Non-Euclidian Economics

From Econospeak:

SCIOD 12: Euclidean Rhapsodies

"It is fairly obvious," John Maurice Clark, explained to Irving Fisher, Frank Knight and other participants in a 1920 American Economic Association seminar, "that there are systems of economics with axioms fully as far removed from each other as the geometries of Euclid and the non-Euclideans..."

Non-Euclidean geometry was topical in 1920. On May 29, 1919, a total eclipse of the sun could be viewed from Brazil and Africa and provided the opportunity to test a prediction of Einstein's theory of general relativity about the displacement of light from a star as it passes the sun. The conclusions from those observations were hailed as "the most important result obtained in connection with the theory of gravitation since Newton's day."

Clark's paper, "Soundings in non-Euclidean Economics," was not the first foray into this particular metaphor, nor would it be the last. In his inaugural lecture as Professor of Political Economy at Cambridge, "Economic science in relation to practice," Arthur Cecil Pigou quoted extensively from Bertrand Russell's Principles of Mathematics regarding the relationship between the Euclidean and non-Euclidean geometries, which "are equally true," and realistic science, which can only be decided, "so far as any decision is possible, by experiment and observation." 

In 1920, Pigou recycled his 1908 non-Euclidean ruminations -- and the Russell quote -- in The Economics of Welfare, arguing that Russell's distinction was "applicable to the field of economic investigation. It is open to us to construct an Economic Science either of the pure type represented by pure mathematics or of the realistic type represented by experimental physics."

In The General Theory of Employment, Interest and Money Keynes also employed the geometrical metaphor, comparing classical theorists (Professor Pigou among them!) to:

Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight as the only remedy for the unfortunate collisions which are occurring.

Of course it was not literally the axioms of Euclidean geometry that classical economic theorists clung to but rather the doctrine, taught by them "from the time of Say and Ricardo..." that "supply creates its own demand..."

-- meaning by this in some significant, but not clearly defined, sense that the whole of the costs of production must necessarily be spent in the aggregate, directly or indirectly, on purchasing the product.

As it informs a theory of employment --"practically without discussion" -- that doctrine suggests what Keynes described as "two fundamental postulates," that: "1. The wage is equal to the marginal product of labour" and "2. The utility of the wage when a given volume of labour is employed is equal to the marginal disutility of that amount of labour."...MUCH MORE

Here's the real Euclidean Rhapsody:

If you have three lines
And they're made equally
Put them together
Each angle is sixty degrees
Now it is time, to learn a new shape from me
It is a rhomboid, a quadrilat'ral, see
That it has four sides, on a plane, all their lengths, are the same
It is not a square since angles aren't ninety degrees

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