Welcome

I study economics as a hobby. My interests lie in Post Keynesianism, (Old) Institutionalism, and related paradigms. These seem to me to be approaches for understanding actually existing economies.

The emphasis on this blog, however, is mainly critical of neoclassical and mainstream economics. I have been alternating numerical counter-examples with less mathematical posts. In any case, I have been documenting demonstrations of errors in mainstream economics. My chief inspiration here is the Cambridge-Italian economist Piero Sraffa.

In general, this blog is abstract, and I think I steer clear of commenting on practical politics of the day.

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.