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Economics is Confusing!

June 5, 2012

There is quite possibly nothing in the “subject of economics” that applies to the world of “economics” that we know and deal with every day, and one can readily see that some of the most fundamental and revered “truths” of the modern “subject of economics” are simply false and even derisible.

Here are three of them (and, no doubt, we’ll have a lot more to say about that):

1. “Risk” and “volatility” are almost always assumed to be the same thing. We ought to have heeded the simple observation that “volatility is not risk; it is volatility” (von Neumann 1943) and we might have been spared several decades of investment anxiety and volatility caused by the pandemic use of the Capital Assets Pricing Model (CAPM) and Modern Portfolio Theory (MPT) to obviate the same.

2. The only solution to the Arrow-Debreu equations of general economic equilibrium is the activity of placing two beads into three buckets; three beads is already too many.

3. Two economists were walking in the woods discussing the problem of “The Prisoner’s Dilemma” when they were surprised by a mother grizzly and her two cubs. “Run! said one to the other. No, said he, everybody knows that we can’t outrun a bear! Of course, I know that, but I also know that I can run faster than you.” End of story. The logic is correct but the outcome is unpredictable – the bear will decide – and our adventures in “investing and monetary policy on the best advice of the best economists” using statistics, preference relations, game theory and psychology are just as unreliable and inconclusive. With information like that, and assumptions like those (“save your own ass, primal”) how is one supposed to make policy that affects the real economy?

To understand (2), one can think that the economy is made up entirely of three types of “buckets”, Rα ”what is owed to α”, Pβ  “what β owes” and Nγ “what γ owns” and a specific “triple” (Rα, Pα , Nα ) can be used to represent the entire economic activity of any and all firms or persons regardless of what mechanism is used to decide who owns what or owes what to whom; all of the accounts can be verified in the books of others and “money” is whatever “objects” – call them “beads”, not necessarily all alike – are used in exchange and, of course, we allow for new firms and enterprise at any time but these must be engendered by partitioning what is already there, basically, an “investment” must be made in order to create a new triple (R, P, N) because “triples” cannot suddenly appear from nothing – “investing” is a societal activity and something must be put into one or more of the accounts, even if only to N (what it owns).

Ormand Van Quine, the philosopher and logician ( “Fermat’s Last Theorem in Combinatorial Form”, American Mathematical Monthly, 1988). has shown that the number of ways of distributing the beads that shuns any two buckets is never the same as the number of ways that includes them both and that result is equivalent to Fermat’s Last Theorem (17th century), finally resolved in the affirmative by Andrew Wiles in 1995 ( “Modular elliptic curves and Fermat’s Last Theorem”, Annals of Mathematics 141 (3): 443–551 (1995)) and not for want of trying for three hundred and fifty years.

For example, if there are only two beads and three buckets, then there is only one way to distribute the beads so as to shun two of the buckets and only one way to distribute the beads to include them both. If there are three beads, then there is only one way in the former (all the beads are in N) but three in the latter.

One might plausibly suppose that the introduction or disappearance of one firm or two accounts of any sort would not markedly change the economy but Van Quine’s result shows that such economies can never be isomorphic because the possible distributions or opportunities of “beads” must be different in number and we must expect to lurch – not necessarily transition by substitution or “smooth” reallocations of resources – from one to the other.

Recent examples of “lurching” abound such as the demise of the leader of Libya or the firm, Lehman Brothers, or the success or failure of some new technology or process, none of which can be explained by a general equilibrium model of the economy to have such dramatic effects, nor can said lurching be deemed to be insignificant in the long run. It happens all the time.

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