Parallel Thoughts By Wittgenstein And Sraffa

Apparently Wittgenstein wrote the following in 1937:

"The origin and the primitive form of the language game is a reaction; only from this can more complicated forms develop.

Language - I want to say - is a refinement, 'in the beginning was the deed'." -- Ludwig Wittgenstein, Culture and Value (Translated by Peter Winch) (1980)

And Sraffa, I guess, wrote the following in the early 1930s:

"If the rules of language can be constructed only by observation, there can never be any nonsense said. This identifies the cause and the meaning of a word.

The language of birds, as well as the language of metaphysicians can be interpreted consistently in this way.

It is only a matter of finding the occasion on which they say a thing, just as one finds the occasion on which they sneeze.

And if nonsense is 'a mere noise' it certainly must happen, as sneeze, when there is cause: how can this be distinguished from its meaning?

We should give up the generalities and take particular cases, from which we started. Take conditional propositions: whan are they nonsense, and when are they not?" -- Piero Sraffa as quoted by Heinz D. Kurz, "'If some people looked like elephants and others like cats, or fish...' On the difficulties of understanding each other: the case of Wittgenstein and Sraffa", The European Journal of the History of Economic Thought, V. 16, n. 2 (2009): pp. 361-374

Colander Testimony On Risks Modeling

Last September, the Committee on Science and Technology's Subcommittee on Investigations and Oversight, a subcommittee of the United States House of Representatives heard testimony on the risks of financial modeling. I looked at David Colander's testimony.

Colander advocates modeling economies as complex dynamical systems. He thinks economists should be aware of the limitations of models. Macroeconomists, in settling on the Dynamic Stochastic General Equilibrium (DSGE) model, failed to consider a wide range of models. The assumptions of the DSGE model do not fit the real world. (In objecting to the use of the "assumption" of the existence of a representative agent, I am on the side of such economists as Alan Kirman and Frank Hahn & Robert Solow.)

Colander discusses how mainstream economists are indoctrinated. Colander recommends that peer review for grants from the National Science Foundation for economics research include, "for example, physicists, mathematician[s], statisticans, and even business and govermental representatives".

This bit about the NSF reminds me of a story Paul Davidson tells:

"In 1980 I applied for a grant from the National Science Foundation to write International Money and the Real World... One of the [insider peer reviewers] had the most telling observation of them all. He said something like, 'It is true that Davidson has a very good track record and surprisingly good publications, but he marches to a different drummer. If he's marching to a different drummer, if his music is different, then he ought to get his own money and not use ours.'" -- Paul Davidson in J. E. King, Conversations with Post Keynesians (1995)

Davidson did not get the grant.

Weird Science II

A bit from Avatar reminds me of Ursula K. LeGuin's "Vaster Than Empires and More Slow", a short story republished in her collection The Wind's Twelve Quarters (1975). LeGuin postulates a world in which nodes in tree roots act like synapses. The plant life is one sentience. Maybe even vines and spores partake in it. As before, a cultural work reminds me of some science:

• The longest lived thing is arguably Pando, a grove of aspens in Utah that seems to be one plant, connected at the roots and propagating through runners like strawberries or mrytle.
• Or maybe it is an instance of the fungus Armillaria bulbosa in Oregon.

A Wikipedia article lists other such organisms, for what it's worth. (The references in this post are reminders for me to look up sometime.)

Wage-Rate Of Profits Curves

1.0 Introduction
I have written about so-called factor price curves and frontiers in many posts. They are so-called because the interest rate is not a price of any factor of production. In this post, I use the more neutral expressions "Wage-Rate of Profits Curve" and "Wage-Rate of Profits Frontier". I consider the concepts denoted by these terms to be elements of mathematical economics that arise, in particular, in the analysis of steady states.

2.0 Derivation of a Wage-Rate of Profits Curve
Consider an economy in which n commodities are produced. Each commodity j is produced in a corresponding industry in which it is the sole output of a single process. This process:

• Requires inputs of labor and commodities. These inputs are represented as a_{0, j} person-years per unit output and a_{i, j} units of the ith commodity per unit output.
• Exhibits Constant Returns to Scale (CRS).
• Requires a year to complete.
• Totally uses up its commodity inputs.

A technique consists of a process for each of the n industries. The technique is represented by the row vector a₀ of direct labor coefficients and the square Leontief Input-Output matrix A. Assume:

• Each commodity enters either directly or indirectly into the production of all commodities. That is, all commodities are basic in the sense of Sraffa.
• The economy is viable. That is, there exists a level of operation of all processes such that the outputs can replace the commodities used up in their production and leave a surplus product to be paid out in the form of wages and profits.
• Wages are paid at the end of the year.
• The same rate of profits is earned on advances in all industries.

The assumptions of CRS and of all commodities being basic are made for ease of exposition.

Under these assumptions, the constant prices that allow the economy to smoothly reproduce satisfy the following system of n equations:

p A (1 + r) +w a₀ = p

where p is the row vector of prices, w is the wage, and r is the rate of profits. Given the rate of profits, this is a linear system in n + 1 variables. The last equation imposed in the model sets the value of the numeraire to unity:

p e = 1

where e is a column vector denoting the units of each commodity that comprise the numeraire. Only solutions in which all prices are positive and the wage is non-negative are considered.

The price equation can be transformed into:

w a₀ = p [I - (1 + r)A]

where I is the identity matrix. Or:

w a₀ [I - (1 + r)A]^-1 = p

where the assumption of viability guarantees the existence of the inverse for all rates of profits between zero and a maximum rate of profits. Right multiply both sides of the above equation by the numeraire:

w a₀ [I - (1 + r)A]^-1 e = p e = 1

The wage-rate of profits curve for the technique is then:

w = 1/{a₀ [I - (1 + r)A]^-1 e}

3.0 Properties of Wage-Rate of Profits Curves
The Wage-Rate of Profits Curve for a technique, under the assumptions above, has the following properties:

• There is a finite maximum rate of profits for which the wage is zero. (If no commodity were basic, this maximum would not be finite.)
• There is a maximum wage for which the rate of profits is zero.
• The wage-rate of profits curve is strictly decreasing between the rate of profits of zero and the maximum rate of profits.
• The wage rate of profits curve can be both convex to the origin and concave to the origin. (If the number of commodities n is greater than 2, the convexity can vary throughout the curve.)
• If the vector of direct labor coeffients is a left-hand eigenvector of the Leontief Input-Output matrix, the wage-rate of profits curve is a straight line, that is, affine. (This is Marx's case of equal organic composition of capitals.)
• If the numeraire is a right-hand eigenvector of the Leontief Input-Output matrix, the wage-rate of profits curve is affine. (This is the case of Sraffa's standard commodity.)

Figure 1 illustrates the wage-rate of profits curve for five techniques (α, β, δ, ε, and τ). Pasinetti uses π, not r, to denote the rate of profits. These curves are drawn under the assumption that the organic composition of capitals is not constant for any technique, and the numeraire is not the standard commodity for any of the techniques. Figure 1 also shows the wage-rate of profits frontier, formed from the outer envelope of all the wage-rate of profits curves for the individual techniques. This frontier is used to analyze the choice of technique for long-period, circulating capital models with single production.

Figure 1: The Frontier Formed From Factor-Price Curves (from Pasinetti (1977), p. 157)

Selected References

• Heinz D. Kurz and Neri Salvadori (1995) Theory of Production: A Long-Period Analysis, Cambridge University Press
• Heinz D. Kurz and Neri Salvadori "Production Theory: An Introduction"
• Luigi L. Pasinetti (1977) Lectures on the Theory of Production, Columbia University Press

Paul A. Samuelson, 1915-2009

I've been influenced by Samuelson's work. I've referenced him here on such topics as:

• Aggregate production functions
• Cambridge Capital Controversies, Joan Robinson, and Piero Sraffa
• Growth theory
• International trade, theory of
• Linear programming
• Marginal productivity theory
• Marxist economics
• Revealed preference theory

I don't think I've referenced him on overlapping generations models when I've used them. But I believe he originated such models.

Negative Price Wicksell Effect, Positive Real Wicksell Effect

1.0 Introduction
I have previously suggested a taxonomy of Wicksell effects. This post presents an example with:

• The cost-minimizing technique varying continuously along the so-called factor-price frontier
• Negative price Wicksell effects
• Positive real Wicksell effects
• Price Wicksell effects greater in magnitude than real Wicksell effects.

This example is due to Saverio M. Fratini ("Reswitching and Decreasing Demand for Capital").

2.0 Technology
Suppose technology consists of a continuum of techniques indexed by the parameter θ, where θ is a real number restricted to the interval [0, 1]:

0 ≤ θ ≤ 1

Each technique consists of the three Constant-Returns-to-Scale processes in Table 1. No commodity is basic, in Sraffa's sense, in any technique in this technology. In the first process in a technique, θ-grade iron is produced directly from unassisted labor. In the second process, labor transforms the θ-grade iron into θ-grade steel. Finally, in the third process, labor transforms θ-grade steel into corn, the consumption good in the model. All processes take a year to complete, and all processes totally use up their input.

Table 1: The Technique Indexed by θ

Inputs	Industry Sector
	θ-Grade Iron	θ-Grade Steel	Corn
Labor (Person-Yrs)	1/(1 + θ)	θ	3/(1 + θ)
Iron (Tons)	0	1	0
Steel (Tons)	0	0	1
Corn (Bushels)	0	0	0
Output	1 Ton	1 Ton	1 Bushel

Capital goods are specific in their uses in this example. θ₁-grade steel cannot be made out of θ₂-grade iron when θ₁ ≠ θ₂.

3.0 Stationary-State Quantity Flows
Suppose in Table 1 that:

• The first process is used to produce (1 + θ)/(4 + θ + θ²) tons of θ-grade iron
• The second process is used to produce (1 + θ)/(4 + θ + θ²) tons of θ-grade steel
• The third process is used to produce (1 + θ)/(4 + θ + θ²) bushels corn

Then one person-year would be employed over these three processes. Capital goods would consist of (1 + θ)/(4 + θ + θ²) tons of θ-grade iron and (1 + θ)/(4 + θ + θ²) tons of θ-grade steel. The capital goods would be used up throughout the latter two sectors, but reproduced at the end of the year. Net output would consist of (1 + θ)/(4 + θ + θ²) bushels corn per person-year.

4.0 Prices
Given the technique, stationary state prices must satisfy the following three equations:

[1/(1 + θ)] w = p₁

p₁(1 + r) + θ w = p₂

p₂(1 + r) + [3/(1 + θ)] w = 1

where:

• p₁ is the price of a ton θ-grade iron;
• p₂ is the price of a ton θ-grade steel;
• w is the wage;
• r is the rate of profits.

A bushel corn is the numeraire. The above equations embody the assumption that labor is paid at the end of the year.

The above is a system of three equations in four unknowns, given the technique. It is a linear system, given the rate of profits. The solution in terms of the rate of profits is easily found. The so-called factor-price curve for a technique is:

w(r, θ) = (1 + θ)/[3 + θ(1 + θ)(1 + r) + (1 + r)²]

The price of a ton θ-grade iron is:

p₁(r, θ) = 1/[3 + θ(1 + θ)(1 + r) + (1 + r)²]

The price of a ton θ-grade steel is:

p₂(r, θ) = [(1 + r) + θ(1 + θ)]/[3 + θ(1 + θ)(1 + r) + (1 + r)²]

Given the technique and the rate of profits, these prices can be used to evaluate the value of the capital goods used in a stationary state.

5.0 The Cost-Minimizing Technique
The optimal technique to use at any given rate of profits maximizes the wage. The first-order condition for such maximization is found by equating the derivative of the factor-price curve to zero:

dw/dθ = 0

Or:

3 + θ(1 + θ)(1 + r) + (1 + r)² - (1 + θ)(1 + 2θ)(1 + r) = 0

For 0 ≤ r ≤ 2, the cost-minimizing technique is then:

θ(r) = {[3 + (1 + r)²]/(1 + r)}^1/2 - 1

For r > 2, a corner solution is found:

θ(r) = 1

Figure 1 illustrates the cost-minimizing technique.

Figure 1: The Choice of Technique

The graph in Figure 1 reaches a minimum at a rate of profits of (3^1/2 - 1). For (12^1/4 - 1) < θ < 1, two rate of profits have the corresponding cost-minimizing technique indexed by the given value of θ. In other words, this is an example of reswitching.

The index for the cost-minimizing technique can be plugged into the factor price curve for the technique to which it corresponds at a given rate of profits. Figure 2 displays the resulting so-called factor price frontier. The index θ varies continuously for 0 ≤ r ≤ 200% in Figure 2. As the rate of profits increases without bound, the frontier approaches a wage of zero.

Figure 2: The Factor-Price Frontier

6.0 Capital and Labor "Markets"
Fratini’s notes that this is a reswitching example in which the capital market initially appears to be in accord with out-dated neoclassical intuition. The above analysis has shown how to find physical quantities of capital goods per worker, how to evaluate them at equilibrium prices, and how to find net output per worker. Figure 3 shows the resulting plot of the value of capital per unit output. Fratini looks at the value of capital per worker instead. Either curve is continuous and downward-sloping. The regions above and below the rate of profits of (3^1/2 - 1) appear qualitatively similar and visually indistinguishable. This curve might be said to be a downward-sloping demand function for capital.

Figure 3: The Capital Market

The analogous curve looks very different for the labor market (Figure 4). The region with a positive Wicksell effect is a region with a high rate of profits and thus a low real wage. The demand function for labor might be said to be upward-sloping in the region with a positive real Wicksell effect.

Figure 4: The Labor Market

7.0 Conclusion
The example makes Fratini’s point. The shape of the relationship between the value of capital, either per worker or per unit output, and the rate of profits is not necessarily a good indicator of the presence of reswitching or reverse capital-deepening.

Two Blogs Critical Of Economics

The post-autistic movement now has a blog: The Real-World Economics Review Blog.

I'm much less enthusiastic about the Counter-Economics Blog, which I stumbled over recently. Shaun Snapp claims to be applying critical thinking to economics, but he is too popular and too focused on finance for my taste. His claim that nobody reads either Adam Smith or Karl Marx is belied by the many serious scholars that do. (I've read major works by both.)

Herbert Gintis, Amazon Reviewer

Herb Gintis has now posted 231 reviews to Amazon. He has something to anger everybody.

Here he describes Jerry Cohen as a "supporter of virtually unsupportable Marxian doctrines" and having "studied ignorance of standard social and psychological theory."

He gives only two stars to Keen's Debunking Economics because, according to Gintis, it attacks a straw person. Mainstream economics is not as depicted by Keen, only undergraduate teaching is. "Abjectly brainless", "often just plain wrong", and "like teaching ... phlogiston and ether in physics class" are Gintis' phrases. I like how defenders of the mainstream cannot and will not defend economics as taught.

Gintis also gives only two stars to Ontology and Economics: Tony Lawson and His Critics. Basically, he disagrees that "Lawson's arguments are so powerful that few economists now feel that his case can be ignored." According to Gintis, his case can too be ignored; economists just ignore methodology. Gintis doesn't really engage the give and take in the book. I think he should have noted his agreement with John Davis's take on the openness of mainstream economics to some kinds of heterodox contributions.

I found this review of a recent George Soros book of interest. Some blame the current financial meltdown on failures of either individual or collective rationality. Gintis says that even if everybody were as rational as some (Chicago?) economists posit, market fundamentalism would still be unfounded. He bases this claim on the failure of the Arrow-Debreu model of General Equilibrium to have any attractive dynamical properties. He recommends agent-based modeling to analyze capitalist economies.

Gintis has quite a few positive reviews of rightists. For example, he gives four stars to Hazlitt's Economics in One Lesson. (Despite most of the reviews I'm highlighting, he also has some extremely positive reviews for liberals and leftists.) I think his reviews of right wing books generate more comments, and Gintis replies. (The worst are full of passionate intensity.) One review of a book that I would think is not worth reading currently has 103 comments.

In addition to politics and economics, he has also reviewed books on language, biology, and logic. I want to recall the existence of Torkel Franzen's Godel's Theorem: An Incomplete Guide to Its Use and Abuse.

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.

Table 1: Possibilities

	Technology Property		Labor Market Response	Capital Market Response
	Price Wicksell Effects	Real Wicksell Effects	Higher Wage	Lower Interest Rate
A	Negative	Negative	Less Employment	Increased Value of Capital
B	Negative	Positive	More Employment	Indeterminate
C	Positive	Negative	Less Employment	Indeterminate
D	Positive	Positive	More Employment	Decreased Value of Capital
E	Zero	Negative	Less Employment	Increased Value of Capital
F?	Zero	Positive	More Employment	Decreased Value of Capital
G	Negative	Zero	Unchanged Employment	Increased Value of Capital
H	Positive	Zero	Unchanged Employment	Decreased Value of Capital
I	Zero	Zero	Unchanged Employment	Unchanged Value of Capital

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.

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.

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, x_i 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.

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.

"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

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.

Error Built Upon Error

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

My Dead Tree Austrian Library

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

A Neoricardian Model of International Trade

Hoisted from comments of October 28:

"Your interest has much in common with my research field. I am a Sraffian and works in the field of international trade theory.

You have cited several times Steedman and Metcalfe. They have worked on the open small country case. As a trade theory, this is not general enough. It cannot analyse the South-North problem, to cite an obvious example. The Ricardian trade theory should be extended to the many country case with the traded commodities across countries. As Sraffa named his major work Productions of commodities by means of commodities, the production is circular in its character and cannot be arranged linearly as it is assumed in the Austrian tradition. Heckscher-Ohlin theory also assumes this linearity, starting with the endowed production factors, then sometimes intermediates goods and final goods. This is completely inadequate as production structure. But the task to develop a trade theory with this circular structure is quite hard. Steedman and Metcalfe did not succeed in this attempt. I recently found the method how to overcome this difficulty. Please look into my paper: A New Construction of Ricardian Trade Theory—A Many-country, Many-commodity Case with Intermediate Goods and Choice of Production Techniques" -- Yoyo_the_economist

I have not had a chance to read this paper. Based on the claims in the introduction, it does sound quite intriguing.

Energy Return On Energy Investment (EROEI)?

According to this New York Times article:

"Last week, about 50 scholars in economics, ecology, engineering and other fields met at the State University of New York's College of Environmental Science and Forestry for their second annual conference on biophysical economics. The new field shares features with ecological economics, a much more established discipline with conferences boasting hundreds of attendees...

...Central to their argument is an understanding that the survival of all living creatures is limited by the concept of energy return on investment (EROI): that any living thing or living societies can survive only so long as they are capable of getting more net energy from any activity than they expend during the performance of that activity.

For instance, if a squirrel burns energy eating nuts, those nuts had better give the squirrel more energy back then it expended, or the squirrel will inevitably die. It is a rule that lies at the core of studying animal and plant behavior, and human society should be looked at no differently, as even technologically complex societies are still governed by EROI...

...Through analyzing historical production data, experts say the petroleum sector's EROI in this country was about 100-to-1 in 1930, meaning one had to burn approximately 1 barrel of oil's worth of energy to get 100 barrels out of the ground. By the 1990s, it is thought, that number slid to less than 36-to-1, and further down to 19-to-1 by 2006..."

I haven't looked up how these scholars calculate EROEI. But it seems to me that an approximate value for EROEI is easily found from Leontief Input-Output tables, as available in, for example, the United States National Income and Product Accounts (NIPA). Consider the reciprocals, expressed as percentages, of the diagonal elements of the Leontief inverse, (I - A)^-1. The NIPA express the entries in Leontief matrices in dollar terms, not the physical terms I prefer for theory. But since these percentages are pure numbers, calculated as ratios, this makes no difference.

I gather the EROEI is approximately this reciprocal for the petroleum sector. In the North American Industry Classification System (NAICS), the sector of concern is industry code 211, "Oil and Gas Extraction".

A better approximation would account for the energy embodied in the other inputs in the vertically integrated oil and gas extraction industry, that is, the corresponding column of the Leontief inverse. An even better approximation would include some concern for depreciation of fixed capital.

On Some Rightists

Alex, the Yorkshire Ranter had some comments about "libertarians", that is, propertarians. (I've previously mentioned Alan Haworth, another Britisher I find amusing on that topic.)

I've wondered about Gavin Kennedy. I agree that it's bad history to claim Adam Smith's metaphor of the invisible hand is about allocative efficiency and clarified by the first welfare theorem. Consider:

"Yet the project of appropriating the politics of the Wealth of Nations to the consideration of the present has not lost its attractions... Examples of this proliferate. One has only to look to ...Gavin Kennedy (2005, a former Scottish Nationalist Party economics spokesperson)..." -- Murray Milgate & Shannon C. Stimson (2009) After Adam Smith: A Century of Transformation in Politics and Political Economy, Princeton University Press.

Ken Kesey Poster

Reading a Book

I bought the poster a bit over ten years ago. As I understand, Kesey's farm outside Eugene, Oregon, makes the label below appropriate.