## Sunday, November 29, 2009

### A Taxonomy Of The Effects Of Wicksell Effects

Consider a typical circulating capital model, in which commodities are produced from commodities and labor. The technique in use is described by a square Leontief input-output matrix and a vector of labor coefficients. In a long run equilibrium, in which prices are stationary, the technique is selected from a set of techniques to minimize production costs at a given interest rate. That set is known as the technology.

Suppose the composition and quantity of output is taken as given, along with the interest rate and the technology. The difference in the value of the capital goods at two different interest rates is the sum of the price Wicksell and real Wicksell effects. The price Wicksell effect is the sum of the differences in prices among the capital goods for a given technique. But the cost-minimizing technique might not be the same at two interest rates. The real Wicksell effect is the difference in the value of the capital goods for two techniques, given the price system at a one interest rate.

I want to compare the relative magnitude of price and real Wicksell effects at a given interest rate. Thus, I want to consider derivatives at a given interest rate. Therefore, suppose the technology consists of a continuum of techniques that might be eligible along the so-called factor price frontier. Table 1 shows all combinations of price and real Wicksell effects. A Wicksell effect is negative when the equilibrium at the higher interest rate has a lower value of capital, from the effects of price and quantity changes, respectively.

 Technology Property LaborMarketResponse CapitalMarketResponse PriceWicksellEffects RealWicksellEffects HigherWage LowerInterestRate A Negative Negative LessEmployment IncreasedValue ofCapital B Negative Positive MoreEmployment Indeterminate C Positive Negative LessEmployment Indeterminate D Positive Positive MoreEmployment DecreasedValue ofCapital E Zero Negative LessEmployment IncreasedValue ofCapital F? Zero Positive MoreEmployment DecreasedValue ofCapital G Negative Zero UnchangedEmployment IncreasedValue ofCapital H Positive Zero UnchangedEmployment DecreasedValue ofCapital I Zero Zero UnchangedEmployment UnchangedValue ofCapital

Row A in Table 1 conforms to the outdated neoclassical intuition of equilibrium prices as indices of relative scarcity. But, as Edwin Burmeister has noted, nobody knows what special case assumptions need to be imposed on technology to ensure that Wicksell effects happen to fall in any given direction.

I have the response in the capital market shown as indeterminate for rows B and C. The claim is that, for the case of a technology representable by a continuum of techniques, the price Wicksell effect can, but need not, swamp the real Wicksell effect. It is essential for this swamping to occur at a single interest rate that the technology be continuous. Pierangelo Garegnani, Heinz D. Kurz & Neri Salvadori, and Saverio M. Fratini have examples that illustrate some possibilities with a continuum of techniques.

Row E is the case of Samuelson's Surrogate Production Function. Price Wicksell effects are zero when the factor price curve for a given technique is a straight line. The question mark after the label for Row F reflects my belief that this row catalogs an impossibility. If factor price curves are straight lines along their entire length, capital-reversing cannot arise.

Rows G, H, and I are cases in which the real Wicksell effect is zero. The real Wicksell effect is zero in the discrete case when the factor price curves are tangent at a switch point. I'm not sure how this extends to the continuous case, in which all points along the factor price frontier are non-switching points. If the Row I case is possible, the technique is not determined by the location of the corresponding factor price curve. I think this may be so for non-straight line factor price curves, but I'm unsure about this case.

These remarks suggest a research program. First, demonstrate that no possibilities exist that are not listed in Table 1. This would seem to be obvious. But I don't understand Andreu Mas-Colell's paper "Capital Theory Paradoxes: Anything Goes" (in Joan Robinson and Modern Economic Theory (ed. by G. Feiwel) (1989)). He shows some multi-valued relations where I would expect functions. Second, for those rows that are impossible in Table 1, demonstrate this impossibility. Third, for each possible row, construct a numeric example. For rows B and C, one should construct at least two examples, one for each direction of the capital market response. I suppose a third example, in which price and real Wicksell effects are exactly matched in magnitude would be amusing. Much of this research would be non-original; many components are in the literature.

## Sunday, November 22, 2009

### Nietzsche On The Individual As A Society

I have previously noted the problems for utility theory created by the application of Arrow's impossibility theorem to a single individual. And I had quoted a number of classic authors who wrote of themselves as being composed of more than one mind. Here's another:
"'Freedom of the will' - that is the expression for the complex state of delight of the person exercising volition, who commands and at the same time identifies himself with the executor of the order - who, as such, enjoys also the triumph over obstacles, but thinks within himself that it was really his will itself that overcame them. In this way the person exercising volition adds the feelings of delight of his successful executive instruments, the useful 'underwills' or undersouls - indeed our body is but a social structure composed of many souls - to his feelings of delight as commander. L'effet c'est moi. What happens here is what happens in every well-constructed and happy commonwealth; namely, the governing class identifies itself with the successes of the commonwealth. In all willing it is absolutely a question of commanding and obeying, on the basis, as already said, of a social structure composed of many 'souls'." -- Friedrich Nietzsche, Beyond Good and Evil: Prelude to a Philosophy of the Future (Kaufmann translation), paragraph 19
By the way, the idea of modeling an individual choice with a structure underlying the textbook treatment of preferences over the elements of a linear space of commodities is not necessarily non-mainstream. I cannot say I know much about the relevant literature. However, I stumbled over an example - a paper, "Multiple Temptations", from John E. Stovall, a graduate student at the University of Rochester.

## Wednesday, November 18, 2009

### An Indeterminate Two-Person Zero-Sum Game With Perfect Information

1.0 Introduction
I have stumbled upon some odd mathematics, some mathematics that I have not validated. Consider the claim that all two-person zero-sum games with perfect information have a value. Apparently, this claim is inconsistent with the Axiom of Choice, an axiom in set theory. This inconsistency is shown by the Banach-Mazur game and its variants. I guess it is essential to this demonstration that these games have a potentially countable infinite number of moves.

I don't know that this demonstration is as important for economics as, for instance, W. F. Lucas' example of a cooperative game without an equilibrium.

A game has perfect information if the results of all moves prior to any given move are known to all players. Simple examples of games with imperfect information are card games in which the deal gives a player a hand which only he knows. A two-person zero-sum game is determinate if one can prove either (1) the first player wins some definite amount, (2) the second player wins some definite amount, or (3) the game is a draw. Chess is a determinate game, although it is in practice impossible to expand the tree enough to determine its value.

2.0 A Game
I steal this example from a Usenet post by Herman Rubin.

The game is fully specified by the rules and by defining a set C, where C is a given subset of the real numbers between 0 and 1, inclusive. The two players alternatively select the successive binary digits of the base-two expansion of a number within the interval [0, 1].

In other words, consider the number:

(1/2) x1 + (1/4) x2 + (1/8) x3 + (1/16) x4 + ...
where, for all i, xi is in {0, 1}. The first player chooses the binary digits with the odd indices, and the second player chooses the binary digits with the even indices. But they take turns and go in order.

The game ends with the second player paying the first player a unit when it is guaranteed that any further expansion will result in a number within C. The game ends with the second player winning a unit payment from the first player when it is guaranteed that any further expansion will result in a number in the complement of C.

A simple example is C = [0.5, 1]. The first player wins in this case. A more complicated game arises when C is the set of all irrational numbers in the unit interval. I gather this game is determinate, but I don't see offhand who wins. Finally, consider a set C that does not have a Lebesque measure. (The Axiom of Choice is necessary for the definition of such a set.) I gather that in this case, the game is not determinate. Nobody can tell a priori who will win.

## Sunday, November 15, 2009

### Lee Boldeman's Critique From Australia

Lee Boldeman's book, The Cult of the Market: Economic Fundamentalism and its Discontents is available in PDF. Boldeman does report some internal critiques of orthodox economics, such as Lipsey and Lancaster's theory of the second best. But, without having read the whole book yet, his perspective seems to be more about emphasizing an external critique of methodological individualism. Individuals are embedded in society. Boldeman says he wrote his book because he didn't know of another that covered what he wanted to say. I think his approach parallels Stephen Marglin's The Dismal Science: How Thinking Like an Economist Undermines Community. If Boldeman had read Marglin, he might still have wanted to write, since Marglin doesn't address the context of Australian public policy. Catholics in classes taught by the soon-to-be-gone department at Notre Dame would probably find Boldeman's book at interest.

## Thursday, November 12, 2009

### "And A Whole Generation Were Butchered And Damned"

"I spent the evening walking around the streets, especially in the neighborhood of Trafalgar Square, noticing cheering crowds and making myself sensitive to the emotions of passers-by. During this and the following days, I discovered to my amazement that average men and women were delighted at the prospect of war. I had fondly imagined what most pacifists contended, that wars were forced upon a reluctant population by despotic and Machiavellian governments. I had noticed during previous years how carefully Sir Edward Grey lied in order to prevent the public from knowing the methods by which he was committing us to the support of France in the event of war. I naively imagined that when the public discovered how he had lied to them, they would be annoyed; instead of which, they were grateful to him for having spared them the moral responsibility." -- Bertrand Russell, The Autobiography of Bertrand Russell: The Middle Years: 1914-1944

## Monday, November 09, 2009

### Back Issues of Methodus Available On-Line

I've just discovered the International Network for Economic Method (INEM). They publish the Journal of Economic Methodology. This journal replaced Methodus, INEM's bulletin. Back issues of Methodus are freely available. I've barely begun sampling what's here - for example, a 1992 Geoff Harcourt comment on political economy or a 1991 Kevin Hoover review of Mirowski's More Heat Than Light.

## Friday, November 06, 2009

### Error Built Upon Error

This inspired the picture below. Of course, I have more in soft-copy.

## Sunday, November 01, 2009

### Nicholas Georgescu-Roegen

I find Nicholas Georgescu-Roegen an intriguing economist. He discovered the non-substitution theorem and, apparently, the Hawkins-Simon condition.

Georgescu-Roegen developed a critique of neoclassical production functions. He argued that it applied to Leontief input-output theory too. This critique relies on distinctions among fund, flow, stock, and service. Funds are unchanged in the production process, while flows are altered. A stock is a productive input that can be used to generate flows at any rate, while a fund can generate services up to some maximum rate. In Sraffa's approach, land, I guess, is modeled as a fund. In artisan production, funds are idle most of the time, while a factory keeps their funds in use by having many laborers work slightly out of parallel. Georgescu-Roegen argued that production functions should be replaced with functionals, in which the arguments show the use of factors as functions of time.

Georgescu-Roegen accused other economists, such as Robert Solow, of ignoring the increased entropy that production causes. Usable mineral resources are finite. Georgescu-Roegen formulated what he called the fourth law of thermodynamics, which says that available matter decreases. Waste products become scattered and unusable.

He also made a distinction between what he called arithmomorphic and dialectic concepts. Arithmomorphic concepts are suitable for mathematical reasoning. Dialetic concepts are distinct but overlapping, and they are suitable for qualitative reasoning, as appropriate for a good understanding of economic development.

Georgescu-Roegen's analysis included a system of energy accounting, without accepting an energy theory of value. As forerunners, he mentions, for example, Frederick Soddy. (Soddy, apparently a Nobel laureate for discovering the existence of isotopes, called his economic philosophy ergosophy.)

Georgescu-Roegen's policy conclusions focused on converting socities to ones in which their economies were sustainable, with a concomitant smaller population in what are now considered advanced countries.

I don't think I've done justice to the subtlety and insightfulness of Georgescu-Roegen's contributions to economics with these scattered observations.

References
• Nicholas Georgescu-Roegen (1986) "Man and Production", in Foundations of Economics: Structures of Inquiry and Economic Theory (Ed. by M. Baranzini and R. Scazzieri) Basil Blackwell
• John Gowdy and Susan Mesner (1998) "The Evolution of Georgescu-Roegen's Bioeconomics" Review of Social Economy, V. 56, N. 2 (Summer)
• Eberhard K. Seifert (1994) "Georgescu-Roegen, Nicholas", in The Elgar Companion to Institutional and Evolutionary Economics (Ed. by G. M. Hodgson, W. J. Samuels, and M. R. Tool), Edward Elgar