Thursday, 11 June 2015

The Utility of Futility

Suppose there is a market which clears- i.e. a price is established at which everyone who wants to buy can do so and everyone who wants to sell can get rid off their stock. Suppose further that no buyer or seller now has an unanticipated change in wealth. Suppose this is true of all markets and that everything people want to buy and sell has a market.
Then, Economists say the Market has achieved an equilibrium with a certain valuable property- it is Pareto efficient. No one can be made better off without someone being made worse off.
By some magic, it appears that individuals, knowing only their own endowments and preferences and the price called out by the auctioneer, can co-ordinate their activities just as well as an omniscient God.
However, there is a problem with this story. Suppose my buying the last chocolate eclair at one dollar means that, unknown to me, my diabetic twin brother, kidnapped by Monetarists and raised in a freak show, doesn't get that life saving confection for which he was prepared to pay 99 cents. The market may have cleared but, with hindsight, it wasn't Pareto efficient.
(The same thing is true is I didn't have a twin brother of that description but you, with unknown probability, believe you might do so and there exists some series of arbitrageurs, or 'externality internalising entities, to connect us.)
More generally, at the margin, unless I know the endowments and preferences of everybody else, the Market may be inefficient even if there are no unanticipated wealth effects.
One way round this scandal for 'Democratic' Social Choice- which is that there is no way to co-ordinate human beings as efficiently as an omniscient God- is to believe that God, for some reason of his own, wants us to put zero value on any gain or loss received outside the market.
Call this new 'Purushartha' Utility and define it as follows- suppose God only wants you to know what our theory assumes you know, then, Utility is the Purushartha that God has ordained for you to maximize. Surely, in this case, Utility theory is Muth Rational- i.e. free of hysteresis effects?
Following Samuelson, we could go on to say 'Ours is the only true Economics because we have the assurance that we are only dealing with ergodic processes. Otherwise, our subject would be empty or 'anything goes'. It is surely reasonable that we all constrain our discourse to path-independent Utility functions.'
In other words, just as ritualists accept certain constraints on what they can do so as to have an inter-subjective 'Purushartha' which they can fulfill as a signal to God of their devotion- this is like making Mum a mud cake for her birthday coz u know she like Black Forest gateaux- so too can people foolish enough to have studied Economics at University pretend Utility functions are integrable and hysteresis free.
Though Monetarists and Libertarians and other such fucktards disliked Samuelson, they raised no objection to a well paid class of Pundits arising who pretended to believe that this sort of Utility function was indeed Man's Purushartha.
Sadly, Moore's Law kept making computing cheaper and so from the Eighties onward larger and larger data sets became available which attracted the attention of, not failed Physicists, but the real deal.
A prominent 'Econo-physicist', Joseph L McCauley, wrote a scathing paper some fifteen or twenty years ago titled 'the Futility of Utility' in which he said- ' Economists usually assume that price is the gradient of utility in equilibrium, but I observe instead that price as the gradient of utility is an integrability condition for the Hamiltonian dynamics of an optimization problem...
'Hamiltonian dynamics shows that it is dangerous blindly to assume that the question of path dependence of a utility functional can be divorced from the question of integrability of the underlying dynamics. Gibbs tried but failed to make a similar point to I. Fisher , who was not as strong a mathematician as was Gibbs and didn’t understand integrability. Gibbs pointed out that the utility is generally path dependent, and suggested that Fisher address the problem of nonintegrability in relation to a possible underlying dynamics. Fisher did not understand nonintegrability of differential forms (neither did Walras or Pareto), so that Gibbs’ point was entirely lost on Fisher, who erased all mention of nonintegrability from his last papers on utility after he had become established as an economist... Fisher’s failure to address the path dependence of utility left Samuelson and other economists to worry about nonintegrability some fifty years later. The economists finally stopped worrying about it, but never solved the problem. It is not clear that they became aware of Liouville’s integrability theorem, connecting the existence of a utility function to integrability of the dynamical system, during the heyday of deterministic chaos.'

The problem here is that, Muth rationality can still obtain in over determined dynamical systems- indeed, must do, otherwise the sort of noise needed to drive liquidity would actually dissolve it- thus price can be the gradient of anything it likes, including the Utility function.
No alethic or instrumental argument Econophyics can marshal in this connection gains any purchase because, whereas agents have some knowledge of price and endowment vectors and could choose to subscribe to Samuelson type integrable, non-path dependent Utility by reason of Muth rationality, of almost any Walrasian equilibrium involving such agents, all we can know is that its price vector is not effectively computable in the life time of the Physical Universe.

Utility, thus, isn't futile at all. It is about co-ordination problems and reflexivity and Schelling focal points, on the one hand, and, on the other, it is Ninomiya concession and Upanishadic neti, neti.
In other words, if Econ aint empty, Utility is that Purushartha wherein, uniquely, God might find us wanting but only to show all wanting futile thus leaving only the undiminishable plenitude of Om Purnamadah Purnamidam &c

No comments: