Sunday, December 27, 2009

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

Monday, December 21, 2009

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.

Saturday, December 19, 2009

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.)

Monday, December 14, 2009

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 a0, j person-years per unit output and ai, 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.

Wednesday, December 09, 2009

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
InputsIndustry Sector
Labor (Person-Yrs)1/(1 + θ)θ3/(1 + θ)
Iron (Tons)010
Steel (Tons)001
Corn (Bushels)000
Output1 Ton1 Ton1 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
  • 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
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 (31/2 - 1). For (121/4 - 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 (31/2 - 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.

Saturday, December 05, 2009

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.)

Wednesday, December 02, 2009

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.

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.

Table 1: Possibilities
Technology PropertyLabor
Value of
Value of
Value of
Value of
Value of
Value of
Value of

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.
My Dead Tree Austrian Library

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.

  • 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

Friday, October 30, 2009

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.

Monday, October 26, 2009

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.

Saturday, October 24, 2009

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.

Wednesday, October 21, 2009

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.

Saturday, October 17, 2009

Heterodox Economics Movements I Don't Pay Much Attention To

As I understand it, each of the following had advocates around the globe in the first half of the twentieth century:
  • Georgism (I have read Progress & Poverty)
  • Silvio Gesell (Mentioned by Keynes in Chapter 23 of the General Theory)
  • Social credit (Keynes also mentions Major Douglas in Chapter 23 of the General Theory)
  • Technocracy
I gather remnants of their advocate organizations still exist. But I gather they have little representation among academic economists.

Sunday, October 11, 2009

Unemployment In A Barter Economy

" may be doubted whether under a system of barter the decisions of individuals would have their full effects..." - Piero Sraffa (1932)
In the General Theory, Keynes presents an argument for how widespread unemployment can come about. I think money enters in an essential way in Keynes' argument. This raises the question whether unemployment would exist if it were not for monetary phenomena.

Sraffa, in Production of Commodites by Means of Commodities, has a lot to say about numeraires, including the Standard Commodity. One can read Sraffa as making certain points about a monetary economy.

But put that reading of Sraffa aside. Instead, think of Sraffa's model as half of a limit point of a neoclassical model of general equilibrium. The other half of such a model of a steady state consists of utility maximization. This is a model of a barter economy. And steady state models can exhibit multiple equilibria, bifurcations, and catastrophes. I think these phenomena suggest the possibility of complex dynamics. Thus, even though neither general overproduction nor an uncleared labor market can arise in a long run competitive equilibrium in a barter economy, such an equilibrium may never be reached. Instead, the economy may cycle around with unemployment continually being recreated.

The idea that unemployment could be cured by making labor and product markets more flexibile is unsupported by price theory.

Thursday, October 08, 2009

Endogenous Money Supply In The Long Run

This post is not about how the United States Federal Reserve cannot control, on a day-to-day basis, the quantity of money in circulation. Rather, I consider financial innovation over time leads to the creation of new debt instruments that fall under a reasonable definition of "money".

One way of looking at money is that, under capitalism, money buys goods, and goods sell for money, but goods do not buy goods. A simple example: I understand one can write checks against a hedge fund. So hedge funds are money.

The emergence of new forms of money illustrates why no final systems of regulations can exist in a capitalist economy. Should something like the Federal Deposit Insurance Corporation be set up to guarantee these new forms of money? If so, some capital requirements, restrictions on leverage ratios, and so on would need to be instituted. Maybe some sort of firewalls, as in the Glass-Steagall act, should be rebuilt.

Sunday, October 04, 2009

Friday, October 02, 2009

Enrico Barone, The Originator Of The Socialist Calculation Argument

Arguably, socialism, when implemented with a centrally planned economy, is guaranteed to not produce a fairly high standard of living. Market prices are needed. This argument was originated by Enrico Barone:
"25. But it is frankly inconceivable that the economic determination of the technical coefficients can be made a priori, in such a way as to satisfy the condition of the minimum cost of production which is an essential condition for obtaining that maximum to which we have referred. The economic variability of the technical coefficients is certainly neglected by the collectivists; but that it is one of the most important sides of the question Pareto has already very clearly shown in one of his many ingenious contributions to the science.

The determination of the coefficients economically most advantageous can only be done in an experimental way: and not on a small scale, as could be done in a laboratory, but with experiments on a very large scale, because often the advantage of the variation has its origin precisely in a new and greater dimension of the undertaking. Experiments may be successful in the sense that they may lead to a lower cost combination of factors; or they may be unsuccessful, in which case that particular organization may not be copied and repeated and others will be preferred, which experimentally have given a better result.

The Ministry of Production could not do without these experiments for the determination of the economically most advantageous technical if it would realize the condition of the minimum cost of production which is essential for the attainment of the maximum collective welfare.

It is on this account that the equations of the equilibrium with the maximum collective welfare are not soluble a priori, on paper.

26. Some collectivist writers, bewailing the continual destruction of firms (those with higher costs) by free competition, think that the creation of enterprises to be destroyed later can be avoided and hope that with organized production it is possible to avoid the dissipation and destruction of wealth which such experiments involve, and which they believe to be the peculiar property of 'anarchist' production. Thereby these writers simply show that they have no clear idea of what production really is, and that they are not even disposed to probe a little deeper into the problem which will concern the Ministry which will be established for the purpose in the Collectivist State.

We repeat, that if the Ministry will not remain bound by the traditional technical coefficients, which would produce a destruction of wealth in another sense - in the sense that the greater wealth which could have been realized will not be realized - it has no other means of determining a priori the technical coefficients most advantageous economically, and must of necessity resort to experiments on a large scale in order to decide afterwards which are the most appropriate organizations, which it is advantageous to maintain in existence and to enlarge to obtain the collective maximum more easily, and which, on the other hand, it is best to discard as failures.

27. Conclusions. From what we have seen and demonstrated hitherto, it is obvious how fantastic those doctrines are which imagine that the production in the collectivist regime would be ordered in a manner substantially different from that of 'anarchist' production.

If the Ministry of Production proposes to obtain the collective maximum - which it obviously must, whatever law of distribution may be adopted - all the economic categories of the old regime must reappear, though maybe with other names: prices, salaries, interest, rent, profit, saving, etc..." -- Enrico Barone, translated from "The Ministry of Production in the Collectivist State" Giornale delgi Economisti (1908)

Tuesday, September 29, 2009

Keynes All The Rage

I noticed some articles and posts on Keynes recently. The ones I noticed are somewhat different than those highlighted by the Sandwichman. I think Robert Skidelsky's new book, Keynes: The Return of the Master, is getting more buzz than Paul Davidson's new book, The Keynes Solution: The Path to Global Economic Prosperity. Paul Krugman's review of Skidelsky's book in the Observer contrasts the rejection of Say's law with an emphasis on fundamental uncertainty. Davied Warsh also alludes to the debates over what Keynes really meant. Here is a year old oped by Skidelsky, while here is a more recent article quoting him. Aaron Swartz has been reading The General Theory of Employment, Interest, and Money. He has both a chapter-by-chapter summary and a brief explanation.

I think Keynes book was primary about economic theory and only secondary about advocating policy based on that theory. One can perhaps explain why an economy might deviate from a full employment equilibrium. Workers are constrained to budget based on the income they receive, not on the income they would receive if they were fully employed. This idea could be basis of a dynamic story. But Keynes argued, building on Richard Kahn's multiplier, that it could also explain an equilibrium with involuntary unemployment.

I think that Keynes argued that such an unemployment equilibrium could hold in both the Marshallian short run and the long run. To make sense of Keynes' claim, one must construct a model in which money enters in some essential way. And I would expect money to be non-neutral in all runs. To me, this introduction of money into an economic model is connected with modeling fundamental uncertainty. In short, I see Keynes' rejection of Say's law and his emphasis (e.g., in Chapter 12) on uncertainty as complementary.

(Apropos of none of the above - some might be amused by this cartoon. H/T to Brian Leiter.)

Saturday, September 26, 2009

O Brave New World That Has Such Bacteria In It

The BioBricks Foundation (BBF) has Request For Comments (RFCs), just like the Internet Engineering Task Force (IETF). They have a BioBrick language, a graphical language, and are working on an RDF-based framework for a synthetic biology ontology. (The Resource Description Framework (RDF) is a standard for the semantic web.)

BBF is using this this computer science technology and organizational structure to create "standard biological parts" that "encode basic biological functions". The goal is to enable biological engineers to "program living organisms in the same way a computer scientist can program a computer".

(Hat Tip to Michael Specter's New Yorker 28 September 2009 article.)

Tuesday, September 22, 2009

From Alexander Rosenberg On Cochrane On Krugman

Brian Leiter reports Alexander Rosenberg's thoughts. I'll select one extract:
"Add in [Chicago economists'] ideological attachment to the nonsensical ideas that the marginal productivity of labor or capital measures its causal role, and therefore its moral right to a proportional slice of the profits, and you easily slip from Laissez-faire 'science' to 'trickle down' political philosophy."
(Rosenberg's views remind me of this comment.) The nonsense isn't limited to Chicago. I have seen positive references to Rosenberg's book, Economics: Mathematical Politics or Science of Diminishing Returns, but I have not read it.

Monday, September 21, 2009

Stiglitz Reports

Joseph Stiglitz has been chairing commissions. The draft report of the Commission of Experts of the President of the UN General Assembly on Reform of the International Monetary and Financial System is downloadable from here. The Report of the Commission on the Measurement of Economic Performance and Social Progress is downloadable from here. (Amartya Sen was the Chair Advisor for the latter commission.)

Samir Amin has some criticisms of the former report. Amin thinks the report treats the global financial crisis as a short-term downturn, not as a manifestation of a Fordist accumulation regime that needs to be replaced.

It does seem like a new Bretton Woods, along with a meeting like the Bandung conference in 1955, might be a good thing at this conjuncture.

To Read:
  • M. Aglietta (1979) A Theory of Capitalist Regulation: The U.S. Experience, Verso Books.
  • Giovanni Arrighi (1994) The Long Twentieth Century, Verso Books.

Friday, September 18, 2009

Piling On

A fool writes:
"Paul's Keynesian economics requires that people make logically inconsistent plans to consume more, invest more, and pay more taxes with the same income... In economics, stimulus spending ran aground on Robert Barro's Ricardian equivalence theorem. This theorem says that debt-financed spending can't have any effect because people, seeing the higher future taxes that must pay off the debt, will simply save more." -- John H. Cochrane, "How did Paul Krugman get it so Wrong?"
On the other hand:
"Ricardian equivalence was another property of rational expectations monetarism. It was tested, in effect, by the Bush administration, which swung the federal budget into large deficit. The increase in the deficit was not compensated by increased private saving. Instead, American households decreased their savings to basically nothing. This violation of Ricardian equivalence suggests that the transversality condition imposed in intertemporal general equilibrium models has no empirical counterpart. Without such a condition consistency of all decisions is no longer guaranteed in intertemporal models. But bubbles and crashes are admitted." -- Axel Leijonhufvud (2009) "Out of the corridor: Keynes and the crisis", Cambridge Journal of Ecnomics, V. 33: pp. 741-757

Tuesday, September 15, 2009

Special Issues on Global Financial Crisis

Some journals with articles on current problems:

Monday, September 14, 2009

Economists With Ethics

The Association for Integrity and Responsible Leadership in Economics and Associated Professions (AIRLEAP) is "deeply concerned about the issues of integrity and responsible leadership in economics as they relate to economic discourse, economic decision making, and the career development of economists and related professionals."

Thursday, September 10, 2009

One Math, Three Applications

I previously pointed out that the same math that can formalize classical economics is used by Google to find page ranks. Now Stefano Allesina and Mercedes Pascual have found that the Perron-Frobenius theorem also supports the detection of critical species in ecosystems.

Tuesday, September 08, 2009

Only Mainstream Macroeconomists Exist For Krugman

Many have already written about Paul Krugman's article, "How Did Economists Get It So Wrong?" in the September 6 issue of the New York Times Magazine. Krugman himself followed up with blog comments. Brad DeLong has prepublication and postpublication comments, as well as comments on other commentators. I like Colin Danby's take, in comments, on the intolerance of the orthodoxy. Mark Thoma has a comment on Sean Carroll's take. Some commentators, such as Ramanan get it.

In Krugman's article, all macroeconomists are either freshwater or saltwater. Post Keynesian criticisms that apply to both types are not mentioned. Although I am not too familiar with mainstream macro, I can think of three:
  • Both situate their models in logical, not historical time
  • Both assume a representative agent
  • Both assume a single good that functions as both a capital and a consumption good.
These limitations rule out a priori the possibility of some interesting dynamics and perhaps make it difficult to see why agents in the model would want to hold money or even trade with one another.

  • Paul Davidson (1982-83) "Rational Expectations: A Fallacious Foundation for Studying Crucial Decision-Making Processes", Journal of Post Keynesian Economics, V. V, N. 2 (Winter): pp. 182-198
  • Alan P. Kirman (1992) "Whom or What Does the Representative Individual Represent" Journal of Economic Perspectives, V. 6, N. 2 (Spring): pp. 117-136
  • Graham White (2004) "Capital, Distribution and Macroeconomics: 'Core' Beliefs and Theoretical Foundations", Cambridge Journal of Economics, V. 28, N. 4: pp. 527-547

Friday, September 04, 2009

Samuelson’s Revealed Preference: A Failed Research Program

Wong (1978, 2006) grew out of what may have been the last doctorate thesis Joan Robinson supervised. As it is, Wong did not complete his thesis under Robinson's supervision. Luigi Pasinetti and then Geoffrey Harcourt later became Wong's supervisor.

Wong’s study is centered around three publications by Paul Samuelson, in 1938, 1948, and 1950. Samuelson, in 1938, according to Wong, attempted to construct a new theory without any reliance on utility theory or any concept that relies on non-observational phenomena. This theory was intended to be a replacement, not a complement for utility theory.

Samuelson, in 1940, according to Wong, attempted to construct indifference maps from observed consumer choices in a space of price and quantity observations. "The whole theory of consumer's behavior can thus be based upon operationally meaningful foundations in terms of revealed preference." -- Samuelson (1948)

Samuelson, in 1950, according to Wong, was responding to work primarily by Hendrik Houthakker, who showed that ordinal utility theory and revealed preference theory were logically equivalent. Thus, utility theory has the same empirical implications and operational foundations.

Wong interprets the observational equivalence of utility and revealed preference as a defeat for Samuelson's 1938 program. Samuelson, however, asserted this finding was the completion of a victorious research program. And mainstream economists have let him get away with this claim, without ever subjecting it to a critical inquiry.

"I soon realized that [the weak axiom of revealed preference] could carry us almost all the way along the path of providing new foundations for utility theory. But not quite all the way. The problem of integrability, it soon became obvious, could not yield to this weak axiom alone." -- P. A. Samuelson (1950)

  • Paul A. Samuelson (1938) “A Note on the Pure Theory of Consumer’s Behaviour”, Economica, v. 5: pp. 61-71.
  • Paul A. Samuelson (1948) “Consumption Theory in Terms of Revealed Preference”, Economica, v. 15: pp. 243-253.
  • Paul A. Samuelson (1950) “The Problem of Integrability in Utility Theory”, Economica, v. 17: pp. 355-385.
  • Stanley Wong (1978, 2006) Foundations of Paul Samuelson’s Revealed Preference Theory: A Study by the Method of Rational Reconstruction, Revised Edition, Routledge.

Friday, August 28, 2009

On The Road From Mont Pelerin

I have been reading The Road from Mont Pelerin: The Making of the Neoliberal Thought Collective, a collection edited by Philip Mirowski and Dieter Plehwe (Harvard University Press, 2009). One theme I find emergent in this book is the influence of funders (e.g., Harold Luhnow, Jasper Crane) on the redirection of economic thought, without any corresponding empirical evidence.

But I'm not yet ready to offer too many thoughts on this book. Instead I'm interested in the cover photo, reproduced as Figure 1.
Figure 1: Cover Photo
I cannot find photo credits in the book. Presumably, this photo is of attendees at a Mont Pelerin society meeting, maybe the first. Can anybody identify these people? Figure 2 letters them to facilitate referring.
  • F. Ludwig Von Mises
  • G. Friedrich Hayek
Figure 2: Cover Photo with Annotations

Monday, August 24, 2009

Some Issues In Joint Production

1.0 Introduction
Sraffa's work on single product systems is sufficient for demonstrating the incorrectness of neoclassical economics, at least in applications in which equilibrium prices supposedly are ultimately, in some sense, scarcity indices. Sraffa's work on joint production is important in justifying a claim that Sraffa has rediscovered the logic behind the Classical theory of value. An interesting question is whether Sraffa's treatment of joint production holds up to a rigorous theoretical analysis. Christian Bidard, Heinz Kurz & Neri Salvadori, and Bertram Schefold are some economists who have gone into this question in some detail.

An example developed by J. E. Woods (1990: pp. 281-285) illustrates some questions raised by joint production. Unfortunately, I am not sure Woods is correct in his analysis; he constrains all goods to have positive prices in his example. I do not impose this constraint in my treatment of his example.

2.0 Technology
Consider an economy in which two goods, iron and coal, are produced. The managers of firms each know of three Constant-Returns-to-Scale processes for producing these goods (Figure 1). In each process, the inputs need to be available at the start of the year. The inputs are totally used up in these production processes, and the outputs become available at the end of the year. Since each process produces both iron and corn, this is an example of a model of joint production.
TABLE 1: Processes Exhibiting Joint Production
INPUTSProcess IProcess IIaProcess IIb
Labor5 Person-Yrs10 Person-Yrs10 Person-Yrs
Iron18 Tons12 Tons
Coal10 Cwt
Iron48 Tons12 Tons12 Tons
Coal10 Cwt30 Cwt30 Cwt

3.0 Quantity Flows
Suppose the final demand in this economy is for a composite good consisting of an equal amount of iron and coal. Four techniques can be formed from the technology to produce such a commodity. Two processes are used in each of the first two techniques. The Alpha technique consists of Process I and Process IIa operated in the proportions shown in Table 2. Notice that after the outputs are used to replace the inputs, the net output consists of one ton iron and one Cwt. coal, as required.
TABLE 2: Quantity Flows in Alpha Technique
INPUTSProcess IProcess IIa
Labor1/6 Person-Yr2/9 Person-Yr
Iron9/15 Ton4/15 Ton
Iron1 9/15 Tons4/15 Ton
Coal1/3 Cwt2/3 Cwt

The Beta technique consists of Process I and Process IIb used in the proportions shown in Table 2. Here too the net output is one ton iron and one Cwt. coal.
TABLE 3: Quantity Flows in Beta Technique
INPUTSProcess IProcess IIb
Labor1/360 Person-Yr1/108 Person-Yr
Iron3/10 Ton
Coal5/12 Cwt
Iron4/5 Ton1/2 Ton
Coal1/6 Cwt1 1/4 Cwt

If Process I is operated alone at unit level, the net output of the economy is 30 tons iron and 10 cwt. coal. The requirements for use would be satisfied if 20 tons of iron were thrown away - free disposal is assumed. If this technique is adopted, iron is a free good.

The last technique to be considered is the operation of process IIb alone. In this case more coal would be produced net than is needed. If this technique is cost minimizing, coal is a free good. (Notice than the combination of Process IIa and Process IIb would just produce more of coal, a free good. This is not economical.)

4.0 Prices
Since I want to consider cases where either iron or coal is a free good, neither can be chosen as the numeraire in an analysis of prices. Accordingly, suppose a person-year - in other words, labor commanded - is the numeraire.

4.1 The Alpha Technique
The price equations for the Alpha technique show the same rate of profits being obtained in the processes comprising the technique:
18 pI(1 + r) + 5 = 48 pI + 10 pC
12 pI(1 + r) + 10 = 12 pI + 30 pC
where pI is the price of iron in units of person-years per ton, pC is the price of coal in units of person-years per Cwt., and r is the rate of profits. By assumption, workers are paid at the end of the year. If the rate of profits as taken as given, the above system consists of two equations in two unknowns. The solution is:
pI = 5/[6 (15 - 7 r)]
pC = (5 - 2 r)/(15 - 7 r)
An economic restriction is that both prices be non-negative. Thus, the solution only obtains in the following interval for the rate of profits:
0 ≤ r ≤ 15/7

4.2 The Beta Technique
The price system for the Beta technique is:
18 pI(1 + r) + 5 = 48 pI + 10 pC
10 pC(1 + r) + 10 = 12 pI + 30 pC
Its solution is:
pI = -5 r/[6 (r - 1)(3 r - 8)]
pC = (4 - 3 r)/[(r - 1)(3 r - 8)]
Both prices are nonnegative if:
(4/3) ≤ r ≤ (8/3)

4.3 Choice of Technique
First, suppose Process I were operated alone. Since iron would be in excess supply, its price would be zero person-years per ton. Revenues would be equated to costs in Process I if pC were 1/2 person-years per Cwt. But revenues would exceed costs in Process IIa by five person-years when operated at the unit level. Thus, firms would want to adopt Process IIa. Thus, operating Process I alone could not be cost-minimizing. (Since Process IIa alone cannot satisfy final demand, Process IIa could also not be operated alone.)

Second, suppose Process IIb were operated alone. In this case, coal would be a free good, and the price of iron would be 5/6 person-years per ton. For any non-negative rate of profits, revenues would never cover costs in Process IIa. On the other hand, for any rate of profits below approximately 133%, Process I would earn pure economic profits (Figure 1). That is, for rates of profits below this level, Process IIb would never be operated alone.
Figure 1: Profitability of Process I (Process IIb Prices)

Third, suppose prices corresponding to the Alpha technique were ruling. Figure 2 shows the difference in revenues and costs for Process IIb, the one process not in the Alpha technique. As usual in this analysis, costs include interest charges on the value of advanced capital. The Alpha technique is cost-minimizing only for rates of profits between zero and 200%, inclusive.
Figure 2: Profitability of Process IIb (Prices for Alpha Technique)

Last, suppose prices solved the price system for the Beta technique. Figure 3 shows the resulting difference in revenues and costs for process IIa, which lies outside the Beta technique. The Beta technique is cost-minimizing for rates of profits between 133 1/3 percent and 200%.
Figure 3: Profitability of Process IIa (Prices for Beta Technique)

5.0 Conclusions
The above analysis demonstrates that, for rates of profits between 0% and approximately 133%, the Alpha technique is cost-minimizing. For rates of profits above approximately 133%, Process IIb is operated alone and coal is free.

In a comparison of the Alpha and Beta techniques alone (without considering the possibility of operating a single process alone):
  • The Alpha technique would be cost minimizing if the rate of profits were between 0% and 200% and the prices associated with the Alpha technique were ruling.
  • The Beta technique would also be cost minimizing if the rate of profits were between approximately 133% and 200% and the prices associated with the Beta technique were ruling.
  • The Beta technique would be cost minimizing if the rate of profits were between 200% and approximately 214% and the prices associated with the Alpha technique were ruling.
  • The Alpha technique would be cost minimizing if the rate of profits were between 200% and approximately 267% and the prices associated with the Beta technique were ruling.
In short, the cost-minimizing technique would not be unique between the rate of profits of approximately 133% and 200%, if it were not for the possibility of operating Process IIb alone. The cost-minimizing technique would not exist between the rate of profits of 200% and approximately 267%, once again if it were not for the possibility of operating process IIb alone.

This example raises a question: Can examples arise with these sorts of non-uniqueness and non-existence problems, even allowing for the possibility of free goods? This is a theme in some of Christian Bidard's and Bertram Schefold's work. (Bidard amusingly names one of his articles "Is von Neumann Square?") I do not recall their conclusions. I think Bidard comes down negatively on Sraffa, based, I guess, partly on his analysis of joint production.

  • Christian Bidard (2004) Prices, Reproduction, Scarcity, Cambridge University Press
  • Heinz D. Kurz and Neri Salvadori (1995) Theory of Production: A Long-Period Analysis, Cambridge University Press
  • Bertram Schefold (1989) Mr. Sraffa on Joint Production and Other Essays, Unwin-Hyman
  • Bertram Schefold (1997) Normal Prices, Technical Change and Accumulation, Macmillan
  • J. E. Woods (1990) The Production of Commodities: An Introduction to Sraffa, Humanities Press International

Friday, August 14, 2009

Good Timing, Paul

Compare and contrast this:
"Some of us were skeptical. A couple of months after Mr. Obama gave that speech, I warned that his vision of a 'different kind of politics' was a vain hope, that any Democratic who made it to the White House would face 'an unending procession of wild charges and fake scandals, dutifully given credence by major media organizations that somehow can't bring themselves to declare the accusations unequivocally false.'" -- Paul Krugman, "Republican Death Trip", New York Times, 14 August 2009, p. A19 (Emphasis added)
to this:
"The stubborn yet false rumor that President Obama's health care proposal would create government-sponsored 'death panels' to decide which patients were worthy of living seemed to arise from nowhere in recent weeks.

Advanced even this week by Republican stalwarts including ... Sarah Palin and Charles Grssley ..., the nature of the assertion nonetheless seemed reminiscent of the modern-day viral Internet campaigns that dogged Mr. Obama last year, falsely calling him a Muslim and questioning his nationality." -- Jim Rutenberg and Jackie Calmes, "Getting to the Source of the 'Death Panel' Rumor", New York Times, 14 August 2009, Page A1 (Emphasis added)

Tuesday, August 11, 2009

More On Economic Reasoning

All ten of the letters in the 8-14 August issue of The Economist are responses to the critique of academic economics in the 18-24 July issue. My favorite is from Meghnad Desai:
"SIR - When I was a student we studied business cycles, but the topic disappeared with the rise of mathematical equilibrium theorising. The idea that capitalism is an equilibrium system is common among Keynesian and neoclassical economists; they only differ as to whether the equilibrium is at full employment or under employment. The grand synthesis being taught makes the equilibrium stochastic and dynamic, but that is all.

Capitalism is, however, a disequilibrium dynamic stochastic system as Marx, Wicksell, Schumpeter and Hayek have told us over the past two centuries. Richard Goodwin tried his best to present a mathematical theory of such a disequilibrium system. After the crisis we need to revive that tradition if we are not to be surprised by another crisis."
The on-line Lucas Roundtable at The Economist doesn't have any invited contributions from left-leaning non-mainstream economists.

Tuesday, August 04, 2009

Still A Man Hears What He Wants To Hear And Disregards The Rest

Mark Blaug has another paper criticizing Sraffianism. Here's one quotation from it:
"One of the striking features of the Sraffian side of the debate, the victorious side, was their categorical refusal to throw light on the debate by empirical research, insisting along with Sraffa himself that an anomaly such as reswitching is a theoretical flaw, which can only be repaired by discarding the theory in which it occurs. This is a position that has been steadfastly maintained through a half century and has only recently been broken by two Sraffians, namely, Lynn Mainwaring and Ian Steedman (2000)... Despite diligent combing through the literature, I have been unable to find more than one or two pieces of empirical work inspired by the theoretical ideals of Sraffian economics." -- Mark Blaug, "The Trade-Off between Rigor and Relevance: Sraffian Economics as a Case in Point, History of Political Economy, V. 41, N. 2 (2009): 219-247
I still don't see how empirical work is necessary to demonstrate a logical error. But confining myself to work before Mainwaring and Steedman (2000) and work in English, I find more than two: Albin (1975), Prince and Rosser (1985), and Ozanne (1996). Asheim (2008) is based on work written up long ago.

Those works, though, are looking for empirical evidence of Sraffa effects. But a plethora of empirical work is somewhat consistent with Sraffianism. I refer to work following in Leontief's wake. Blaug even acknowledges the relevance of this tradition:
"I have inadverently slipped into the language of Leontief's input-output analysis, which of course is rooted in physiocracy and classical economics, but was later adapted by Leontief himself to the mode of analysis of G[eneral] E[quilibrium] T[heory]" -- Mark Blaug, ibid
I find tendentious the assignment of Leontief to General Equilibrium Theory.

Tuesday, July 28, 2009

Marc Lavoie - Quite Fierce

I think I downloaded Marc Lavoie's paper, "Neoclassical Empirical Evidence: On Employment and Production Laws as Artefact" from some conference proceedings. It's downloadable from his site, but I'm not sure for which recent conference it was presented.

Lavoie summarizes the orthodox response to the Cambridge Capital Controversy and the counterexamples:
  • "Neoclassical authors minimize the capital paradoxes, making an analogy with Giffen goods in microeconomics, which do not question the entire neoclassical edifice;
  • They look for the mathematical conditions that would be required to keep production functions as 'well-behaved', or they claim that this is a simple aggregation problem that can be resolved;
  • They claim that Walrasian general equilibrium theory is impervious to the critique;
  • They claim that they have the faith, or they plead ignorance;
  • Empiricism (It works, therefore it exists)."

And he also mentions how some react to the arguments of such economists as Franklin Fisher and Anwar Shaikh:
"I have discussed some of these issues with a few of my neoclassical colleagues - those that I thought would be most open to dialogue. Amazingly, their response has been to fake that they did not understand the implications of the Shaikh or McCombie papers that I emailed them. The most genuine answers have been that without these elasticity estimates they could not say anything anymore. But they would rather continue making policy proposals based on false information than make no proposition at all. In other words, they would rather be precisely wrong than approximately right."

Tuesday, July 21, 2009

Unsent Letter

Others have already commented on the three articles on the breakdown of macroeconomics and financial economics in the July 18-24 issue of The Economist.
SIR - You write:
"[Macroeconomists'] framework reflected an uneasy truce between the intellectual heirs of Keynes, who accept that economies can fall short of their potential, and purists who hold that supply must always equal demand. The models the epitomise this synthesis ... incorporate imperfections in labour markets ('sticky' wages, for instance, which allow unemployment to rise)..."
But the idea that persistent unemployment is the result of wages sticky downward is a pre-Keynesian idea. Keynes explicitly rejected this explanation of the cause of unemployment:
"...the Classical Theory has been accustomed to rest the supposedly self-adjusting character of the economic system on an assumed fluidity of money-wages; and, when there is rigidity, to lay on this rigidity the blame of maladjustment... My difference from this theory is primarily a difference of analysis." (John Maynard Keynes, The General Theory of Employment, Interest and Money, "Chapter 19. Changes in Money Wages"
Apparently neither saltwater nor freshwater macroeconomists follow Keynes.

Sunday, July 19, 2009

Woodstock Thirtieth Anniversary

They did not hold the 30th anniversary concert at Woodstock. They held it in my backyard.
Crowd for Dave Matthews. Dave Did "Watchtower"

Naked Man and Photographer

The man in the purple shirt is Ken Kesey's
business partner.


What With The Arson, That Didn't Work Out So Well, Did It?

Saturday, July 18, 2009

Now, Judge, I Had Debts No Honest Man Could Pay/The Bank Was Holding My Mortage And They Were Gonna Take My House Away

1.0 Introduction
This example illustrates one aspect of how Sraffa analyzed natural resources. In this case, natural resources consist of land of various qualities or grades. The quantity of each grade is given; more land cannot be produced. Land is not destroyed either. Appropriate production processes yield as much land as a joint output as given as input. So this sort of model does not incorporate a natural resource like oil that is used up in production.

This example demonstrates that owners of less efficient (productive) natural resources can receive a greater rent.

By the way, Sraffa introduces a distinction between basic and non-basic commodities. Lands with positive rent are non-basic, and therefore their rent is a candidate for taxation.

2.0 Technology
This is a simple economy in which only corn is produced. Table 1 shows the available processes that have corn as an output. Each process requires the use of one grade of land, and no more than one process is known for each grade of land. (This is an example of a model of extensive rent.) Suppose this economy has available 150 acres of land of grade I, 162 acres of grade II land, and 210 acres of grade III land.
Table 1: Technology
Labor (Person-Years)2/512/7
Grade I Land (Acres)100
Grade II Land (Acres)03/20
Grade III Land (Acres)001
Corn (Bushels)2/51/64/7
Output (Bushels)111

3.0 Prices
The question to be addressed is what prices and distribution of income are compatible with a long-period position, given the technology. The amount of corn required for net output is a parameter that must be known to answer this question.

3.1 When Only One Grade Of Land Is Cultivated
Suppose the requirements for use for corn in this economy can be satisfied by cultivating any one of the three grades of land. Two grades, and maybe some of the third grade, can lie fallow. So at most 90 bushels are produced each year, after replacinging up the seed corn.

And suppose that the wage is 1/2 bushels per person-year. The wage is paid out at the end of the year. These assumptions are enough to derive the factor-price curves shown in Figure 1. These curves are drawn under the assumption that all grades of land paid no rent.
Figure 2: Factor Price Curves

Since the beta factor-price curve is rightmost (on the outer frontier) at the given wage, all corn is produced on land of the second grade, and this land pays no rent. The wage and the rate of profits must satisfy the following equation:
(1/6)(1 + r) + w = 1
where a bushel corn is the numeraire. For a wage of 1/2 bushels per person-year, the rate of profits is 200%.

Under the given assumptions, the cost of producing a bushel corn on the first grade of land, even if that land were to pay no rent, is 7/5 bushels. Since this cost exceeds the revenues from selling a bushel of land, no capitalist would want to produce on the first grade of land. The reader can check that the cost of producing a bushel corn on the third grade of land also exceeds unity.

3.2 When Two Grades Of Land Are Cultivated
Now suppose the requirements for use are such that two grades of land must be cultivated. The net output of this economy is between 90 and 180 bushels corn. The wage remains 1/2 bushels per person-year. In this case, the first and second grades are cultivated, with the second grade paying rent. The price equations are:
(2/5)(1 + r) + (2/5)w + ρ1 = 1
(1/6)(1 + r) + w + (3/2)ρ2 = 1
ρ1 ρ2 = 0
ρ1, ρ2 ≥ 0
The equations specify that no land can have a negative rent and that at least one grade of land must have a rent of zero. The rate of profits is 100%, when the wage is 1/2 bushels per person-year. Land of grade I pays no rent, and the rent on land of grade II is 1/9 bushels per acre.

The cost of producing a bushel corn on the third grade of land, accounting just for outlays of seed corn and labor, is 9/7 bushels. Capitalists will not want to cultivate the third grade of land, even if it is free.

3.3 When Three Grades Of Land Are Cultivated
Finally, suppose the requirements for use for use require all three grades of land to be cultivated. The price equations are:
(2/5)(1 + r) + (2/5)w + ρ1 = 1
(1/6)(1 + r) + w + (3/2)ρ2 = 1
(4/7)(1 + r) + (2/7)w + ρ3 = 1
ρ1 ρ2, ρ3 = 0
ρ1, ρ2, ρ3 ≥ 0
The rate of profits is 50%, when the wage is 1/2 bushels per person-year. The rent on land of grade I is 1/5 bushels per acre. The rent on grade II land is 1/6 bushels per acre

3.4 Orders Of Efficiency And Rentability
The above analysis has identified a definite order in which different grades of land will be cultivated as greater quantities of output are required to be produced. This is the order of efficiency. In this example, the order of efficiency, from most efficient to least efficient, is: Grade II, Grade I, Grade III.

One can also rank the grades of land from high rent to low rent, when all three grades of land are cultivated and the wage is 1/2 bushels per person-year. The order of rentability, from highest rent to zero rent, is: Grade I, Grade II, Grade III.

The orders of rentability and efficiency differ. It is possible for a less productive, that is, the less efficient, resource to provide its owner with a greater rent than the more efficient resource.

This example is not driven by the existence of switch points.

  • Alberto Quadrio-Curzio, "Rent, Income Distribution, and Orders of Efficiency and Rentability", in Essays on the Theory of Joint Production (Edited by L. L. Pasinetti), Columbia University Press, 1980.