Asghar Qadir's crazy Quantum Economics.

Asghar Qadir, a Pakistani physicist and mathematician, published a paper titled 'Quantum Economics' back in the late Seventies which is now cited by some cranks and nutjobs. 

It is wholly ridiculous. Judge for yourself-

Man's behaviour is quantifiable with respect to what he buys and sells. Aggregating demand (buying) and supply (selling) enables predictions to be made on the basis of the 'law of large numbers'. No infinities of agents, or perfect homogeneity of commodities, or perfectly continuous functions are required. These statistical regularities are the basis of actuarial and economic science which both improve over time, just like any other mathematical discipline, as better data and superior mathematical techniques and technologies become available. They do not predict what a given person will buy today anymore than an actuarial table predicts the day that person will die. The statistical regularities discovered by Economics are based on individual randomness cancelling out, so to speak, in aggregate.
Over time, since humans have evolved under Knightian uncertainty and face scarcity, mimetic effects channelise behaviour such that 'Muth Rationality' prevails- i.e. there is a robust convergence of expectations and behaviours around the predictions of the correct Economic Theory. In particular, we are socialised to have preferences and to employ efficient search techniques. We aren't memoryless elementary particles but conscious, memorious, mimetic beings.

This is not to say that indeterminacy or discontinuous saltations aren't features of our Economic life. Suppose a situation where the number of sellers or buyers is small. Here Game Theory has purchase. If, over time, agents who make poor game theoretic choices are weeded out- which is what happens if there is scarcity and thus the field lies within the scope of Economics- predictions can still be made.

There is no 'Americanised version' of Keynesian or any other type of economics which 'proves that profits or interest rates will be zero'. Only if there is no risk in the Economy will there be zero profit as a return for Entrepreneurship and only if there is no 'time preference' will there be a zero rate of interest.
Workers don't read papers on mathematical economics. Nor do most of the people queuing to buy vegetables at the local stall. It is not justifiable to believe that mathematical economists are trying to brainwash the factory workers or housewives in Dario Fo's 'Can't Pay! Won't pay!'

Wonderful! In this world, people make an infinite number of comparisons, or have such comparisons made for them, before buying or selling anything!
I suppose, Qadir thinks what he is doing is clearing the ground for Spectral analysis. However, this only yields estimators of a biased type- it is not the case that the numbers speak for themselves. Interestingly, a decade or so previously, Hannan had made some suggestions in this regard such that estimators would be regret minimising- i.e. there is a Muth rational solution. However, it does not depend on some forcible resolution of concurrency- e.g. stipulation of the order in which the requirement determining operator examines options- so the solution is not arbitrary. However it works only if agents have regret minimizing preference formation. This is plausible. We have some preferences- not full ones by any means- and regret minimizing considerations allow them to be extended in a manner that is Muth rational in aggregate.
Qadir, of course, is blissfully ignorant of any such contemporary developments. He says-

Where is the prediction? All you have here is an average value. 'Non-commutativity' is irrelevant. There is no Quantum type uncertainty here because both price and quantity are exactly known for each individual as well as at the aggregate level post facto. Where do the ex ante values come from? You are saying that all the determining factors can't be quantified in advance. So how do you get them? Basically, all you are doing is pretending that your expected values are not derived post facto so as to give the appearance of ex ante freedom to the individual.

So, by stipulating that price and quantity be canonical conjugates the author is bringing back the assumption of perfect market clearing and downward sloping demand curves and so forth! But how is the Hamiltonian to be constructed? How are we to know the requirement for the ith commodity at any given price? We don't know the preferences of any agent so we can't aggregate them. Where does the information come from? Conjugacy is linked to duality and convexity with respect to the optimisation problem. But how is that optimisation actually done? Revealed Preference theory states that agents are doing the optimisation so the theory has content. If markets clear and there are no externalities, uncertainty etc, then conjugacy can do useful work for us in the theory of the consumer or the theory of the firm. We can then look at more 'real world' type behaviour involving search costs, 'wariness', mimetic effects and so on.

In quantum mechanics it is genuinely impossible to measure both position and momentum simultaneously because both are self-adjoint operators- i.e. bounded in a certain way- and have conjugacy. In Economics this is never the case- both value and price are unbounded. There is also no 'observer effect' in Economics. We always know both the price and quantity purchased.

Wow! I can't know that I like cheese but dislike butter. I have to find out by looking at each dairy product one after the other to discover my commodity requirements. Since there are infinitely many commodities, I starve to death. Is this really an 'economically reasonable assumption' to make?

So this is just a stupid theory which assumes that a biological entity could have evolved so as to make decisions based on 'infinitely many factors' because cognition isn't costly at all! Unlike Revealed Preference theory, it has zero content! It just says there is a Hamiltonian without telling us how to construct it!
The mention of Pontryagin principle is sheer lunacy. A sequential determination of infinite requirements can't be the best possible control mechanism for a dynamical system getting from one state to another. What the author is doing is assuming that micro-economics magically moves along an optimal trajectory. The assumptions of 'perfect competition' and 'rational man' are artificial but at least they don't invoke magic!

This theory can't deal with imperfect competition, non convexity, Knightian uncertainty, information asymmetry, costly search, externalities or anything else. It is just a piece of mathematical voodoo. First you stipulate that the economy has an optimal trajectory- by magic! And then, it turns out this is because it behaves like perfect competition without convexities, uncertainty, externalities etc!

Mention of 'Quantum theory' is just misdirection. There are no quantum effects in macroscopic activities- economic or otherwise.