Not even wrong

By the classical theory, we mean the theory that labour is the source of value. This was generally accepted from the time of Ibn Kaldun through Adam Smith down to that of Karl Marx1. But if you have had an economics course at school or college, this is unlikely to be the theory you were taught. Instead you would have been taught the neo-classical theory which was developed in the late 19th century by writers like Jevons or Marshall. It is arguable that this theory gained its popularity because the classical theory, having by then been adapted by socialist writers, had a rather disreputable image in polite society. The neo-classical theory appeared considerably more sophisticated. It was more mathematical and had a sciency feel2. Its plausibility to young students is enhanced by a beguiling use of diagrams. For those of you who did not do an economics course at school, Figure 1 is what millions of school students have been given as the theory of price.

 sdcurve

Figure 1: The theory of price taught to millions of students.

 

There are two lines, sometimes they are drawn slightly curved, one is called the supply function the other the demand function. The demand function rests on the commonsense notion that if something is cheap, people will buy more of it, so it slopes down. Teachers have little difficulty getting this idea across to their class.

The other line, called the supply function is shown sloping the other way. What it purports to show is that as more is supplied, the cost of each item goes up. Teachers have more difficulty with this, as common knowledge and experience will have taught students that actually the reverse is the case: as industries ramp up production they find they can produce more efficiently and supply the output at a lower cost. Such objections provoke some hand waving at the blackboard and excuses3.

The great thing about a classic diagram is that it is both memorable and intuitively understandable. If you can present maths this way you leverage the processing ability of our visual cortex to understand it. That is why Venn diagrams are so much easier for students to grasp than axiomatic set theory[Lakoff and Nunez, 2001]. Our brains tell us that if it looks right, it not only is right, but it is real. So having seen the diagrams students come out thinking that supply and demand functions are real things, after all they have seen them. Not only that, one can see that the intersection of these functions exactly predicts both the quantity of the commodity sold q, and its price p.

Had the theory been presented entirely in algebraic form it would be both more confusing, less appealing, and more subject to critical analysis. We will demonstrate that once you convert it to algebraic notation it is evident that the theory violates two cardinal principles of the scientific method. Its sciency feel is faked.

Occam’s razor   is the principle widely credited to the monk William of Ockham in the middle ages, who is supposed to have said that in an explanation entia non sunt multiplicanda praeter necessitatem or entities must not be multiplied without cause. His dictum has been widely adopted by scientists who interpret it to mean that when constructing a hypothesis you should keep it simple4.

Why is this a good principle for science?

Beyond philosophical beliefs that the laws of nature are simple and elegant, there are pragmatic reasons why sticking to Occam’s razor is good scientific practice. The main one is that if you make your theory complicated enough you can make it fit any particular set of observations, but this is at a cost of loss of generality predictive ability. A famous example is the way that the Greek geocentric theory of astronomy was extended by adding epicycles to account for the retrograde apparent movement of Mars5. Ptolemy was able to get good predictions, something that classical economists signally fail to do, but he got them at the cost of a theory with little inner logic, and which, we now know was totally inside out.

The neoclassical supply and demand theory does multiply entities without cause. Each of the functions has at least two parameters specifying its slope and and position6. But the real observed data only has two parameters : a price and quantity on a particular day. So the theory attempts to explain two numbers and in the process introduces four new numbers – entities lacking necessity.

For Ptolemy the epicyclic complexity bought precision in predicting planetary motion, and in the sense that there were no more epicycles than was necessary to achieve that precision, Ptolemy’s theory obeyed Occam’s razor. But the profligacy with which the economists strew free variables around, brings the opposite effect. Their price theory is underdetermined and makes no testable predictions at all.

Testability   is another cornerstone of the scientific method. A causal theory should be testable to see if it is true. For that to work, the entities you use have to be measurable. But what testable predictions does the neoclassical theory make about the structure of industrial prices in, for example, the US economy?

It can make none, since the supply and demand functions for the various commodities are not only contingently unknown, but are in principle unknowable. The theory says that the two functions uniquely define the price and quantity that will be sold on a particular day, but there are infinitely many pairs of lines that could be so drawn as to intersect at the point (q,p) in Figure 1. It is no good trying to look at how the prices and quantities sold vary from day to day, since the theory itself holds than any changes in price or quantity must be brought about by ‘shifts’ in the functions. What this means is that the economics teacher goes to the board with her ruler and draws two more lines intersecting at the new price and quantity. This, she tells the class, is what happens in a real market, prices change because the supply and demand functions move about.

But splatter any arbitrary set of points on the price quantity graph, and you can obviously draw intersecting lines through each an every one of them. Let these points be prices on successive days, there could never be a sequence of these price value measurements that could not be ‘explained’ by suitably shifting a ruler about and drawing pairs of intersecting lines. So the theory is unfalsifiable. It makes no specific operational predictions about prices and quantities. It is true by definition and vacuous by definition. It is not even wrong[Woit, 2002].

References

[1]
Ibn Khald¯un, Franz Rosenthal, and Nessim Joseph Dawood. The Muqaddimah: an introduction to history; in three volumes. 1. Number 43. Princeton University Press, 1969.

[2]
G. Lakoff and R. Nunez. Where mathematics comes from: How the embodied mind brings mathematics into being. Basic Books, 2001.

[3]
Karl Marx. Value, price, and profit. CH Kerr & Company, 1910.

[4]
P. Mirowski. More Heat Than Light: Economics as Social Physics, physics as Nature’s Economics. Cambridge University Press, 1989.

[5]
Isaac Newton. The Principia: mathematical principles of natural philosophy. Univ of California Press, 1999.

[6]
Adam Smith. The Wealth of Nations. 1974.

[7]
Peter Woit. Is string theory even wrong? American Scientist, 90 (2): 110-112, 2002.

Footnotes:

1Ïf all this has been established, it should be further known that the capital a person earns and acquires, if resulting from a craft, is the value realized from his labor. This is the meaning of ‘acquired (capital)’. There is nothing here (originally) except the labor, and (the labor) is not desired by itself as acquired (capital, but the value realized from it).

Some crafts are partly associated with other (crafts). Carpentry and weaving, for instance, are associated with wood and yarn (and the respective crafts needed for their production). However, in the two crafts (first mentioned), the labor (that goes into them) is more important, and its value is greater.

If the profit results from something other than a craft, the value of the resulting profit and acquired (capital) must (also) include the value of the labor by which it was obtained. Without labor, it would not have been acquired.

In most such cases, the share of labor (in the profit) is obvious. A portion of the value, whether large or small, comes from (the labor). The share of labor may be concealed. This is the case, for instance, with the prices of food­stuffs. The labor and expenditures that have gone into them show themselves in the price of grain, as we have stated before. But they are concealed (items) in regions where farming requires little care and few implements. Thus, only a few farmers are conscious of the (costs of labor and expenditures that have gone into their products).

It has thus become clear that gains and profits, in their entirety or for the most part, are value realized from human labor. The meaning of the word ßustenance” has become clear. It is (the part of the profit) that is utilized. Thus, the meaning of the words “profit” and ßustenance” has become clear. The meaning of both words has been explained.” Khald¯un et al. [1969],Book 1, Chapter 5, Section 1

Ät all times and places, that is dear which it is difficult to come at, or which it costs much labour to acquire; and that cheap which is to be had easily, or with very little labour. Labour alone, therefore, never varying in its own value, is alone the ultimate and real standard by which the value of all commodities can at all times and places be estimated and compared. It is their real price; money is their nominal price only.” Smith [1974],Page 136

Äs the exchangeable values of commodities are only social functions of those things, and have nothing at all to do with the natural qualities, we must first ask: What is the common social substance of all commodities? It is labour. To produce a commodity a certain amount of labour must be bestowed upon it, or worked up in it. And I say not only labour, but social labour. A man who produces an article for his own immediate use, to consume it himself, creates a product, but not a commodity. As a self-sustaining producer he has nothing to do with society. But to produce a commodity, a man must not only produce an article satisfying some social want, but his labour itself must form part and parcel of the total sum of labour expended by society. It must be subordinate to the division of labour within society. It is nothing without the other divisions of labour, and on its part is required to integrate them.

If we consider commodities as values, we consider them exclusively under the single aspect of realized, fixed, or, if you like, crystallized social labour. In this respect they can differ only by representing greater or smaller quantities of labour, as, for example, a greater amount of labour may be worked up in a silken handkerchief than in a brick. But how does one measure quantities of labour? By the time the labour lasts, in measuring the labour by the hour, the day, etc. Of course, to apply this measure, all sorts of labour are reduced to average or simple labour as their unit. We arrive, therefore, at this conclusion. A commodity has a value, because it is a crystallization of social labour. The greatness of its value, or its relative value, depends upon the greater or less amount of that social substance contained in it; that is to say, on the relative mass of labour necessary for its production. The relative values of commodities are, therefore, determined by the respective quantities or amounts of labour, worked up, realized, fixed in them. The correlative quantities of commodities which can be produced in the same time of labour are equal. Or the value of one commodity is to the value of another commodity as the quantity of labour fixed in the one is to the quantity of labour fixed in the other.” Marx [1910],Section 6

2Mirowski [1989] argues that it deliberately borrowed from the the then relatively modern Lagrangian formulations of physical field theory.

3 These tend to be to the effect that the class must distinguish between the short term equilibrium of supply and demand shown in the diagram, and long term processes which involve something quite different, a shift in the supply line to the right. This is a classic example of historians of science call adding an epicycle to a theory to cover up embarassing conflicts with evidence.

4“We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.

To this purpose the philosophers say that Nature does nothing in vain, and more is in vain when less will serve; for Nature is pleased with simplicity, and affects not the pomp of superfluous causes.”Newton [1999],Rule of reasoning I

5Since Fourier we have known that any function can be well approximated by a sum of sine waves. We use this routinely now in things like digital TV. What adding epicycles to an astronomical model does is put in additional harmonic components. Since you can approximate any function by such harmonic components, with enough epicycles upon epicycles you can, by Fourier’s theorem, get an arbitrarily good approximation of any apparent celestial motion.

6If we assume straight line functions then we have two equations

p = a −dq

for demand and

p = b+sq

for supply, where d and s are the absolute gradients of the curves, and a and b the positions where they intercept the Y axis. Clearly these equations have 4 parameters.

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