
to
On Sat, 17 May 2003 04:07:13 -0400, Robert Vienneau
<rv...@see.sig.com> wrote:

>In article <3ec40148...@news.telus.net>, ro...@telus.net wrote:
>
>> On Thu, 15 May 2003 05:20:54 -0400, Robert Vienneau
>> <rv...@see.sig.com> wrote:
>
>> >In article <3ec1ce88...@news.telus.net>, ro...@telus.net wrote:
>
>> >> On Tue, 13 May 2003 17:10:40 -0400, Robert Vienneau
>> >> <rv...@see.sig.com> wrote:
>
>> > > > Consider Question 4.1 in:
>
><http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/LTV-FAQ.html>
>
>> >> > This post provides an algebraic presentation of the mentioned
>> >> > theorem
>> >> > for a simple case...
>
>
>> >> > Definition: Labor is exploited if and only if
>> >> >
>> >> > e > 0
>> >> >
>> >> > Theorem: r > 0 if and only if e > 0.
>> >> >
>> >> > In other words, the rate of profits is positive if and only if
>> >> >labor is exploited.
>
>> >> All that, just to redefine profit as exploitation?
>
>> >What utter and complete bollocks.
>
>> It is simple fact, Robert. All you have done is define _any_ profit
>> as exploitation.
>
>Balderdash. I have defined exploitation as arising when e > 0.

??? That's what I said:

>> There is no other possible interpretation for
>
>> >> > In other words, the rate of profits is positive if and only if
>> >> >labor is exploited.
>

>One none-too-bright fellow once described an earlier exposition
>of the same ideas as:
>
> "A slew of mathematical economics which is readily accessible to,
> perhaps, 100 people in the world, and which seems likely to be
> accessible to an unusually well-trained and mathematically-minded
> economist after perhaps several days of continuous effort."
>
>I didn't quite see how saying I had the understanding of one of
>the top 100 mathematical economists in the world amounted to a
>refutation.

You're right: he was none too bright.

-- Roy L

John F. Opie

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May 18, 2003, 8:21:30 AM5/18/03
to
On Sat, 17 May 2003 04:07:13 -0400, Robert Vienneau
<rv...@see.sig.com> wrote:

<snip>



>> >> All that, just to redefine profit as exploitation?
>
>> >What utter and complete bollocks.
>
>> It is simple fact, Robert. All you have done is define _any_ profit
>> as exploitation.
>
>Balderdash. I have defined exploitation as arising when e > 0. And
>"all that" has other uses. John Opie could say so, but he won't.

Hmmm...

I could but I won't?

Hmmmmmmm....

Went and looked at what you said, I would agree, but with one
littttttle change:

The rate of profits is positive if and only if the rate of labor
compensation is less than the rate of productivity growth.

Now, you might make a case of calling that exploitation, but there are
some hard equations in microeconomics: somewhere somebody's gotta get
the short stick, or no one wants to play the game.

<snip>

John