In my previous post on this subject, I asserted the non-applicability of higher mathematics to economic analysis, arguing that true functions (in the mathematical sense) are missing from all economic relationships. Abiola asked for a demonstration or proof.

Very well. What follows is a slight re-working of a comment I posted to Brad Delong's web site a few weeks back, which ought to satisfy any reasonable person who has doubts on this question:

The root of the problem lies in the belief, held by academic economists, that deep down and in some mysterious way -- maybe only statistically -- the laws of supply and demand are like the laws of physics -- as, for example, the laws governing the attraction and repulsion of electrons and protons. But consider:

In physics, the law which describes the inverse relation between distance and force between charges (or masses) is not just a rough approximation, qualitative description, or statistical generalization. Rather, it is an extremely precise description, to roughly 20 decimal places of significance, in which measurement error plays a very small part.

What's more, each electron is considered to be not just similar to every other electron (to continue the example) but rather exactly like every other electron, to the point of electrons having no individual identity when two or more are together at the same time and place.

In addition, in the world of physics the charge on an electron (keeping to the same example) is assumed not to vary with time and place, but to remain exactly the same everywhere and always throughout the entire observable universe and for all time, to the very last decimal place that we are able to measure.

Given these assumptions (which have frequently been tested) physicists have a reasonable basis to believe they are

dealing with actual functions (in the mathematical sense) when they write a formula such as F=G(mm'/rr) for gravitation, or F=qq'r/4(pi)errr for electrostatics and therefore feel justified to hazard the use of sophisticated mathematical analysis for purposes of prediction -- yet always humbly leaving open the possibility that they could be wrong regarding any and all of their assumptions, including constancy of charge, precision of the inverse law, etc.

And yet, even then, physicists will be the first to admit that even the most powerful mathematical machinery they are able to bring to bear on a problem can deal successfully with only the very simplest situations, beyond which their equations are useless. Thus, for example, their equations can be solved for the two body problem but not the three body problem in Newtonian mechanics; they can solve the Schrödinger equation when there is only one proton and one electron interacting, but not when there are even two protons and two electrons, let alone anything more complicated than that.

Furthermore, on those occassions when physicists do make complex predictions -- such as that nuclear fission would occur en mass, before the first atom bomb was tested (to choose an historical example) -- they do so with caution, double checking all their calculations, and hoping that they haven't overlooked something, or might accidentally set the atmosphere on fire. (See Richard Rhodes excellent The Making of the Atomic Bomb for more on this subject). *

Contrast this with the situation in economics. Here the elementary particle, so to speak, is the individual human being, no two of which are alike. What's more, the forces of attraction and repulsion that each individual feels for the goods of this world cannot be measured with any precision at all, much less to an accuracy of 20 decimal places. Furthermore, these forces of attraction and repulsion do not remain constant, even approximately so, over time and place for the same individual, let alone for different individuals, who vary enormously in their likes and dislikes.

Does any of this deter economists from using the machinery of calculus and systems of linear equations and so forth, to try to model the most complex dynamic systems imaginable, involving multiple individuals and multiplicity of goods? Noooooooooooo. They rush right in; and this, my friends, is precisely what physics envy is all about.

One final note on the idea of utility. Utility is a useful heuristic concept, in my judgment, with a well-understood intuitive content: it refers to how much satisfaction or displeasure one feels as a result of acquiring or losing some good. (For the theoretical usefulness of the concept, see what William Stanley Jevons did with it in his revolutionary breakthrough to marginal analysis in the middle of the 19th century.) Now, admittedly, utility cannot be measured -- but even so, it has a hell of a lot more reality in the real world of economics than an indifference curve, which exists only in the minds of mathematical Platonists like Paul Samuelson and company -- who, I predict, will be remembered in the annals of economics about as long as the acolytes of Talcot Parsons were remembered in the annals of sociology, after that distinguished gentleman departed from the scene.

Bottom line: the field of economics is in a high state of academic decadence for now, the likes of which only a Jonathan Swift could love.

*The combination of caution and open-mindedness in the physics community is illustrated by a funny anecdote I heard during the cold-fusion fiasco a few years back, when scientists were first trying to reproduce the results. As a rule, chemists tended to be more credulous, and physicists more skeptical, of the claims of Fleischman and Pons. (btw, I have a newspaper photo of those two posing with Marylin Lloyd, our local congresswoman, who was sitting on the House Energy Committee at the time; Marilyn had long ringlets of hair falling all over her forehead, and I told her (she was a gardening client of ours) that for all the world the three of them together looked like the Marx brothers; she didn?t think it was funny.) Anyway, the joke at the time was that you could always tell the chemists from the physicists: the chemists were the guys sitting around tables with glass beakers on top, and confidence written all over their faces; while the physicists were the one's with more dubious expressions, crouching behind lead shields.