Transform my....

[ComradeRed]

I have been studying at Caltech's library and I came upon this gem by an "economist" named Steedman. A book called Marx after Sraffa where he essentially uses a method developed by Sraffa to "destroy" the Labor theory of value.

The method developed by Sraffa is really quite interesting. The inputs of an industry determines its price. So suppose we have an industry that produces 250 commodities A, it requires 500 commodities B and 1000 commodities C. Thus by division we have 1 commodity A is equivalent in value to 2 commodities B + 4 commodities C.

Got that clear? Good. Now profit, according to Sraffa, originates from overproduction. If we have two industries, A and B, where 280 A + 8 B -> 575 A and 120 A + 12 B -> 20 A, then we introduce a rate of profit "r". We multiply the left-hand side of both equations by "1+r" then subtract. In this equation the rate of profit is 25%. Thus 15 commodities A is equal in value to 1 commodity B.

Now, what Steedman did is he used three industries for a hypothetical economy and used labor and iron as inputs. The three sectors were iron, gold, and corn. The inputs for these sectors was as follows: 28 t. iron + 56 units labor -> 56 units iron
16 t. iron + 16 units labor -> 48 oz. gold
12 t. iron + 8 units labor -> 8 qr. corn
And it is assumed that 5 units of corn feeds all the labor, or in other words 16 units of labor lives off of 1 qr. corn.

What steedman did was fallacious: he subtracted the iron on the left hand side in the iron sector then divided both sides by "28". He reasoned that the value of iron is equal to 2 units of labor.

However, if he had seen that 1 t. iron + 2 units labor -> 2 t. iron, then substituted in a sigma series with an upper limit of "n" cycles back, with the variable being "i", the equation is thus 2^-i. This is asymptotic to 3. The logical thing to do is use "3" units of labor is equal to 1 t. iron.

After the use of complex algebra, Steedman concluded that the real, i.e. Sraffian, price of each commodity is as follows (iff gold is notionally set to $1): 1 t. iron = $1.71
1 oz. gold = $1 (notionally!)
1 qr. corn = $4.3
If you substitute in the asymptote of value each time (since no matter how many cycles you go through it will never exceed 3), and then follow Marx's method, you come up with the same answer(!).

The only problem is that the rate of profit in this hypothetical economy exceeds 100%, which disagrees with Marx's theory. Oh well, that is forgiveable!

Is there a "transformation" problem? Only if you have no reading comprehension.

[Seeker]

If we have two industries, A and B, where 120 A + 8 B -> 575 A and 280 A + 12 B -> 20 A

It looks like you are using the same variable to describe two seperate entities. The way it is written, the first industry is making much more efficient use of its raw materials "A" and "B" in production of commodity "A" and so the two cannot be compaired for purposes of assigning a single value to their finished products. The second industry will have a higher cost per unit.


However, if he had seen that 1 t. iron + 2 units labor -> 2 t. iron

It does not. The correct way to write it would be 1 ton of raw materials + 2 units of labor -> 2 units of processed goods.

1 ton of iron ore cannot be processed into 2 tons of iron ore.

[ComradeRed]

I can understand, and share, much of your frustration. The notation was not mine, it was Steedman's.

The iron could represent anything...like the ore itself or an iron tractor. This leaves a large range of variables.

Steedman proposed that "iron tools" and "iron capital" be used to extract "iron ore" and turn it into other forms of "iron capital". You are right, though, 1 unit of iron (regardless of the amount of labor put into it) cannot be turned into 2 units of iron.

And your right about the criticism of the effeciency of the industries, I had it switched. The original post is edited for clarity.

[Seeker]

In that case, 1 t. iron + 2 units labor -> 2 t. iron could be written as:


2 units of labor -> 1 t. iron


However, in order to get 1 unit of labor, you need 1/16th qr. of corn. The 2 units of labor are not free.

(1.5 t. iron + 1 unit of labor)/16 -> 1 qr. of corn/16

3/32 t. iron + 2/32 units of labor -> 1/16th qr. of corn -> 1 unit of labor

3/32 t. iron -> 30/32 units of labor

1 t. iron -> 10 units of labor


You have profits in excess of 100% because t. iron costs more than 3 units of labor. It takes 8 units worth of farming labor to make enough food to accomplish the 2 units of industrial labor that it takes to produce 1 t. iron.



(28 t. iron * 10) + (56 units labor * 5; listed labor values are undercosted by a 10:2 ratio) -> (56 units iron * 10)

280 units of labor + 280 units of labor -> 560 units of labor

If 3 labor -> 1 iron, and listed labor values were undercosted by a 3:2 ratio, you would get this:

84 units of labor + 84 units of labor -> 168 units of labor (a true statement)

When you do it this way, however, you do not take account of the true cost of labor. You can't eat iron, so we can't use the t. iron formula to caclulate the cost of labor. We must instead use the less efficient qr. corn formula, resulting in a higher cost.

[ComradeRed]

However, in order to get 1 unit of labor, you need 1/16th qr. of corn. The 2 units of labor are not free. No, not necessarily true. The value of labor, i.e. wages, are set to reproduce that labor. And in this economy it is 1/16th a qr. of corn. This is independent of the value created by the labor.

The rest of the labor is surplus value.

Suppose we have 1 t. iron + 2 units of labor -> 2 t. iron, we substitute half of this in itself resulting thus: .5(1 t. iron + 2 units labor) + 2 units labor -> 2 t. iron. If we do this indefinately .5(.5(...(1 t. iron + 2 units labor)...)))+2 units of labor -> 2 t. iron we result with 2 + 2^-n units of labor, where n is the number of times you tried to calculate back.

If we have n be equal to infinity, the result is that 2 + 1 units of labor is equal to 2 t. iron. Now we substitute it in for the equation.



When you do it this way, however, you do not take account of the true cost of labor. You can't eat iron, so we can't use the t. iron formula to caclulate the cost of labor. We must instead use the less efficient qr. corn formula, resulting in a higher cost. Sure, if we follow Ricardo's or Adam Smith's plan that would hold. However, we aren't.

If we reduce constant capital to its dated labor, we come up with this solution. We could then, in turn, complicate the matters infinitelly by using the corn method.

But I'm lazy. So, the logical thing to do is stop with the dated labor inputs. The underlying assumption being, of course, that the relations of production do not change. For the sake of simplicity, of course; we all are aware that this would never occur in capitalism.

[novemba]

uhhhhh are you speaking english?

lamens terms please...

[ComradeRed]

Sorry, math is not for the lazy...when did I ever pick up math? :lol:

So, labor produces a certain amount of value. We assume it produces, say, 1 unit of value for every unit of labor.

Now, if you understand chemistry you should be able to understand my first post. If you don't, well allow me to elaborate.

The "Neo-Ricardian" School of economics argues that the cost of production is directly related to the cost of the output. Suppose the total amount of labor and capital cost $1000, then the price per commodity would have to be greater than $1000 per all commodities made.

It gets a little more complicated with the real system. Suppose we had a hypothetical economy with two sectors: iron and corn. If iron were measured in tons and corn in quarters, we measure the economy to be: 280 qr. corn + 12 t. iron produces 400 qr. corn; 120 qr. corn + 8 t. iron produces 20 t. iron.

We determine the values by using Algebra. Huzzah! If A is equal to the value of 1 qr. corn, and B is equal to 1 t. iron, we thus get two equations: 1. 280A + 12B = 400 A
2. 120A + 8B = 20B. By subtraction, and then division, we get 10A=B.

But wait...there is more! The next logical question to ask is "Where the hell is profit?!?" The answer is surprising. With overproduction, i.e. surplus production, comes overprice, i.e. surplus value...surprise!

If we examine the hypothetical economy, and adjust it slightly so that: 280 qr. corn + 12 t. iron produces 575 qr. corn; 120 qr. corn + 8 t. iron produces 20 t. iron. Now we introduce the uniform rate of profit, a variable "r". We adjust the price equations so that: 1. (280A + 12B)(1+r) = 400 A; 2. (120A + 8B)(1+r) = 20B.

We determine through even harder math that the rate of profit is 25%. Thus the "plug and chug" method of algebra allows us to determine that 15 qr. of corn is equal in value to 1 t. of iron.

Now, some crackpot named Steedman used the same method to criticize Marx. If you don't want to follow my complex mathematical ramblings, then go to hell...err, I mean the short version is Marx is right.

Now steedman set up a hypothetical economy with three sectors: iron, gold, and corn. Now corn can be anything from chickenfeed to corn bread, likewise for iron it could be tools or ore.

Labor was part of the inputs, as well as iron. The exact equations were: 28 t. iron + 56 units iron -> 56 t. iron
16 t. iron + 16 units labor -> 48 oz. gold
12 t. iron + 8 units labor -> 8 qr. corn
Now, it is assumed that 1 qr. corn feeds 16 units labor.

Got it so far? No? Good.

What Steedman does is fallacious. He says that logically the iron sector can be reduced down to 1 t. iron + 2 units of iron = 2 t. iron. Then if we subtract 1 t. iron from both sides, we get 1 t. iron = 2 units labor. Steedman simply substitutes this in for iron everywhere.

Steedman then follows Marx's instructions from Das Kapital, vol. III, on how to turn value into price.

HOWEVER, this was grossly unscientific! What we shall do instead is take up where Steedman fucked up.

If we have X be equal to 1 t. of iron, and Y equal to 1 unit of labor, then X + 2Y = 2X. If we divide this by two (i.e. so that it becomes .5X + Y = X) and substitute this in for X, and we do this indefinately, we get 3Y = 2X. Huzzah!

AND NOW we substitute this in every sector. If we do this, and notionally set the price of gold to $1, we come up with the following prices:
* 1 t. iron = $1.71
* 1 oz. gold = $1 (notionally!)
* 1 qr. corn = $4.3

[Seeker]

What exactly do you think it is you are measuring?

How is this useful?

Hasn't history proven that when you don't account for your upkeep costs, it bites you?

[ComradeRed]

Well, my first question is how well do you know the criticisms of Marxist economics? I am not being sarcastic, I am only curious.

Steedman's "critique" is the synthesis of all previous criticisms, so logically it is best to tackle him. He points out the "mathematical difficulties" in changing from value to prices.

However, he (and all the other critics) make a fatal flaw in assuming a mathematically valid but economically incorrect proposition: that there was no past production.

When we take this into effect, we come up with something sorta like this equation: http://en.wikipedia.org/math/1518aefbc269c8fae14193dfba90ba11.png

Where n is the time lag, l_in is the lagged-labour input coefficient, w is the wage and r is the "profit" (or net return) rate.

This defeats Steedman's critique, and subsequently the other bourgeois critics. To me this seems just a little bit important in Marxist economics.

[novemba]

im too lazy. i tried.

just tell me, why is this relevent?

[ComradeRed]

It justifies Marx's hypothesis that capitalism will collapse. :)

That's the short version. The longwinded, mathematically-dense reason is all ready posted.

[Seeker]

How do you calculate l_in?

Does P_i represent the value of labor?

What do you mean by time lag? The ammount of time between some arbitrary point in the past and the present? Does l_in represent the quantity of labor done in that period?

How do you calculate W? Total wages over a finite period of time? Cost per unit of labor?


If there is something that I should have read so I would know this stuff, just point me in the right direction.

[ComradeRed]

Wages is meant to be the wage rate...a rate inversely related to the rate of profit.

P_i represents the value of the object in terms of labor.

I should note here that Sraffa, the fellow who came up with several of the components in the equation, thought it best that labor should be in a fraction. The fraction being the number of employed people out of the total labor mkt.

If you want to read Sraffa's book, that might help a lot more beyond my aid. His book is Production of Commodities by means of Commodities.

[Seeker]

Let me see if I have this right:

The price of a finished product in terms of the labor that went into making it = units of labor completed within 'n' units of time * price per unit of labor * (operating costs + overproduction)^ 'n' units of time



That does not seem quite right. The term (operating costs + rate of overproduction)^n seems like it should be written n(operating costs + rate of overproduction).


However, with either of these equations, the price will drop as production becomes less efficient. If you can't produce enough to cover your operating expenses, profit rate becomes negative. I can see how this could be used as a tool for optimization. If both factories A and B make the same product, and the "price" of the goods coming from factory A is higher, we know A is making better use of its resources. In this way a "virtual market" could be established, where market forces were used as guidelines rather than mandates.

Market: "Factory A does it better, so we are forced to close Factory B or go out of business. Our investors will not tolerate low dividends, and will invest in our competitors if we show compassion to the workers."
Virtual Market: "Factory A does it better. Lets send some workers from A over to B to see if they can turn it around so we don't have to close the factory and put people out of work. We can afford to be patient and make the right long-term decisions."

To try and use these equations to set the retail price of goods and services is lunacy (at least with my current understanding). It would exacerbate the problems caused by Capitalism while removing the parts of it that work (self-regulate) as intended.

[ComradeRed]

Permit me to give an example.

Suppose we examined a reduced form of the iron sector, where 1 unit iron + 2 units labor --> 2 units iron. Now, we plug the formula into itself! So for 1 unit of iron to be produced, the inputs must be halved. We plug this in so: .5 ( 1 unit iron +2 units labor ) + 2 units labor --> 2 units iron.

We can still plug another in! So it is now .5 ( .5 ( 1 unit iron +2 units labor ) +2 units labor ) + 2 units of labor --> 2 units of iron.

But still there is another place to plug it in: .5 ( .5 ( .5 ( 1 unit iron +2 units labor ) +2 units labor ) +2 units labor ) + 2 units labor --> 2 units iron.

Wait! This is a limit! The limit, as x -> infinity, is f(x). Where f(x) = 2^|1-x| for all positive x. The limit is therefore equal to 3! We can infer, that without any change in the method of production, that 3 units of labor produces 2 units of iron.

If the method of production doesn't change, it will remain this way. It is constant.

So this is a different equation explaining the same thing.

[Seeker]

I understand how recursive algorithms work (the horror. the horror! ), but I have a hard time grasping the relevance of this one.

Defining production in terms of production works well enough for comparing like industries or calculating GNP, but says nothing about the sustainability of the system as a whole.

[ComradeRed]

Defining production in terms of production works well enough for comparing like industries or calculating GNP, but says nothing about the sustainability of the system as a whole. Yes, that is true. I won't contest it. However, what has happened is that bourgeois economists are using this "model" to attack the labor theory of value.

Essentially they raise the argument "How do you transform labor inputs to price?" Well, using their own logic, its quite simple. It beautifully rebuttes the so-called "transformation problem" and thus justifies the labor theory of value as true.

[Seeker]

The corn-ratio theory of value does not fall apart until price is introduced. If price can be reduced to labor and vice versa, it is the corn formula (or whatever the weakest mandatory sector of the economy happens to be) that needs to be used to adjust the value of labor in all other sectors.

Even if a steel mill manages to double their surplus without using any additional inputs, the value of that mill's labor may or may not double. Instead, the increase in labor value will be proportional to how steel-intensive the corn sector is. If steel is relatively unimportant to the production of corn, lowering the amount of labor it requires to produce a unit of steel will not have much effect on the amount of labor required to produce a unit of corn.

Yet the amount of labor required to produce a unit of corn effects the labor value of all other commodities because it sets the "price" of a unit of labor. The more labor-intensive an industry is, the more it will benefit from the efficiency of corn production (likewise, the more steel-intensive an industry is, the more it will benefit from efficiency of steel production, which is itself a function of the corn sector.)


*edit*

It should be possible to make a formula that determines price as a function of the cost of labor times some constant representing the current state of supply and demand. In a virtual market, this information could then be used to determine "potential profits" - how much surplus currency would be generated if we allowed the market to be our method of distribution. In such a manner, we could keep the self-regulating and self-evolving mechanisms of the market as our primary decision making tool when deciding where to invest, and at the same time implement a distribution system according to the principal of "to each according to need."

[ComradeRed]

I see what you are saying...the ratio of inputs to output in the corn sector sets the value of labor. Interesting...I never thought about that much.

The main role of the model used to "magnify" the transformation problem, however, was supposed to be very hypothetical. Its purpose was to disprove the Labor Theory of Value altogether.

Ironically, it did just the opposite. Of course, if we were to have a more accurate example, we would need to take into effect how long the capital has been use, how this affects production, how the soil affects the value of labor, and so on.

Piero Sraffa covers a number of these problems in his book. THe only problem is that his book is a hidden gem...all most no library has it.

But the model served its purpose...defeating the myth of any "transformation problem".

[Seeker]

Now I see what your formula is telling us. Over time, capital will increase while wages remain constant. Relative purchasing power, determined by the ratio of wealth between capitalists and wage earners, becomes lopsided to the point where labor becomes prohibitively expensive (at least until the industry can move operations into a third-world economy where 'n' is relatively small).


*edit*


However, with either of these equations, the price will drop as production becomes less efficient.


I said "price", but now that you have explained P_i and I've had some time to think about that explanation, I now understand it to be "capital". Which makes perfect sense.

I still don't understand why you would raise 1+ the profit rate to the power of time instead of multiplying the wage rate by time.

*edit*

I know it has something to do with the number of iterations within itself, but the logic may be too much to take in all at once :blink:

*edit*

OK, so 'n' is not a "time lag" so much as it is a representative of previous iterations of the production cycle, which itself represents the processing of raw materials into goods (or labor into produce) fit for the next stage of production (ie capital).

'W' is a funtion of the "corn formula", and 'r' is a function of 'w'.

l_in = w(1+r)
P_i = l_i1 + l_i2 + l_i3 . . .

Is that about right?

[ComradeRed]

Over time, capital will increase while wages remain constant. Relative purchasing power, determined by the ratio of wealth between capitalists and wage earners, becomes lopsided to the point where labor becomes prohibitively expensive (at least until the industry can move operations into a third-world economy where 'n' is relatively small). Sort of...that the price of commodities will rise, while wages remain constant, creating a serious problem of overproduction/underconsumption.

This will be the silver bullet that will kill the beast of capitalism.



OK, so 'n' is not a "time lag" so much as it is a representative of previous iterations of the production cycle, which itself represents the processing of raw materials into goods (or labor into produce) fit for the next stage of production (ie capital). Correct!



'W' is a funtion of the "corn formula", and 'r' is a function of 'w'.

l_in = w(1+r)
P_i = l_i1 + l_i2 + l_i3 . . .

Is that about right? Well, Piero Sraffa pointed out that the "standard system" where the relation of commodities as inputs to the commodities as outputs would replace the so-called "Corn System".

And frankly he has a point, since corn's value fluctuates just like any other commodities'. So rather than having "W" it should be "R".

[Seeker]

*edit* nevermind :rolleyes:

[ComradeRed]

I can deduce it was about the corn formula...which is incidentally what I was going to talk about next.

I was reviewing your corn formula, and it intrigued me.

But we can just use the ratio of the workers in a given industry to the total workers, then multiply this by 5 units of corn. This then gives us the value of labor in terms of corn.

Now, we can then multiply this by 3.25 units labor per unit corn. This gives us the value of the variable capital.

The constant capital is simply 1.5 times the number of units of iron in whichever sector you look at.

Now the surplus value is equivalent to the value produced by labor in the given industry and then subtract the value of the variable capital.

According to my calculations, the sectors are then designated the values:
Iron: 42c + 11.375v + 44.635s
Gold: 24c + 3.25v + 12.75s
Corn: 18c + 1.625v + 6.375s
The rates of profit for the iron sector is 83.62529274%, the gold sector is 46.78899083%, and for the corn sector it is 33.26810176%. The average of all of these is 54.5607676%.

Now if we take the "mark up" as (c+v)(avg. rate of profit), then add this to (c+v) and finally divide, we are close to finishing. We have to express price in terms of money! Let us not forget that!

We'll notionally set 1 unit of gold to $1 (although this isn't how it happens in reality!). We then divide the value per unit of either iron or corn by the value per unit of gold (we don't bother calculating what gold will be since x divided by x is always 1, so we know already 1 unit of gold = $1).

If we do this, the price per unit of iron is about $1.7 and for corn it is $4.309... We come up with the same answer the vulgar economist did!

So as you can clearly tell from these simple and self evident equations, there really is no transformation problem.

[Seeker]

What I was about to ask is "What about consumption." Then I realized that in this model, all consumption enables production.