Mathematics and Economics

Dan Sullivan

[Reprinted from a Land-Theory, online discussion, 6 October 2000]

Economic students in France [recently circulated] a petition by economic students in France, "protesting against economics' 'uncontrolled use of mathematics'. This indulgence, it said, creates 'a true schizophrenia' because the mathematics has 'become an end in itself' resulting in an 'autistic science'". Bravo, if a century late.

Indeed, Henry George wrote, in *Science of Political Economy*, pp 99-100:

We are justified, therefore, in supposing, and as a matter of fact do generally suppose when we first hear of them, that the works now written by the professors of political economy in our universities and colleges, and entitled *Elements of Economics*, *Principles of Economics*, *Manual of Economics*, etc., are treatises on political economy. Examination, however, will show that many of these are not in reality treatises on the science of political economy, but treatises on what their authors might better call the science of exchanges, or the science of exchangeable quantities. This is not the same thing as political economy, but quite a different thing -- a science in short akin to the science of mathematics.* In this there is no necessity for distinguishing between what is wealth to the unit and what is wealth to the whole, and moral questions, that must be met in a true political economy, may be easily avoided by those to whom they seem awkward.

*The attempts by titular professors of political economy to find mathematical expression for what they call "economics" must be familiar to those who have toiled through recent scholastic literature.

A proper name for this totally different science, which the professors of political economy in so many of the leading colleges and universities on both sides of the Atlantic have now substituted in their teaching for the science they are officially supposed to expound, would be that of "catallactics," as proposed by Archbishop Whately, or that of "plutology," as proposed by Professor Hern, of Melbourne; but it is certainly not properly "economics."

Both the reason for, and what is meant by, the change of title from political economy to economics, which is so noticeable in the writings of the professors of political economy in recent years, are thus frankly shown by Macleod (Vol. I, Chapter VII, Sec. II, *Science of Economics*):

We do not propose to make any change at all in the name of the science. Both the terms "Political Economy" and "Economic Science" or "Economics" are in common use, and it seems better to discontinue the name which is liable to misinterpretation, and which seems to relate to politics, and to adhere to that one which most clearly defines the nature and extent and is most analogous to the names of other sciences. We shall, therefore, henceforth discontinue the use of the term "political economy," and adhere to that of "economics." Economics, then, is simply the science of exchanges, or of commerce in its widest extent and in all its forms and varieties; it is sometimes called the science of wealth or the theory of value. The definition of science we offer is:

Economics is the science which treats the laws which govern the relations of exchangeable quantities.

Now the laws which govern the relations of exchangeable quantities are such laws as 2+2=4; 4-1=3; 2x4=8; 4/2=2; and their extensions.

The proper place for such laws in any classification of the sciences is as laws or arithmetic or laws of mathematics, not as laws of economics. And the attempt of holders of chairs of political economy to take advantage of the usage of language which has made "economic" a short word for "politico-economic" to pass of their "science of economics" as if it were the science of political economy, is as essentially dishonest as the device of the proverbial Irishman who attempted to cheat his partners by the formula, "Here's two for you two, and here's two for me too."

The absurdity of reducing economics to mathematical formulas is exemplified by David's mathematical "proof" of an economic statement, for the mathematics was full of assumptions about economic behavior that defy common sense.

It supposes people projecting the growth of rents to infinity when we all know that projecting rents for more than a few years is shaky, and for more than a decade or two, pure astrology.

It supposes the investors to have no concerns about cash flow, when we know that most investors do indeed have concerns about cash flow.

It supposes real estate to be an absolutely liquid commodity that can be exchanged in the future without transaction costs, when we know that the exchange of real estate is fraught with peril and inconvenience, involving title searches and title insurance, possible hidden liabilities, possibly hidden information about surrounding events that might dramatically reduce land values, etc.

Such assumptions are perfectly reasonable for physics or chemistry or other such hard sciences that do not involve the concerns of human beings, but they are absurd for economics, and wholly absurd for real estate economics, where one's neighbor might set up an amusement park or a slaughterhouse, and where such unpredictable occurrences make future land rents wholly beyond divination.

So, while economic alchemists foist such nonsensical formulas on one another, actual traders in real estate, for the most part, focus their attention on how long it will take to recoup their initial investment, what the return is likely to be immediately after that, and what the risks are that the thing will go sour. Show me an investor who calculates rents to infinity, though, and I will show you an investor who should have become an economist instead of risking real money.