ComradeRed
28th September 2006, 05:50
Introduction: This is a critique that covers the inconsistencies of both the Neoclassical school of economics and the Austrian school of economics (in that order).
First by using the assumptions of the Neoclassical school of thought, it is demonstratable that not only does their model break down but that supply and demand curves cannot be found.
Then it is demonstrated that contrary to the Neoclassical school's wishes that the prices are derived from the rate of profit rather than the other way around.
For the Austrians, the critique will be proven to hold likewise. The terrible irony is that this critique is heavily mathematically based.
The only reason for this is to demonstrate the patent absurdity of the "roundaboutness" method of value.
The reason why this critique is applicable to both the Austrian and Neoclassical Schools is because both accept the Marginalist paradigm which states mathematically the rate of profit is based on the prices. Insomuch as any school accepts the marginalist framework, this critique will still hold.
Author's Notes: It is most likely that most OI "economists" do not know the marginalist paradigm in its entirety (and that is likely to hold with the RevLeft "economists"). Thus I will have to explain the marginalist paradigm, it will either be an appendix or explained as we go along.
Also, this critique is based off of others' critiques of bourgeois economics, so I do not have any claim in originality of content, etc. I do take responsibility for the mathematical formalisms and the demonstration of the inconsistencies in the marginalist paradigm following its own instructions.
I also apologize for the poor writing style as this is probably going to be a hard read for most (all?) of you due to the high math content. I am going to use "LaTeX syntax" for math, so it will be somewhat "unified".
Section I: Neoclassical Nonsense
So, one of the principles of the Marginalist paradigm which comes into question is the "Diminishing Productivity Causes Rising Price" proposition. Let us take an example firm.
This is the input and output of a hypothetical firm:
Labor - Output - Wage Bill - Total Cost - Marginal Product - Marginal Cost - Average Variable Cost - Average Fixed Cost - Average total cost - Total Revenue - Profit
1, 52, 1000, 251000, 52.0, 19.2, 19, 4808, 4827, 208, -250792
9, 611, 9000, 259000, 83.6, 12.0, 15, 409, 424, 2443, -256557
10, 698, 10000, 260000, 87.5, 11.4, 14, 358, 372, 2793, -257207
100, 23333, 100000, 350000, 398.5, 2.5, 4, 11, 15, 93333, -256667
276, 131111, 276000, 526000, 772.5, 1.3, 2, 2, 4, 524444, -1556
277, 131885, 277000, 527000, 773.7, 1.3, 2, 2, 4, 527539, 539
400, 233333, 400000, 650000, 850.0, 1.2, 2, 1, 3, 933333, 283333
500, 316667, 500000, 750000, 800.5, 1.2, 2, 1, 2, 1266667, 516667
700, 443333, 700000, 950000, 401.5, 2.5, 2, 1, 2, 1773333, 823333
725, 452370, 725000, 975000, 323.5, 3.1, 2, 1, 2, 1809479, 834479
730, 453938, 730000, 980000, 307.1, 3.3, 2, 1, 2, 1815753, 835753
735, 455424, 735000, 985000, 290.5, 3.4, 2, 1, 2, 1821698, 836698
740, 456827, 740000, 990000, 273.7, 3.7, 2, 1, 2, 1827307, 837307
745, 458144, 745000, 995000, 256.6, 3.9, 2, 1, 2, 1832576, 837576
746, 458397, 746000, 996000, 253.1, 4.0, 2, 1, 2, 1833588, 837588
747, 458647, 747000, 997000, 249.7, 4.0, 2, 1, 2, 1834587, 837587
748, 458893, 748000, 998000, 246.2, 4.1, 2, 1, 2, 1835572, 837572
800, 466667, 800000, 1050000, 52.0, 19.2, 2, 1, 2, 1866667, 816667
The Assumptions of this table: the worker is paid $1000 for her wage, and the firm has fixed costs of $250000. The market price of the commodity produced is held at $4 per unit.
The idea is that the supply curve has a positive slope ("it goes up") because productivity falls as output rises.
This falling productivity means that there is a rising price. Therefore there is a link between marginal productivity (the amount produced by the last worker) and the marginal cost (the cost of the production of the last unit produced).
You will note this in the table given above in the "code" section.
As the number of workers increase from just one fellow doing all the work, the workers can get relatively more specialized in her selected work.
Note that there is a positive profit with the 277th worker.
The trend of rising "marginal productivity" continues up util the 400th worker. At this time the "marginal costs" have fallen dramatically.
The "marginal product" of the 400th worker is 850 units. THe "marginal cost" of this worker is the wage of $1000 divided by 850 (the number of units produced), which is $1.18 (rounded to 1.2 for the table).
The fixed costs have now becomes trivial with the output level of 233333.
According to the marginalist paradigm, the marginal productivity decreases. The "reasoning" behind this is that the variable input (labor) has exceeded the optimal level for the constant variable (capital, i.e. the means of production).
It is important to bear in mind that the next worker still apparently adds input, but at a diminishing rate. Since "marginal product" is now falling, "maginal cost" will now start to rise.
But please take note of this very important fact: profits continue to rise even though "marginal productivity" is falling and "marginal cost" is rising!
In economic jargon this is because "marginal revenue" exceeds "marginal cost".
The rise of profit ends with the 747th worker added...her marginal product of 249.7 units is sold for $998.8 as opposed to $1000.
At this point, any further worker added would cause a loss of profits.
This is where the "marginal cost" is equal to the "marginal revenue" and where profit is maximized.
Now what happens is that we are on to stage two, falling productivity means rising cost.
But what economists do is rush to argue that EVERYTHING is determined by diminishing "marginal productivity" (see Browning and Browning).
Now where profit is maximized is when the linear total revenue function for output Q minus the curvilinear total cost function for output Q is greatest.
Now if we were to graph this hypothetical firm's "marginal" and average costs, and "marginal revenue" it would be shocking to most students of economics:
http://upload.wikimedia.org/wikipedia/en/e/e6/Profit_max_marginal_small.png
Well, this is fine and dandy, and it looks nice...but as others have pointed out (Sraffa 1926) it doesn't work for an industrial economy.
The crux of Sraffa's argument is simple: the common position would be constant "marginal returns" and therefore horizontal (as opposed to rising) "marginal costs".
The importance of this is that since "marginal returns" determine everything, Sraffa's argument would be a critique of the entire "marginalist" paradigm!
If constant returns are the norm, then the output function instead is a straight line (just like the total revenue line, though with a different slope).
If the slope of the revenue is greater than the slope of the cost curve, then every unit sold after the firm met its costs would spell profit. The more units sold, the more profit.
In fact, the problem is that there would be no limit to the amount a competitive firm would produce (since it would want to maximize profits). The firms would want to produce an infinite number of goods!
This critique is rejected by most economists who use the following "reasoning": if Sraffa was right, then why don't firms want to produce an infinite number of goods? They don't, so Sraffa's wrong.
In other words it is remarking to something that works in practice "Ah, but does it work in theory?" The opposite case should hold true...sure Neoclassical models work in theory, but they don't work in practice.
Here is Sraffa's argument:
Sraffa focused on the assumptions that there were "factors of production" (which were fixed in the short run), and that supply and demand were independent of each other.
He argued that both assumptions could not be held simultaneously.
In circumstances where the "factors of production" were fixed in the short run, supply and demand ceased being independent of each other...so every point on the supply curve would satisfy a different demand curve.
Alternatively, when supply and demand were independent of each other, then it became impossible for the "factors of production" to be held as fixed.
Thus the "marginal costs" of production would be held as fixed.
Sraffa then pointed out that the Classical school also had its own "law of diminishing marginal returns".
But in the Classical School's case it wasn't in price theory...it was in the distribution theory (generally confined to rents).
The concept for the classical school was that farming was done on the best quality land first.
When the population grew, the lesser quality lands were brought into use. This poorer land would have a poorer yield.
"Diminishing marginal returns" thus applied because the quality of the land decreased...not because of relations between "fixed" and "variable" "factors of production".
Sraffa argued that the use of "diminishing marginal returns" in Neoclassical economics was an inappropriate application of this conceptin the context of their model...where the model assumed that all the firms were so small relative to the market that they could not influence the price of their commodity and that all "factors of production" were homogeneous.
IN the Neoclassical model falling quality of inputs couldn't explain "diminishing marginal productivity".
Instead, productivity could only fall because the ratio of "variable factors of production" to "fixed" ones exceeded some optimal level.
But when is it valid to assume that a given "factor of production", e.g. land, to be fixed? Sraffa pointed out that it is valid when industries were defined very broadly...but then Supply and Demand ceased being independent of each other.
So suppose we did take an industry sector, say Agriculture, and treat a "factor of production" (say Land!) to be fixed. Since the only way to add more land is to take it from some other sector (e.g. Tourism or Manufacture) and converting it, it is thus difficult to change the amount of land in the short run. The "Agriculture Sector" will suffer from "Diminishing returns", as predicted.
However, the definition of the agriculture sector is so vast that changes in its outputs must affect other industries. In particular an attempt to change its output would require more labor, which takes away from the workers of other industries... because labor is the only "variable factor of production" for agriculture.
This might appear to make the case for "diminishing returns" stronger since the chief variable input would become increasingly expensive.
However, it undermines two crucial aspects of the model: a) the assumptions that supply and demand are independent of each other and, b) the proposition that one market can be studied indepedent of all other markets.
Instead, if increasing the supply of agriculture changes the relative prices of land and labor, then it will also change the distribution of income. But this changes the demand curve.
This makes it impossible to draw independent supply and demand curves that intersect in just one point. Sraffa says:
Originally posted by Sraffa+1926--> (Sraffa @ 1926)If in the production of a particular commodity a considerable part of a factor is employed, the total amout f which is fixed or can be increased only at a more than proportional cost, a small increase in the production of the commodity will necessitate a more intense utilisation of that factor, and this will affect in the same manner the cost of the commodity in question and the cost of hte other commodities into the production of which that factor enters, and since commodities into the production of which a common special factor enters are frequently, to a certain extent, substitutes for one another...the modification in their price will not be without appreciable effects upon demand in the industry concerned.[/b]
These non-negligible impacts upon demand mean that the demand curve will shift with every movement along its supply curve.
(Which is rather interesting in and of itself...)
Supply and demand therefore intersect in multiple locations, and it is impossibe to say which price or quantity prevails as the "best equilibrium point".
So "diminishing returns" does not exist when industries are broadly defined, no industry can be considered independent of another, as supply and curve analysis would require.
But What If We Define The Sector "Narrowly"? Well, it is then unlikely that "diminishing returns" would exist.
Not because supply and demand curves aren't independent of each other (it most likely is at a smaller scale), but because it would not be reasonable to assume that some "factor of production" is fixed.
Sraffa argues that in the real world, firms and industries will normally be able to vary ll factors of production fairly easily.
This is because these additional inputs can be taken from other industries or garnered from stocks of under-utilised resources.
That is, if there is an increased demand for wheat, then rather than farming a given quantity of land more intensively, farmers will instead convert some land from another crop (e.g. barley) to wheat.
Or perhaps convert some of their own land which is currently lying fallow to wheat production.
Or non-wheat farmers will choose to produce wheat.
As old Sraffa said:
Originally posted by [email protected]
If we next take an industry which employs only a small part of the "constant factor" (which appears more appropriate for the study of the particular equilibrium of a single industry), we find that a (small) increase in its production generally met much more by drawing "marginal doses" of the constant factor from other industries than intensifying its own utilisation of it; thus the increase in cost will be practically negligible...In all cases, the ratio of one factor of production to any other will remain relatively constant, while the total amount of resources given to production will rise.
This results in a straight-line output function.
A straight-line output curve results in constant marignal costs and falling average costs.
This means that every sale after q_{min} is profit, and that sales are not limited by rising cost. Instead, costs for a firm are likely to be constant (or perhaps falling) within the normal range of output. IF economic theory is right that firms are facing a horizontal demand curve, THEN according to economic theory the firm would be trying to produce an infinite output.
This means that "diminishing returns" still doesn't work for either the grandest scopes or the narrowest scopes...and the entire marginalist paradigm falls to pieces.
Sraffian Criticism of Marginalism
Well, I am sure that all the Austrian "economists" are fed up with the mathematical "psychobabble" (:lol:) above. Here's the real beauty of this critique: inasmuch as the Austrians accept the marginalist paradigm, they too are subject to the above critique!
But just for them I have worked a special critique that is especially mathematically complex! It has to do with their "roundaboutness" theory of pricing.
You see, one of the fatal flaws is that the rate of profit is determined by the prices rather than the other way round. This leaves itself open to Sraffa's criticism of the Neoclassical school (Sraffa 1960).
So, to give you all a taste of Sraffa's (1960) critique, here is the arguments he gave. Bear in mind that this is so far a criticism of Neoclassical economics and that I will later demonstrate its validity with respect to the Austrians.
Suppose we had a hypothetical economy:
240 qrs Wheat + 12 t. Iron + 18 pigs -> 450 qrs Wheat
90 qrs Wheat + 6 t. Iron + 12 pigs -> 21 t. Iron
120 qrs Wheat + 3 t. Iron + 30 pigs -> 60 pigs
Please note that the commodities are arbitrary, of course it does not make any sense that a pig makes iron but the logic of the criticism is invariant to changes in the commodities' names.
Now what you do is for each sector substitute in x for the value of 1 qr wheat, y for 1 t. Iron, and z for 1 pig.
240 x + 12 y + 18 z = 450 x
90 x + 6 y + 12 z = 21 y
120 x + 3 y + 30 z = 60 z
Note the change of "->" (which should be read as the chemistry sign "yields" or "produces") to "=" because we changed the units to value.
Now, we have a system of linear equations! We then subtract the sectors inputs to get:
12 y + 18 z = 450 x - 240 x = 210 x
90 x + 12 z = 21 y - 6 y = 15 y
120 x + 3 y = 60 z - 30 z = 30 z
Then we can substitute in for the corresponding units in any arbitrary sector:
12 y + (18/30)(120 x + 3 y) = 210 x
and it carries out to be:
12 y + 72 x + 1.8 y = 210 x
13.8 y = 138 x
y = 10x (QED).
To get the value that 10 qrs of wheat is exchangeable for 1 t. Iron. Now we can substitute this in for the pig sector to get:
120x + 3y = 30z
(120x)(y/10x) + 3y = 30z
12y + 3 y = 30z
15 y = 30z
y = 2z (= 10x) (QED)
So we have our economy solved! 10 qrs of Wheat is exchangeable for 1 t. Iron or 2 pigs.
Now the next step is where Sraffa's model introduces the rate of profit. If we have a hypothetical economy with a surplus output:
280 qrs. Wheat + 12 t. Iron -> 575 qrs. Wheat
120 qrs. Wheat + 8 t. Iron -> 20 t. Iron
We cannot do what we did before. Instead we introduce the rate of profit scalar r such that r>0.
We once again set x to be the value of 1 qr. Wheat, and y to be 1 t. Iron, and introduce the rate of profit mechanism in our calculations:
(1+r)(280 x + 12y) = 575x
(1+r)(120 x + 8y) = 20y
I'm too lazy to teach math, and I'm really not that good at it (doing it over the internet-wise), so I'm going to tell you how to solve this but not show all the steps. You want to determine the rate of profit first.
I'll give you the answer: r = 25% = .25; ok?
Now we can figure out the exchange values rather simply: plug and chug techniques from good old algebra!
We then get:
(1.25)(280x + 12y) = 575x
(1.25)(120x + 8y) = 20y
which then reduces to
350x + 15y = 575x
150x + 10y = 20y
and then subtract the inputs from both sides (the x input for the x sector, and the y input for the y sector, etc.):
350x + 15y - 350x = 575x - 350x = 15y = 225x
150x + 10y -10y = 20y - 10y = 150x = 10y
and then simply divide!
15y/15 = 225x/15 = y = 15x
150x/10 = 10y/10 = y = 15x (QED)
The general scheme is to figure out the rate of profit, then plug it back in, and solve algebraically (remember each sector is an independent equation).
Now, if we were really uptight about realism, we could have this be accurate to any arbitrary degree (depending on how willing the modeller is).
But what about labor now? And wages? Etc.
NOTE: this is getting too complicated, I think, for the general online community here and thus I will avoid some of the models.
Well, supposing we had an explicit amount of labor, wage is an unknown represented by the letter w.
Also, I wish to introduce the "maximum rate of profit" scalar R. You see, Sraffa shows there is an appropriate measuring stick (the "standard ratio of commodities" or more shortly "the standard commodity") which exposes a simple, linear relationship between wage w, the actual rate of profit r, and the maximum rate of profit R.
The wage w falls linearly as the rate of profit r rises towards the Maximum rate of profit R (or in keen math symbols! w->0 as r->R).
Here is an example table:
Maximum R = 25%
Wage (% of surplus) - Profit Rate
0% 25%
10% 23%
20% 20%
30% 18%
40% 15%
50% 13%
60% 10%
70% 8%
80% 5%
90% 3%
100% 0%
So if the workers get a 0% wage, i.e. they work for free or as slaves, the capitalist would get the entire 25%. At 10% wage, the capitalist gets 23%; and so on.
Here's the underlying critique: Rather than prices determining the distribution of income, the distribution of income between wges and profits must be known before prices can be calculated.
What's even more ironic is that Sraffa demonstrates this while the economy is in constant equilibrium and static...the same assumptions that should make the marginalist paradigm work!
The terrible irony is that even in conditions that marginalists assume, marginalism doesn't work!
And Now, For Something Completely Different: Austrian Economics
Now I am guarenteed the Austrians are pissed at me...having to go through all that math and still, I am assured, they say "That model is entirely flawed, the price of a ton of iron is the amount people are willing to pay." etc.
Well it's so hard to criticize a school that rejects both empiricism and math and take them seriously. So I did what any scientist would do in such a situation take empiricism and math and tried to criticize Austrian economics as seriously as possible.
First off, a summary of the "roundaboutness" theory...simply the idea that a cheapening of capital (via a fall of the rate of interest) will lead to a less "roundabout" approach to production, meaning that more direct labor and less indirect capital will be applied to its production.
Now, the problem is the very same of the Neoclassical paradigm: from prices we get the rate of profit, wages, etc. Whereas it is demonstratable that it is not so.
Consider our glorious widget industry. For simplicity, there are two ways to make a widget: Method A which involves the application of 1 wage unit now, 8 units last year, and 1 unit 8 years ago; and Method B which involves 1 unit now and 20 units a year ago; at a higher rate of profit, the order could reverse...and it could reverse again for a higher rate of profit.
This makes the Austrian theory of "roundaboutness" as flawed as the Neoclassical Marginal productivity theory. Of course, to find out about how flawed that is, you need to read the above parts of this long critique.
And now for a horribly ironic ending of my mini-critique. The Austrians, who are quite vocal against equilibrium analysis (arguing in favor of disequilibrium), their preference for capitalism as a social system is dependent on the belief that it will remain close to equilibrium. If (instead) capitalism is endogeneously unstable, then it may remain substantially distant from equilibrium situations all the time. This weakens the Austrian school, to the extent that its support for capitalism emanates from conditions which are assumed to apply in equilibrium!
Post-Script: A Critique of Marginal Utility
Most of you, I am guessing, expected it to come to this eventually.
Well, any elementary introductory Microeconomics text (e.g. Browning and Browning) will tell you that it is feasible to measure the demand curve.
Well, it is worthwhile to quote the "economists" themselves:
Originally posted by Browning and [email protected] Chapter Two, Page 55
Utility is simply a subjective measure of usefulness, or want satisfaction, that results from consumption. Units in which it is measured are arbitrary, but they are commonly referred to as utils: a util is one unit of utility. --emphasis in bold is mine added
Now, it is first off important to note that "arbitrariness" is a quality given to a mathematical quantity that denotes that the quantity itself is heuristic, and used to find something else that's more important.
E.g. in Riemannian geometry, the affine parameter \lambda satisfies an arbitrary linear function such that a*\lambda + b exists. It doesn't matter what a and b are, what matters is that lambda satisfies it.
In other words "arbitrary" used in math (as it is used in its mathematical sense here) means "heuristic".
However, the measurement of utility is rather vital... are we measuring in terms of the utility "gained" from a tea spoon of sugar or the utility of a human life?
Worse, who decides the utility of these things? Someone who has no use for sugar wouldn't get anything from tea spoons of sugar (supposing that there is some measure of utility here). And how does it compare to a human life???
Well, those of you who are not really well read in Economics may be saying by now "Yeah yeah, no measure of utility, who cares?" Well here's the problem:
Browning and [email protected] Chapter 2, page 58
The slope of an indifference curve equals the ratio of the marginal utilities of the two goods. --emphasis is Browning and Browning's, not mine.
So we find the demand curve from the ratio of the diminishing marginal utility curves. (Remember: money is also a commodity, though I don't see how it could have a diminishing marginal utility curve.)
You can simply change the Y axis to be the money-commodity (or assuming that it is not a commodity-standardized economy, e.g. an economy off the gold standard, it would be money itself).
But marginal utility's measurement is still a problem in reality. Although the ratios are all that is important, if you cannot measure a util you are out of luck. That is a SERIOUS problem for the Neoclassical paradigm!
It totally defeats the ability to predict (and indeed measure!) the demand curve...which then defeats the entire idea of "supply and demand" for a "theory of value".
Bibliography (This is probably not in any order)
Bohm-Bawerk. Karl Marx and the Close of His System Orien Ed. 1949.
Browning, Edgar K., Browning, Jacquelene M. Microeconomic Theory and Applications Third Ed. 1986.
Lord Robbins An Essay on The Nature & Significance of Economic Science Third Ed. 1984.
Rothbard, M. America's Great Depression.
Rothbard, M. Power and the Market.
Sraffa, Piero. "The Laws of Returns Under Competitive Conditions." Economic Journal, 40: 538-550.
Sraffa, Piero. The Production of Commodities by means of Commodities First Ed. 1960.
First by using the assumptions of the Neoclassical school of thought, it is demonstratable that not only does their model break down but that supply and demand curves cannot be found.
Then it is demonstrated that contrary to the Neoclassical school's wishes that the prices are derived from the rate of profit rather than the other way around.
For the Austrians, the critique will be proven to hold likewise. The terrible irony is that this critique is heavily mathematically based.
The only reason for this is to demonstrate the patent absurdity of the "roundaboutness" method of value.
The reason why this critique is applicable to both the Austrian and Neoclassical Schools is because both accept the Marginalist paradigm which states mathematically the rate of profit is based on the prices. Insomuch as any school accepts the marginalist framework, this critique will still hold.
Author's Notes: It is most likely that most OI "economists" do not know the marginalist paradigm in its entirety (and that is likely to hold with the RevLeft "economists"). Thus I will have to explain the marginalist paradigm, it will either be an appendix or explained as we go along.
Also, this critique is based off of others' critiques of bourgeois economics, so I do not have any claim in originality of content, etc. I do take responsibility for the mathematical formalisms and the demonstration of the inconsistencies in the marginalist paradigm following its own instructions.
I also apologize for the poor writing style as this is probably going to be a hard read for most (all?) of you due to the high math content. I am going to use "LaTeX syntax" for math, so it will be somewhat "unified".
Section I: Neoclassical Nonsense
So, one of the principles of the Marginalist paradigm which comes into question is the "Diminishing Productivity Causes Rising Price" proposition. Let us take an example firm.
This is the input and output of a hypothetical firm:
Labor - Output - Wage Bill - Total Cost - Marginal Product - Marginal Cost - Average Variable Cost - Average Fixed Cost - Average total cost - Total Revenue - Profit
1, 52, 1000, 251000, 52.0, 19.2, 19, 4808, 4827, 208, -250792
9, 611, 9000, 259000, 83.6, 12.0, 15, 409, 424, 2443, -256557
10, 698, 10000, 260000, 87.5, 11.4, 14, 358, 372, 2793, -257207
100, 23333, 100000, 350000, 398.5, 2.5, 4, 11, 15, 93333, -256667
276, 131111, 276000, 526000, 772.5, 1.3, 2, 2, 4, 524444, -1556
277, 131885, 277000, 527000, 773.7, 1.3, 2, 2, 4, 527539, 539
400, 233333, 400000, 650000, 850.0, 1.2, 2, 1, 3, 933333, 283333
500, 316667, 500000, 750000, 800.5, 1.2, 2, 1, 2, 1266667, 516667
700, 443333, 700000, 950000, 401.5, 2.5, 2, 1, 2, 1773333, 823333
725, 452370, 725000, 975000, 323.5, 3.1, 2, 1, 2, 1809479, 834479
730, 453938, 730000, 980000, 307.1, 3.3, 2, 1, 2, 1815753, 835753
735, 455424, 735000, 985000, 290.5, 3.4, 2, 1, 2, 1821698, 836698
740, 456827, 740000, 990000, 273.7, 3.7, 2, 1, 2, 1827307, 837307
745, 458144, 745000, 995000, 256.6, 3.9, 2, 1, 2, 1832576, 837576
746, 458397, 746000, 996000, 253.1, 4.0, 2, 1, 2, 1833588, 837588
747, 458647, 747000, 997000, 249.7, 4.0, 2, 1, 2, 1834587, 837587
748, 458893, 748000, 998000, 246.2, 4.1, 2, 1, 2, 1835572, 837572
800, 466667, 800000, 1050000, 52.0, 19.2, 2, 1, 2, 1866667, 816667
The Assumptions of this table: the worker is paid $1000 for her wage, and the firm has fixed costs of $250000. The market price of the commodity produced is held at $4 per unit.
The idea is that the supply curve has a positive slope ("it goes up") because productivity falls as output rises.
This falling productivity means that there is a rising price. Therefore there is a link between marginal productivity (the amount produced by the last worker) and the marginal cost (the cost of the production of the last unit produced).
You will note this in the table given above in the "code" section.
As the number of workers increase from just one fellow doing all the work, the workers can get relatively more specialized in her selected work.
Note that there is a positive profit with the 277th worker.
The trend of rising "marginal productivity" continues up util the 400th worker. At this time the "marginal costs" have fallen dramatically.
The "marginal product" of the 400th worker is 850 units. THe "marginal cost" of this worker is the wage of $1000 divided by 850 (the number of units produced), which is $1.18 (rounded to 1.2 for the table).
The fixed costs have now becomes trivial with the output level of 233333.
According to the marginalist paradigm, the marginal productivity decreases. The "reasoning" behind this is that the variable input (labor) has exceeded the optimal level for the constant variable (capital, i.e. the means of production).
It is important to bear in mind that the next worker still apparently adds input, but at a diminishing rate. Since "marginal product" is now falling, "maginal cost" will now start to rise.
But please take note of this very important fact: profits continue to rise even though "marginal productivity" is falling and "marginal cost" is rising!
In economic jargon this is because "marginal revenue" exceeds "marginal cost".
The rise of profit ends with the 747th worker added...her marginal product of 249.7 units is sold for $998.8 as opposed to $1000.
At this point, any further worker added would cause a loss of profits.
This is where the "marginal cost" is equal to the "marginal revenue" and where profit is maximized.
Now what happens is that we are on to stage two, falling productivity means rising cost.
But what economists do is rush to argue that EVERYTHING is determined by diminishing "marginal productivity" (see Browning and Browning).
Now where profit is maximized is when the linear total revenue function for output Q minus the curvilinear total cost function for output Q is greatest.
Now if we were to graph this hypothetical firm's "marginal" and average costs, and "marginal revenue" it would be shocking to most students of economics:
http://upload.wikimedia.org/wikipedia/en/e/e6/Profit_max_marginal_small.png
Well, this is fine and dandy, and it looks nice...but as others have pointed out (Sraffa 1926) it doesn't work for an industrial economy.
The crux of Sraffa's argument is simple: the common position would be constant "marginal returns" and therefore horizontal (as opposed to rising) "marginal costs".
The importance of this is that since "marginal returns" determine everything, Sraffa's argument would be a critique of the entire "marginalist" paradigm!
If constant returns are the norm, then the output function instead is a straight line (just like the total revenue line, though with a different slope).
If the slope of the revenue is greater than the slope of the cost curve, then every unit sold after the firm met its costs would spell profit. The more units sold, the more profit.
In fact, the problem is that there would be no limit to the amount a competitive firm would produce (since it would want to maximize profits). The firms would want to produce an infinite number of goods!
This critique is rejected by most economists who use the following "reasoning": if Sraffa was right, then why don't firms want to produce an infinite number of goods? They don't, so Sraffa's wrong.
In other words it is remarking to something that works in practice "Ah, but does it work in theory?" The opposite case should hold true...sure Neoclassical models work in theory, but they don't work in practice.
Here is Sraffa's argument:
Sraffa focused on the assumptions that there were "factors of production" (which were fixed in the short run), and that supply and demand were independent of each other.
He argued that both assumptions could not be held simultaneously.
In circumstances where the "factors of production" were fixed in the short run, supply and demand ceased being independent of each other...so every point on the supply curve would satisfy a different demand curve.
Alternatively, when supply and demand were independent of each other, then it became impossible for the "factors of production" to be held as fixed.
Thus the "marginal costs" of production would be held as fixed.
Sraffa then pointed out that the Classical school also had its own "law of diminishing marginal returns".
But in the Classical School's case it wasn't in price theory...it was in the distribution theory (generally confined to rents).
The concept for the classical school was that farming was done on the best quality land first.
When the population grew, the lesser quality lands were brought into use. This poorer land would have a poorer yield.
"Diminishing marginal returns" thus applied because the quality of the land decreased...not because of relations between "fixed" and "variable" "factors of production".
Sraffa argued that the use of "diminishing marginal returns" in Neoclassical economics was an inappropriate application of this conceptin the context of their model...where the model assumed that all the firms were so small relative to the market that they could not influence the price of their commodity and that all "factors of production" were homogeneous.
IN the Neoclassical model falling quality of inputs couldn't explain "diminishing marginal productivity".
Instead, productivity could only fall because the ratio of "variable factors of production" to "fixed" ones exceeded some optimal level.
But when is it valid to assume that a given "factor of production", e.g. land, to be fixed? Sraffa pointed out that it is valid when industries were defined very broadly...but then Supply and Demand ceased being independent of each other.
So suppose we did take an industry sector, say Agriculture, and treat a "factor of production" (say Land!) to be fixed. Since the only way to add more land is to take it from some other sector (e.g. Tourism or Manufacture) and converting it, it is thus difficult to change the amount of land in the short run. The "Agriculture Sector" will suffer from "Diminishing returns", as predicted.
However, the definition of the agriculture sector is so vast that changes in its outputs must affect other industries. In particular an attempt to change its output would require more labor, which takes away from the workers of other industries... because labor is the only "variable factor of production" for agriculture.
This might appear to make the case for "diminishing returns" stronger since the chief variable input would become increasingly expensive.
However, it undermines two crucial aspects of the model: a) the assumptions that supply and demand are independent of each other and, b) the proposition that one market can be studied indepedent of all other markets.
Instead, if increasing the supply of agriculture changes the relative prices of land and labor, then it will also change the distribution of income. But this changes the demand curve.
This makes it impossible to draw independent supply and demand curves that intersect in just one point. Sraffa says:
Originally posted by Sraffa+1926--> (Sraffa @ 1926)If in the production of a particular commodity a considerable part of a factor is employed, the total amout f which is fixed or can be increased only at a more than proportional cost, a small increase in the production of the commodity will necessitate a more intense utilisation of that factor, and this will affect in the same manner the cost of the commodity in question and the cost of hte other commodities into the production of which that factor enters, and since commodities into the production of which a common special factor enters are frequently, to a certain extent, substitutes for one another...the modification in their price will not be without appreciable effects upon demand in the industry concerned.[/b]
These non-negligible impacts upon demand mean that the demand curve will shift with every movement along its supply curve.
(Which is rather interesting in and of itself...)
Supply and demand therefore intersect in multiple locations, and it is impossibe to say which price or quantity prevails as the "best equilibrium point".
So "diminishing returns" does not exist when industries are broadly defined, no industry can be considered independent of another, as supply and curve analysis would require.
But What If We Define The Sector "Narrowly"? Well, it is then unlikely that "diminishing returns" would exist.
Not because supply and demand curves aren't independent of each other (it most likely is at a smaller scale), but because it would not be reasonable to assume that some "factor of production" is fixed.
Sraffa argues that in the real world, firms and industries will normally be able to vary ll factors of production fairly easily.
This is because these additional inputs can be taken from other industries or garnered from stocks of under-utilised resources.
That is, if there is an increased demand for wheat, then rather than farming a given quantity of land more intensively, farmers will instead convert some land from another crop (e.g. barley) to wheat.
Or perhaps convert some of their own land which is currently lying fallow to wheat production.
Or non-wheat farmers will choose to produce wheat.
As old Sraffa said:
Originally posted by [email protected]
If we next take an industry which employs only a small part of the "constant factor" (which appears more appropriate for the study of the particular equilibrium of a single industry), we find that a (small) increase in its production generally met much more by drawing "marginal doses" of the constant factor from other industries than intensifying its own utilisation of it; thus the increase in cost will be practically negligible...In all cases, the ratio of one factor of production to any other will remain relatively constant, while the total amount of resources given to production will rise.
This results in a straight-line output function.
A straight-line output curve results in constant marignal costs and falling average costs.
This means that every sale after q_{min} is profit, and that sales are not limited by rising cost. Instead, costs for a firm are likely to be constant (or perhaps falling) within the normal range of output. IF economic theory is right that firms are facing a horizontal demand curve, THEN according to economic theory the firm would be trying to produce an infinite output.
This means that "diminishing returns" still doesn't work for either the grandest scopes or the narrowest scopes...and the entire marginalist paradigm falls to pieces.
Sraffian Criticism of Marginalism
Well, I am sure that all the Austrian "economists" are fed up with the mathematical "psychobabble" (:lol:) above. Here's the real beauty of this critique: inasmuch as the Austrians accept the marginalist paradigm, they too are subject to the above critique!
But just for them I have worked a special critique that is especially mathematically complex! It has to do with their "roundaboutness" theory of pricing.
You see, one of the fatal flaws is that the rate of profit is determined by the prices rather than the other way round. This leaves itself open to Sraffa's criticism of the Neoclassical school (Sraffa 1960).
So, to give you all a taste of Sraffa's (1960) critique, here is the arguments he gave. Bear in mind that this is so far a criticism of Neoclassical economics and that I will later demonstrate its validity with respect to the Austrians.
Suppose we had a hypothetical economy:
240 qrs Wheat + 12 t. Iron + 18 pigs -> 450 qrs Wheat
90 qrs Wheat + 6 t. Iron + 12 pigs -> 21 t. Iron
120 qrs Wheat + 3 t. Iron + 30 pigs -> 60 pigs
Please note that the commodities are arbitrary, of course it does not make any sense that a pig makes iron but the logic of the criticism is invariant to changes in the commodities' names.
Now what you do is for each sector substitute in x for the value of 1 qr wheat, y for 1 t. Iron, and z for 1 pig.
240 x + 12 y + 18 z = 450 x
90 x + 6 y + 12 z = 21 y
120 x + 3 y + 30 z = 60 z
Note the change of "->" (which should be read as the chemistry sign "yields" or "produces") to "=" because we changed the units to value.
Now, we have a system of linear equations! We then subtract the sectors inputs to get:
12 y + 18 z = 450 x - 240 x = 210 x
90 x + 12 z = 21 y - 6 y = 15 y
120 x + 3 y = 60 z - 30 z = 30 z
Then we can substitute in for the corresponding units in any arbitrary sector:
12 y + (18/30)(120 x + 3 y) = 210 x
and it carries out to be:
12 y + 72 x + 1.8 y = 210 x
13.8 y = 138 x
y = 10x (QED).
To get the value that 10 qrs of wheat is exchangeable for 1 t. Iron. Now we can substitute this in for the pig sector to get:
120x + 3y = 30z
(120x)(y/10x) + 3y = 30z
12y + 3 y = 30z
15 y = 30z
y = 2z (= 10x) (QED)
So we have our economy solved! 10 qrs of Wheat is exchangeable for 1 t. Iron or 2 pigs.
Now the next step is where Sraffa's model introduces the rate of profit. If we have a hypothetical economy with a surplus output:
280 qrs. Wheat + 12 t. Iron -> 575 qrs. Wheat
120 qrs. Wheat + 8 t. Iron -> 20 t. Iron
We cannot do what we did before. Instead we introduce the rate of profit scalar r such that r>0.
We once again set x to be the value of 1 qr. Wheat, and y to be 1 t. Iron, and introduce the rate of profit mechanism in our calculations:
(1+r)(280 x + 12y) = 575x
(1+r)(120 x + 8y) = 20y
I'm too lazy to teach math, and I'm really not that good at it (doing it over the internet-wise), so I'm going to tell you how to solve this but not show all the steps. You want to determine the rate of profit first.
I'll give you the answer: r = 25% = .25; ok?
Now we can figure out the exchange values rather simply: plug and chug techniques from good old algebra!
We then get:
(1.25)(280x + 12y) = 575x
(1.25)(120x + 8y) = 20y
which then reduces to
350x + 15y = 575x
150x + 10y = 20y
and then subtract the inputs from both sides (the x input for the x sector, and the y input for the y sector, etc.):
350x + 15y - 350x = 575x - 350x = 15y = 225x
150x + 10y -10y = 20y - 10y = 150x = 10y
and then simply divide!
15y/15 = 225x/15 = y = 15x
150x/10 = 10y/10 = y = 15x (QED)
The general scheme is to figure out the rate of profit, then plug it back in, and solve algebraically (remember each sector is an independent equation).
Now, if we were really uptight about realism, we could have this be accurate to any arbitrary degree (depending on how willing the modeller is).
But what about labor now? And wages? Etc.
NOTE: this is getting too complicated, I think, for the general online community here and thus I will avoid some of the models.
Well, supposing we had an explicit amount of labor, wage is an unknown represented by the letter w.
Also, I wish to introduce the "maximum rate of profit" scalar R. You see, Sraffa shows there is an appropriate measuring stick (the "standard ratio of commodities" or more shortly "the standard commodity") which exposes a simple, linear relationship between wage w, the actual rate of profit r, and the maximum rate of profit R.
The wage w falls linearly as the rate of profit r rises towards the Maximum rate of profit R (or in keen math symbols! w->0 as r->R).
Here is an example table:
Maximum R = 25%
Wage (% of surplus) - Profit Rate
0% 25%
10% 23%
20% 20%
30% 18%
40% 15%
50% 13%
60% 10%
70% 8%
80% 5%
90% 3%
100% 0%
So if the workers get a 0% wage, i.e. they work for free or as slaves, the capitalist would get the entire 25%. At 10% wage, the capitalist gets 23%; and so on.
Here's the underlying critique: Rather than prices determining the distribution of income, the distribution of income between wges and profits must be known before prices can be calculated.
What's even more ironic is that Sraffa demonstrates this while the economy is in constant equilibrium and static...the same assumptions that should make the marginalist paradigm work!
The terrible irony is that even in conditions that marginalists assume, marginalism doesn't work!
And Now, For Something Completely Different: Austrian Economics
Now I am guarenteed the Austrians are pissed at me...having to go through all that math and still, I am assured, they say "That model is entirely flawed, the price of a ton of iron is the amount people are willing to pay." etc.
Well it's so hard to criticize a school that rejects both empiricism and math and take them seriously. So I did what any scientist would do in such a situation take empiricism and math and tried to criticize Austrian economics as seriously as possible.
First off, a summary of the "roundaboutness" theory...simply the idea that a cheapening of capital (via a fall of the rate of interest) will lead to a less "roundabout" approach to production, meaning that more direct labor and less indirect capital will be applied to its production.
Now, the problem is the very same of the Neoclassical paradigm: from prices we get the rate of profit, wages, etc. Whereas it is demonstratable that it is not so.
Consider our glorious widget industry. For simplicity, there are two ways to make a widget: Method A which involves the application of 1 wage unit now, 8 units last year, and 1 unit 8 years ago; and Method B which involves 1 unit now and 20 units a year ago; at a higher rate of profit, the order could reverse...and it could reverse again for a higher rate of profit.
This makes the Austrian theory of "roundaboutness" as flawed as the Neoclassical Marginal productivity theory. Of course, to find out about how flawed that is, you need to read the above parts of this long critique.
And now for a horribly ironic ending of my mini-critique. The Austrians, who are quite vocal against equilibrium analysis (arguing in favor of disequilibrium), their preference for capitalism as a social system is dependent on the belief that it will remain close to equilibrium. If (instead) capitalism is endogeneously unstable, then it may remain substantially distant from equilibrium situations all the time. This weakens the Austrian school, to the extent that its support for capitalism emanates from conditions which are assumed to apply in equilibrium!
Post-Script: A Critique of Marginal Utility
Most of you, I am guessing, expected it to come to this eventually.
Well, any elementary introductory Microeconomics text (e.g. Browning and Browning) will tell you that it is feasible to measure the demand curve.
Well, it is worthwhile to quote the "economists" themselves:
Originally posted by Browning and [email protected] Chapter Two, Page 55
Utility is simply a subjective measure of usefulness, or want satisfaction, that results from consumption. Units in which it is measured are arbitrary, but they are commonly referred to as utils: a util is one unit of utility. --emphasis in bold is mine added
Now, it is first off important to note that "arbitrariness" is a quality given to a mathematical quantity that denotes that the quantity itself is heuristic, and used to find something else that's more important.
E.g. in Riemannian geometry, the affine parameter \lambda satisfies an arbitrary linear function such that a*\lambda + b exists. It doesn't matter what a and b are, what matters is that lambda satisfies it.
In other words "arbitrary" used in math (as it is used in its mathematical sense here) means "heuristic".
However, the measurement of utility is rather vital... are we measuring in terms of the utility "gained" from a tea spoon of sugar or the utility of a human life?
Worse, who decides the utility of these things? Someone who has no use for sugar wouldn't get anything from tea spoons of sugar (supposing that there is some measure of utility here). And how does it compare to a human life???
Well, those of you who are not really well read in Economics may be saying by now "Yeah yeah, no measure of utility, who cares?" Well here's the problem:
Browning and [email protected] Chapter 2, page 58
The slope of an indifference curve equals the ratio of the marginal utilities of the two goods. --emphasis is Browning and Browning's, not mine.
So we find the demand curve from the ratio of the diminishing marginal utility curves. (Remember: money is also a commodity, though I don't see how it could have a diminishing marginal utility curve.)
You can simply change the Y axis to be the money-commodity (or assuming that it is not a commodity-standardized economy, e.g. an economy off the gold standard, it would be money itself).
But marginal utility's measurement is still a problem in reality. Although the ratios are all that is important, if you cannot measure a util you are out of luck. That is a SERIOUS problem for the Neoclassical paradigm!
It totally defeats the ability to predict (and indeed measure!) the demand curve...which then defeats the entire idea of "supply and demand" for a "theory of value".
Bibliography (This is probably not in any order)
Bohm-Bawerk. Karl Marx and the Close of His System Orien Ed. 1949.
Browning, Edgar K., Browning, Jacquelene M. Microeconomic Theory and Applications Third Ed. 1986.
Lord Robbins An Essay on The Nature & Significance of Economic Science Third Ed. 1984.
Rothbard, M. America's Great Depression.
Rothbard, M. Power and the Market.
Sraffa, Piero. "The Laws of Returns Under Competitive Conditions." Economic Journal, 40: 538-550.
Sraffa, Piero. The Production of Commodities by means of Commodities First Ed. 1960.