Krishna Bharadwaj, A Sraffian Economist

A web site devoted to freeing Binayak Sen reprints an article from The Telegraph-Calcutta. This article draws a parallel between Sudha Bharadwaj and Binayek Sen.

I don't know anything about B. Sen or S. Bharadwaj. But if Arundathi Roy and Amartya Sen are protesting your arrest, I assume you should be freed. The People's Union for Civil Liberties, at first glance, sounds like a fine organization.

Apparently Sudha Bharadwaj is the daughter of Krishna Bharadwaj. I happen to have read her review of Sraffa's book - or at least the extracts that Harcourt and Laing (1971) reprint. As I recall from somewhere, she took a couple of years to write this review. When given Sraffa's book to review, she felt obligated to reread Adam Smith and David Ricardo. This was a perceptive understanding.

I first became aware of Krishna Bharadwaj's work, though, by stumbling upon her 1989 collection of essays. These are reprinted from such journals as Australian Economic Papers, the Cambridge Journal of Economics, and others. I found these essays quite good. I later read her 1978 lecture and the 1990 conference volume she co-edited with Bertram Schefold. Until the last few years, that conference seems to have been the most thorough assessment of Sraffa's contributions - not that economists such as Pierangelo Garegnani and Paul Samuelson could agree. She also has some applied work which I haven't read.

References

• Krishna Bharadwaj (1963) "Value Through Exogenous Distribution", Economic Weekly (Bombay), 24 August: 1450-1454
• Krishna Bharadwaj (1978) Classical Political Economy and the Rise to Dominance of Supply and Demand Theories, Orient Longman
• Krishna Bharadwaj (1989) Themes in Value and Distribution: Classical Theory Reappraised, Unwin Hyman
• Krishna Bharadwaj and Bertram Schefold (editors) (1990) Essays on Piero Sraffa: Critical Perspectives on the Revival of Classical Theory, Unwin Hyman
• G. C. Harcourt and N. F. Laing (editors) (1971) Capital and Growth, Penguin

Reswitching With Smooth Production Functions

I cite authority:

"Something precious I gained from Robinson's work and that of her colleagues working in the Sraffian tradition. As I have described elsewhere, prior to 1952 when Joan began her last phase of capital research, I operated under an important misapprehension concerning the curvature properties of a general Fisher-von Neumann technology.

What I learned from Joan Robinson was more than she taught. I learned, not that the general differentiable neoclassical model was special and wrong but that a general neoclassical technology does not necessarily involve a higher steady-state output when the interest rate is lower. I had thought that such a property generalized from the simplest one-sector Ramsey-Solow parable to the most general Fisher case. That was a subtle error and, even before the 1960 Sraffa book on input-output, Joan Robinson's 1956 explorations in Accumulation of Capital alerted me to the subtle complexities of general neoclassicism.

These complexities have naught to do with finiteness of the number of alternative activities, and naught to do with the phenomenon in which, to produce a good like steel you need directly or indirectly to use steel itself as an input. In other words, what is wrong and special in the simplest neoclassical or Austrian parables can be completely divorced from the basic critique of marginalism that Sraffa was ultimately aiming at when he began in the 1920s to compose his classic: Sraffa (1960). To drive home this fundamental truth, I shall illustrate with the most general Wicksell-Austrian case that involves time-phasing of labor with no production of any good by means of itself as a raw material.

As in the 1893-1906 works of Knut Wicksell, translated in Wicksell (1934, Volume I), let corn now be producible by combining labor yesterday, labor day-before-yesterday, etc):

Q_t = f(L_t-1, L_t-2, ..., L_t-T) = f(L)                                                     (1)

Q = f(L₁, L₂, ..., L_T) in steady states                                              (2)

    = L₁ f(1, L₂/L₁, ..., L_T/L₁) 1st^o-homogeneous and concave      (3)

    = L₁ (df(L)/dL₁) + ... + L_T (df(L)/dL_T), Euler's theorem            (4)

df/dL_j = f_j(L), d²f/(dL_i dL_j) = f_ij(L) exist for L ≥0                         (5)

f_j > 0, (z₁, ..., z_T)[f_ij(L)](z₁, ..., z_T)' < 0 for z_j ≠ b L_j > 0                (6)

Nothing could be more neoclassical than (1)-(6). If it obtained in the real world, a Sraffian critique could not get off the ground.

Yet it can involve (a) the qualitative phenomena much like 'reswitching', (b) so-called perverse 'Wicksell effects', (c) a locus between steady-state per capita consumption and the interest rate, a(i, c) locus, which is not necessarily monotonically negative once we get away from very low i rates. This cannot happen for the 2-period case where T = 2. But for T ≥ 3, all these 'pathologies' can occur, and there is really nothing pathological about them. No matter how much they occur, the marginal productivity doctrine does directly apply here to the general equilibrium solution of the problem of the distribution of income.

Remarks. What eternal verities do always obtain, even when corners in the technology make derivatives [dQ_j/dL_j, dQ_j/dQ_ij] be somewhat undefined? Always, it remains true:

(a) To go from an initial sub-golden-rule steady state to a maintainable golden-rule steady state of maximal per capita consumption, must involve for society a transient sacrifice of current consumptions ('waiting' or 'abstinence' a la Senior, Böhm, and Fisher!).

(b) For non-joint-product systems, there is a steady-state trade-off frontier between the interest rate and the real-wage (expressed in terms of any good).

This monotone relation between (W/P_j, i) was obscurely glimpsed by Thunen and other classicists and by Wicksell and other neoclassicists. But the factor-price trade-off frontier did not explicitly surface in the modern literature until 1953, as in R. Sheppard (1953), P. Samuelson (1953), and D. Champernowne (1954). One can prove it to be well-behaved for (1)-(3), or any convex-technology case, by modern duality theory. Before Robinson (1956), I wrongly took for granted that a similar monotone-decreasing relation between ( i, Q/(L₁ + ... + L_T) ) must also follow from mere concavity - just as does the relation -d²C_t+1/(dC_t)² = di/dC_t) > 0. But this blythe expectation is simply wrong! I refer readers to my summing up on reswitching: Samuelson (1966).

I realize that there are many economists who tired of Robinson's repeated critiques of capital theory as tedious and sterile naggings. I cannot agree. Beyond the effect of rallying the spirits of economists disliking the market order, these Robinson-Sraffa-Pasinetti-Garegnani contributions deepen our understanding of how a time-phased competitive microsystem works." -- Paul A. Samuelson (1989) "Remembering Joan" in Joan Robinson and Modern Economic Theory (ed. by George R. Feiwel), New York University Press.

(I have changed some of the symbols above.) I've noted before comments from Samuelson in papers that have made claims much the same as above.

Students at Schools With Interesting Economists

E. Roy Weintraub and Edwin Burmeister are two Duke economists I find worth reading. Here are some Duke students:

Duke, Quaterfinals at Ithaca, 18 May 2008

Below are some Notre Dame students, except for the upper left. Thos are Syracuse University students. I did not ask any Notre Dame fans what they thought of their administration's shameful treatment of some of their economists or talk about an on-line petition.

Notre Dame, Quaterfinals at Ithaca, 18 May 2008

I do not have any photos of U-Mass, Amherst, students, although I did go to Syracuse's last home game of the regular season.

Days Late And A Penny Short

I find from Crooked Timber another interesting blog - Nancy Folbre's Care Talk. I don't know how much, if any, of Folbre's work I've read. She is quite prominent, if I understand correctly, as a developer of feminist economics.

Elsewhere

Some feminists have started blogging on economics: Kathy G. and Allison. Kathy G. doesn't seem to draw on Feminist Economics. I don't know about Allison.

I recently stumbled on the blog of an economist at Cambridge, UK.

As I understand it, this blog is from Edward Nell's son. I might as well give a quote from Edward Nell:

"Joan Robinson started the capital theory/production function controversies in the 1950s. After Sraffa's book in 1960 the next decades saw major battles in the journals, battles which resulted in conclusions widely held today: to wit, the technical errors are conceded, but their significance is contested. This has a practical meaning: open any major journal at random today, and there will be marginal products, aggregate production functions, et hoc genus omnia - with no hint that any technical error is involved. The critique is simply ignored. It can't be answered, but it is held to be unimportant.

The neo-Ricardian project initially aimed at reviving the Classical approach. The idea, it seemed was to develop an alternative economics, a science of economic phenomena grounded on different principles...

...The original idea was to move toward a complete reconstruction of economics, on a revived and revised form of the Classical approach, not merely critism of neo-Classical arguments, nor clarification of Classical arguments. The approach would be different: it would be sound theory, but theory based on a realistic account of institutions and history. Furthermore, such analyses could be expected to lead to new, useful, and progressive formulations of policy. That was also the hope of the summer school in Trieste.

What has emerged must be considered disappointing. A Classical 'general equilibrium' theory has been worked out, together with a critique of neo-Classical [economics] - but there has been no development of a new economics. To be sure, there are a few scattered articles on a number of ... topics. But besides the critical work and the development of price theory, the important and widely recognized work has centered on the History of Economic Thought." -- E. J. Nell (1998), The General Theory of Transformational Growth: Keynes After Sraffa, Cambridge University Press

I am aware that I have only here on this blog touched on the potential of Sraffa's work.

One of the seven bloggers here is Tiago Mata.

Tim Lee has a review of Math You Can't Use, a book by Ben Klemen objecting to software patents. Matthew Yglesias's reacts. Some of Matt's commenter's bring up another book, Patent Failure, by Bessen and Meuer. I've found a post from another blog on Matt's post and another reaction from Matt. By the way, when considering the desirability of software patents, one might distinguish between bad patents in an area of technology and the (un)desirability in principle of having patents in an area. As I understand, software patents differ from copyrights in that they impose a burden on developers of doing searches of already established intellectual property, while copyrights don't.

Robert Murphy On Sraffa: In Error

Some discussion with Peter Boettke has inspired me to point out some technical mistakes in Robert Murphy's on-line comments on Sraffa and reswitching.

I begin with Murphy's comments on reswitching. He looks at Samuelson's example in Samuelson's "Summing Up" article. Murphy implicitly suggests that reswitching is only possible in models in which a finite number of techniques are available:

"What Samuelson has done is simply invent a fictitious world in which there are only two ways of producing a particular good... Böhm-Bawerk felt that [his] story was accurate, because at any given time there are more technically efficient but very time-consuming processes 'on the shelf' that are unprofitable at the market rate of interest, but would become profitable at lower rates."

But reswitching is possible when a continuum of techniques lie along the so-called factor price frontier. That is, the possibility of reswitching is consistent with the existence of an uncountably infinite number of techiques. It is also consistent, of course, with the existence of only a countably infinite number and only a finite number of techniques.

Murphy also writes an equally informed comment on Sraffa's book, The Production of Commodities by Means of Commodities. I will adopt Austrian - in fact, Misian - terminology. Sraffa compares prices in Evenly Rotating Economies (EREs) in which the same commodities are produced with the same inputs. Under Sraffa's assumptions in the first part of his book, the construction of the so-called factor price frontier is perfectly valid mathematically. Murphy notes that Sraffa does not model utility-maximization and states that if utility maximization is introduced into the model, the location on the frontier becomes determined uniquely:

"Sraffa's techniques leave no room for the individual members of society to influence the methods of production that end up being used (whether or not there is a surplus), ultimately because there are no individuals in Sraffa's models... However, if we also require that the market rate of interest reflects the subjective premium placed by consumers on present versus future consumption—a feature lacking in Sraffa's aggregate models—then this will eliminate the multiplicity of equilibrium rates of interest."

But Murphy is, again, mathematically incorrect. Multiple equilibrium rates of interest can arise in an ERE model with utility maximization, including intertemporally.

One might look outside a model of an ERE. Murphy suggests he wants to consider models of an approach to an ERE:

"Sraffa's method of determining equilibrium prices in a surplus economy already assumes that the system has settled down at the optimum level of production in all possible lines."

The Arrow-Debreu model of intertemporal equilibrium, despite all its problems, is sufficient for my point here. In such a model of an economy not in an ERE, the equilibrium rate of interest at any point in time for loans of a given length is also not necessarily unique. Not only can multiple equilbrium rates of interest arise, so can a continuum of equilibrium interest rates, if the technology is modeled as discrete.

Why might Murphy be inclined to insist on mathematical error? Consider his statements:

"Sraffa derives results that depict a tradeoff between the real wage and rate of profits. In particular, Sraffa's analysis suggests that in a developed economy, the proportion of the 'surplus' that goes to the workers versus the capitalists is arbitrary, and not at all 'determined' by technological or economic facts... Although he was wrong to condemn interest as an unnecessary and exploitive institution, Sraffa was perfectly correct to criticize the conventional, mainstream justification of the capitalists' income."

But none of these claims, including about exploitation, are made in Sraffa's book.

Contrasting Views On Sraffa's Mathematics

"...Sraffa's prices produce questions, besides whatever else, about the mathematics of his arguments." --S. N. Afriat (2008) "Sraffa's Prices", Sraffa or an Alternative Economics (ed. by G. Chiodi and L. Ditta), Palgrave Macmillan.

Here are two perspectives:

"I think that a very important difference exists between: (i) the process through which a mathematical result is reached, and (ii) a rigorous proof of the result. ... Regarding (i) I mean a sequence of mental objects: examples that appear to contain all of what is essential, graphical tools providing proofs that are only valid for dimensions two or three, incomplete proofs that appear as 'almost' correct, auxiliary constructions that show what is not immediately visible in the problem..."

...We know that all the results contained in Production of Commodities, Part I, can be restated in the language of standard mathematics (matrix theory, eigenvalues, eigenvectors, Perron-Frobenius Theorem, etc.) and rigorously proved. My opinion ... is that Sraffa's presentation is closer to the process that I have indicated by (i) in the Introduction, than to formal proofs. In some cases Sraffa's arguments are defective or insufficient, in others they introduce useless complications." --Marco Lippi (2008) "Some Observations on Sraffa and Mathematical Proofs with an Appendix on Sraffa's Convergence Algorithm", Sraffa or an Alternative Economics (ed. by G. Chiodi and L. Ditta), Palgrave Macmillan.

Lippi's position that Sraffa's mathematics contains defects is strengthed by his demonstration of a bug in Sraffa's algorithm for the construction of the standard commodity.

Is Velupilla in disagreement:

"From a purely mathematical point of view, PCC lacks nothing. The concerns in PCC are the solvability of equations systems and, whenever existence or uniqueness proofs are considered, they are either spelled out in completeness, albeit from a non-formal, non-classical point of view or detailed hints are given, usually in the form of examples, to complete the necessary proofs in required generalities. Pure laziness, inertia and ignorance of alternative traditions in mathematical philosophy have caused untold mischief and created an industry of re-casting and distorting PCC, a work of aesthetic purity and mathematical elegance, into a trivial application, to a large extent, of linear algebra." --Kumaraswamy Velupillai (2008) "Sraffa's Mathematics in Non-Classical Mathematical Modes", Sraffa or an Alternative Economics (ed. by G. Chiodi and L. Ditta), Palgrave Macmillan.

Velupilla is severely critical of the use of Perron-Fobenius theorems in the recasting of Sraffa's theory, when Sraffa essentially gave a constructive proof in demonstrating the existence of the standard commodity.

Firms Run By The Power-Mad

"In a recent biography Eleanor Dulles reports on her experience in a New York hairnet factory circa 1920. 'The owner of the factory never came out there, he just sat in New York and took the money ... The manager was a very sharp type. I told him I could increase production, so I worked out an incentive scheme whereby for a 50 percent increase in production they could make 30 to 40 percent more in wages ... The girls really began to put out. They got very much interested in their work, and the good ones were soon earning 16 dollars and more a week.'

To her astonishment, the manager didn't like it.

'"I'm not going to have those girls thinking they are good," he said. "I'm going to get rid of the good girls. I didn't pay them to get above themselves."'

'He deliberately slowed down supplies and made things awkward for the smarter girls, so they just lost spirit and left.'" -- Harvey Leibenstein (1981) "Microeconomics and X-Efficiency Theory: If There Is No Crisis, There Ought to Be", in The Crisis in Economic Theory (ed. by D. Bell and I. Kristol), Basic Books

Two Problems, One Mathematics (2 of 2)

4.0 Mathematical Notes
4.1 Questions of Existence and Uniqueness
Sections 2 and 3 of the first part present two problems in which the following system of linear equations is derived:

p^T A = p^T

The elements of A are all non-negative, and each row sums to unity. For a non-trivial solution to exist, unity must be an eigenvalue of A. In a physically-meaningful solution, a corresponding left-hand eigenvector must have non-negative entries, with at least some being strictly positive. Furthermore, we would like the solution to be unique, up to a multiple. (In the economics case, multiplying prices by a constant corresponds to a change in the numeraire.) As a matter of fact, the problems as stated do not yet guarantee uniqueness.

It is easy to show that unity is an eigenvalue for right-hand eigenvectors of A. Let e be the n-element column vector where all elements are unity. Since the rows of A all add up to unity, the following equation must hold:

A e = e

So unity is an eigenvalue of A. (This proof relies on the property that the set of eigenvalues for left-hand eigenvectors of A is the same as the set of eigenvalues for right-hand eigenvectors of A.) Non-negativity and uniqueness, when it obtains are less obvious.

4.2 Irreducible Matrices
The left-hand eigenvector P^T corresponding to the eigenvalue unity contains all positive elements if A is irreducible. Furthermore, if A is irreducible, the left-hand eigenvector P^T is unique, up to a multiple. A matrix is irreducible, obviously, if it is not reducible. To explain this, I need to define what it means for a matrix to be reducible.

Suppose A is transformed by interchanging a pair of rows and then interchanging the corresponding columns. Any permutation of rows and columns can be performed by repeating this operation for an appropriate sequence of pairs of row and column indices. In the economics case, such a sequence of operations corresponds to selecting a different ordering of the industries in which to express A. In the case of page ranks, such a sequence consists in taking a different ordering for the (unranked) pages. In both cases, the ordering is arbitrary, so no problem arises here.

The non-negative matrix A is reducible if there exists such a sequence of operations that transform A into the block structure form:

A1,1	A1,2
0	A2,2

where A_1,1 is a square non-negative irreducible matrix.

I think the meaning of reducibility in the two problems is suggested under the special case where:

• All the elements of A_1,2 are zero, and
• A_2,2 is irreducible (as well as A_1,1)

The economics problem would then correspond to two non-trading islands, each in a self-replacing state with no surplus. The web pages would consist of two islands of web pages, in which links can be used to get from any one page on an island to any other page on that island, but with no path between these islands of pages.

Unity would be a repeated eigenvalue for a reducible A. One solution vector P^T has strictly positive prices for the industries corresponding to A_1,1 and zero prices for the remaining industries. The other solution has zero prices for the industries corresponding to A_1,1 and strictly positive prices corresponding to industries for A_2,2. It seems reasonable to me to assume in the economics model one is considering a single economy. I don't see why in the page rank case, some set of pages cannot be partially isolated in some sense from the remaining pages. A page ranking algorithm needs to address this possibility.

I might as well mention a condition for an interesting generalization of the economics problem. Let A be a non-negative, reducible matrix with no row sums that exceed unity. Suppose the maximum eigenvalue of A_1,1 exceeds the maximum eigenvalue of A_2,2. Then A is a Sraffa matrix. I'm not sure if the definition of a Sraffa matrix requires some of the elements of A_1,2 to be non-negative so that this input-output matrix hangs together to describe a single economy. Some such condition makes sense to me for an analysis of an economy with a surplus.

4.3 Perron-Frobenius Theorems
I state a theorem, or rather, a combination of eight theorems:

Theorem: Let A be an irreducible non-negative nxn matrix. Then:

1. λ_m, the maximum eigenvalue of the matrix A is bounded below by the minimimum row-sum of A and is bounded above by the maximum row-sum of A.
2. The maximum eigenvalue of A is a continuous, increasing function of the elements of A.
3. Let μ = 1/ν be strictly positive. If μ > λ_m, then all the elements of the matrices (μ I - A)^-1 and (I - ν A)^-1 are strictly positive.
4. Any eigenvalue α of A is bounded above in modulus by the maximum eigenvalue of A:

|α| ≤ λ_m

5. The maximum eigenvalue of A is associated with a left-hand eigenvector p^T whose elements are strictly positive:

p^T A = λ_m p^T

p_i > 0, for i = 1, 2, ..., n,

6. The maximum eigenvalue of A is associated with a right-hand eigenvector q whose elements are strictly positive:

A q = λ_m q

q_i > 0, for i = 1, 2, ..., n,

7. To each eigenvalue α of A different from the maximum eigenvalue λ_m there corresponds a non-zero left-hand eigenvector which has at least one negative component.
8. To each eigenvalue α of A different from the maximum eigenvalue λ_m there corresponds a non-zero right-hand eigenvector which has at least one negative component.

I deliberately included more Perron-Frobenius theorems above than I need for this problem. Perron-Forbenius theorems of a slightly different form have also been stated for reducible matrices.

Anyways, from the first condition, one sees that unity is the maximum eigenvalue for an irreducible A in both the economics and page rank problems. From the fifth conditon, it follows that there exists a set of strictly positive prices, in the economics case, or of strictly positive page ranks in the other case. And by the seventh condition, I guess, this is an unique solution (up to a multiple of the eigenvector).

5.0 References

• Kurt Bryan and Tanya Leise, "The $25,000,000,000 Eigenvector: The Linear Algebra Behind Google"
• Luigi L. Pasinetti (1977) Lectures on the Theory of Production, Columbia University Press
• Piero Sraffa (1960) Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory, Cambridge University Press

Two Problems, One Mathematics (1 of 2)

"Besicovitch insists that I publish; the fact that I was able to forsee interesting mathematical results shows that there must be be something in the theory." -- Piero Sraffa (Diary entry, 31 May 1958)

1.0 Introduction
In this post, I derive the same equation for two completely different problems. One is an economics model. The other is a simplified presentation of how Google might automatically calculate page ranks to determine the order in which web pages are presented to a user on completion of his search. I could have complicated my exposition by considering a third problem: the steady state probability distribution in a Markov chain.

2.0 Prices for Simple Reproduction
Consider an economy in which n commodities are produced. Each commodity is produced in a process in which it is the only output. In other words, no joint production, such as of wool and mutton, occurs in this economy. n processes are in use, each producing one of the n commodities, and all commodities are produced by one of these processes. Each production process requires a year to complete and uses up all its inputs.

Let a_i,j denote the quantity of the ith commodity used in the production of the jth commodity. Quantities are measured in normalized units, such that the output of each process is one unit of the respective commodity. The nxn matrix A is the Leontief input-output matrix of interindustry quantity flows for this economy. Each element of A is non-negative.

Assume that this economy is undergoing simple reproduction. That is, the output of each process is exactly equal to the total inputs of that commodity used across all processes. (If it helps, one might think of the inputs to each process as including the commodities consumed by the workers operating that process. Labor inputs are not shown in the representation of this economy being considered here.) Anyways, this assumption implies that the sum for each row in A is unity.

Suppose each process is operated by a separate firm. The firm own ats the end of each year a single (normalized) unit of a single commodity. For the firm to continue in operation, it must trade this commodity for an appropriate amount of each of its inputs in all-around markets. Let p^T denote the row vector of the prices in these markets. The condition that the economy continue in operation implies the following equation for prices:

p^T A = p^T

This characterization of prices is a non-neoclassical idea. Markets have not been modeled here as including any sort of maximization process. Nor have these prices been presented as a (stable?) limit point of some sort of dynamic process. Sraffa describes these prices as follows:

"There is a unique set of exchange-values which if adopted by the market restores the original distribution of the products and makes it possible for the process to be repeated; such values spring directly from the methods of production." -- P. Sraffa (1960)

3.0 Google Page Ranks
I now consider a re-definition of all of my symbols. Suppose n web pages have been identified, perhaps by a web-crawler. We want to rank these pages in some way.

These web pages contain links, including to one another. In ranking them, perhaps a page in which a high proportion of the links on other pages goes to that page should have a high rank. But ratios of the proportion of links on other pages that go to that page should be weighted by the ranks of those other pages. These ideas can be formalized.

Let m_i,j be the number of links on the ith web page to the jth web page, for i unequal to j. Let m_i,i be zero. Let m_i be the total number of links on the ith page, excluding links to itself and to pages outside the pages being ranked.

a_i,j = m_i,j/m_i, i = 1, 2, ..., n; j = 1, 2, ..., n

I have now defined a nxn matrix A, where each element is the proportion of the links on a page within a web that go to another specified page in that web. Each element in A is non-negative, and each row adds up to unity. Also, the principal diagonal of A is zero, although that property is not used in the following mathematics.

Let p^T denote the row vector of page ranks. Page ranks satisfy the following system of equations:

p^T A = p^T

In the next part, I consider conditions under which a solution exists and is unique.

5.0 References

• Kurt Bryan and Tanya Leise, "The $25,000,000,000 Eigenvector: The Linear Algebra Behind Google"
• Piero Sraffa (1960) Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory, Cambridge University Press

Letters From Soros

Last month, I noted resemblances between Soros' concept of "reflexivity" and Davidson's use of non-ergodicity to formalize the notion of a model economy set in historical time. Davidson drew this point to Soros' attention over a decade ago. Soros has commented on this resemblance.

The following letter has an Open Society Institute letterhead:

February 28, 1997

Professor Paul Davidson
Holly Chair of Excellence in Political Economy
The University of Tennessee Knoxville
College of Business Administration
Department of Economics
Stokely Management Center
Knoxville, Tennessee 37996-0550

Dear Professor Davidson,

Thank you for sending me your book Economics for a Civilized Society. I found your comments on Samuelson's ergodic hypothesis very pertinent.

Yours Sincerely,

George Soros

From the 15-21 March 1997 issue of The Economist:

Sir - In "Palindrome repents" (January 25th) you accuse me of ignorance of economic theory. In particular, you say that my "claim that economics is inherently flawed on some deep epistemological level is just embarrassing." Is it?

Economics aspires to the status of a hard science. Specifically, it seeks to establish universally valid laws similar to 19th-century physics. For this purpose it relies on the concept of equilibrium, similar to the resting place of the pendulum, which is the same irrespective of any temporary perturbation. Paul Samuelson, an economist, called this the "ergodic hypothesis" and considered it indispensable to making economics a hard science.

The trouble is that economics cannot be made into a hard science, because of the reflexive interaction between the participants' thinking and the actual state of affairs. The interaction does not have a determinate outcome, because the outcome is contingent on the participants' expectations, and the participants' decisions do not merely passively discount the future but also actively help to shape it. There is a two-way feedback mechanism that does not lead to a predetermined resting place, but keeps a historical process in motion. Economic theory can protect the false analogy with 19th-century physics only by eliminating reflexivity. It does so by assuming demand and supply as independently given. The result is an axiomatic system that has little relevance to the real world.

You are correct to claim that, in practice, economists have learnt this, in order to deal with the real world. Alan Greenspan's recent Humphrey-Hawkins testimony is a brilliant exercise in reflexivity. But the theory has never been discarded and it serves as the scientific underpinning for the prevailing belief in the magic of the marketplace.

You are also right to claim that markets do not reign supreme; but you cannot deny that there is a powerful body of opinion that passionately believes that they should. You are plain wrong in asserting that I do not know the "big difference" between laisser-faire and totalitarian ideologies. I stated it explicitly in my Atlantic Monthly article and have been guided by it in my philanthropic activities. I can tolerate personal attacks but I must object when they are used to obfuscate valid arguments.

New York
George Soros

Will Notre Dame Be Serious In Teaching Economics?

Apparently some members of the Department of Economics and Policy Studies would still like to teach classes and hire colleagues. If Notre Dame is serious about educating their students, shouldn't they be taught of the existence of the full range of views on economics? After all Notre Dame has some excellent scholars, including some great historians of economics. (I'm not sure that Esther-Mirjam Sent is still at Notre Dame.)

An on-line petition has been put up in support of these wild ideas. (I haven't yet signed it.)

Hat tip to shagan at daily Kos.

Update: I have now signed the petition. Christopher Hayes comments.