Wednesday, January 01, 2025


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.

I've also started posting recipes for my own purposes. When I just follow a recipe in a cookbook, I'll only post a reminder that I like the recipe.

Comments Policy: I'm quite lax on enforcing any comments policy. I prefer those who post as anonymous (that is, without logging in) to sign their posts at least with a pseudonym. This will make conversations easier to conduct.

Thursday, August 11, 2022

Nonsense Taught At MIT

First Lecture For MIT Microeconomics

I associate Jonathan Gruber with Obamacare. I think the Affordable Care Act is totally insufficient and a great advance. If politicians hire you to model the effects of some policy change, might you want to use, more or less, the most widely accepted techniques? I am also appreciative that I can watch this.

When you are teaching, should you present claims in the most romantic way possible?

"That is why I can teach you the entire field of microeconomics, which is really sort of - macro is kind of a fun application - micro is really economics." (around 9:20)

Thinking of (micro)economics as a matter of constrained optimization is only one approach. I like the idea of investigating the conditions needed for a capitalist economy to reproduce itself. This is mesoeconomics, I guess, but should be mentioned in an honest class on microecnomics.

From Thomas Kuhn, I know history of a subject is often widely distorted in introductory courses. Is this justification for spouting nonsense?

Adam Smith did not have a supply and demand model, that is, of an equilibrium price formed by the intersection of a supply curve and a demand curve (balderdash after about 11:23). Mashall's scissors certainly do not appear in Adam Smith's Wealth of Nations. Maybe Gruber should note the difference between market prices and natural prices. The model Gruber's teaches is known to be incoherent nonsense, not derivable from basic first principles.

Can one coherently talk about a value-free postive economics? I guess saying that a distinction exists between positive and normative economics does not say that positive economics is value-free. But it certainly suggests that. What Gruber presents (after 34:30) for examples is enlightening, albeit not necessarily in the way that he intends. Do some teachers of introductory courses talk about Schumpeter's "vision"?

If economics is a science, why do this preaching after 26:30? By the way, do the Seninelese have a capitalist economy? Or do they practice Stalinist central planning? How about the society envisioned by the P.O.U.M. in Barcelona during the Spanish Civil War?

Sunday, August 07, 2022

Correspondence Between Rudiger Soltwedel And Piero Sraffa

This is C/294 in the Sraffa archives. Rudiger Soltwedel had his own letterhead.

D 66 Saarbrucken 3, 28. Febr. 1968
Waldhausweg 7
Evangelisches Studentenheim

Professor Piero Sraffa
Trinity College

Dear Sir,

I am student of economics at the University of Saarbrucken and I just began my finals work for my diploma.

The topic of this study that Prof. E. Schmen formulated is your essay and its title is exactly that of your book: ‘Sraffa’s production of commodities by means of commodities’.

My task is to state the intention of your book and to explain its relation to input-output analysis.

After looking around in literature I only found three reviews (AER: Reder; Ec. Journ.: Harrod; Jorn. Of Pol. Econ.: Quandt; all 1961) but nothing beyond that.

I would be very indebted to you if you could give me some hints of literature directly concerned with your book or with its subject.

At the moment, I think the aim of your study not to be a theory of distribution or a development of input-output analysis, but rather a theory of price-determination in input-output models, given the physical amount of the surplus, economy in equilibrium and infinite elasticity of factor supply. The outcome is an antithesis to what Dorfman/Samuelson/Solow said about relative prices in the Leontief-model: "... in a Leontief-technology relative prices can’t change". (Lin. Programming …, p. 224) in saying that they have to change with changes in distribution of the surplus, And, finally, the profitability of distinct methods of production is dependent on the distribution of the surplus to wages or profits respectively.

This is a bird-eye look on your essay and it is not equivalent to a complete understanding of it. In particular it is the chapter V that charges my brains with its argumentation of extreme density.

I hope that you are willing to excuse my attack on the ‘pater spiritorum’ and would be very thankful for some advice on your part.

Yours respectfully,
Rudiger Soltwedel

Underlines are presumably Sraffa's. "in equilibrium" and "elasticity of factor supply" have underlines in squiggly lines, while the others are solid lines.

Trinity College

Dear Mr. Soltwedel,

Thank you for your letter. I shall try to help you as far as I can in a short letter. As regard my aims, I have kept them in the background in the hope that the constructions offered might be of use to others, who have different standpoints. I have given hints in the Preface and in Appendix IV. The reviews you have are not very helpful. Reder, in particular, is a string of misunderstandings. A good review is that of Peter Newman, in Schweitrerische Zeitschrift fur Volkswirtschaft u. Statistik, No. 1 of 1962, p. 58-75. I disagree with many of his points & had some correspondence with him; we came only to partial agreement, but his review is a good piece of work. There were also good reviews in the Economic Record (Australia, Sept. 1964, p. 442 ff. by Harcourt and Massaro) and in the Economic Weekly (Indian, 24 Aug. 1963, by Krishna R. Bharadwaj). By the way, I replied to Harrod in the June 1962 number of the Economic Journal (p. 477-9).

As regard your own your own interpretation, I must say frankly that you have gone astray the moment you speak of "equilibrium" or of "elasticity of factor supply": all the quantities considered are what can be observed by taking a photograph. There are no rates of change, etc. This point of view was that of the classical economists (e.g. Ricardo) whereas supply & demand curves were introduced in the middle of the 19th century. Economists are now obsessed with them and cannot think without them. My chapter V, which gives you such a headache, could be understood as an attempt to solve a problem set out by Ricardo, & which I described in my Introduction (sections IV & V) of Vol. I of the Works of Ricardo, 1951.

With good wishes for your work,

Yours sincerely
Piero Sraffa

Any errors in journal names, numbers, pages are presumably from my transcription.

66 Saarbrucken 3, 12. ??. 1968
Waldhausweg 7
Evangelisches Studentenheim

Dear Sir,

I thank you very much for your kind reply to my letter.

There was good progress in my work based on your remarks and on the reviews mentioned, in particular the mathematical proof of some propositions in the work of Newman was of great help.

But there is a point in nearly all reviews I don’t agree with and that receives illumination by your book: the claim of the rates of profits being the same in all industries is interpreted as a condition of long run competitive equilibrium prices. Now the structure of your economy is far away from ??determined by competition that this approach does not fit the problem. It looks like a challenge consequent upon a distinct notion of justice in distribution (that could, however, be attained through perfect competition). Unfortunately, your book provides no explanation.

I hope it not to be too unconscionable asking for another explanation.

Yours sincerely,
Rudiger Soltwedel

Sraffa has handwritten “given up” on the top of this letter.

Friday, August 05, 2022

1975 Letter From Krishna Bharadwaj To Piero Sraffa

This letter is an item removed from printed books in Sraffa's library. It is labeled Sraffa I/38 in the archives where I stumbled into it.

15th Oct, 75

Centre for Economic Studies,

Nehru University,

New Delhi 57

Dear Piero Sraffa,

How are you? A lot of things have happened since my return in July to Delhi. Personally, my health was not too good for some time but has now stabilised somewhat. I had considerable teaching load this term and have had to devote a lot of time to preparation of lectures etc. I am now writing up a part of my lectures material - mainly on classical theories of value and distribution. My intention is to focus on conceptual development and the shift to the supply and demand approach and the implications of such a methodological shift. What I intend to do is mainly to provide the background to interpret your book as a return to the classical theory, to discuss the propositions developed in the book and draw out explicitly the implications. I am intending to make it a reference book, mainly for students. As I have been lecturing on this for the last three years, I should suppose I should be able to write up the first draft not too late and look forward to discussing it with you.

I have done some work on the tenurial conditions in some parts of India based on a student under my guidance. That study has received a favourable reaction.

The books which you gifted me - Wicksteed, Schumpeter, Meek - have proved very helpful.

I hope you are keeping health. Sudha remembers you. She is now very much interested in mathematics and science and has done very well in these subjects at school. She seems to have developed a genuine interest in these subjects.

With regards,

Yours as ever,


Bharadwaj is looking forward to the Romesh Chunder Dutt Lectures on Political Economy, in 1976. Was the setting the Centre for Social Sciences, Calcutta. They were published in 1986. I do not know much of her study of peasants and Indian agriculture.

  • Krishna Bharadwaj. 1986. Classical Political Economy and Rise to Dominance of Supply and Demand Theories. University Press (India) Ltd.

Friday, July 29, 2022

On The Emergence of Multiple Cost-Minimizing Techniques

Figure 1: Wage Curves and Rent for an Example of Intensive Rent

The analysis of the choice of technique has above always been based on the construction of a wage-rate of profits frontier. Given a technology in which requirements for use can be satisfied, prices of production for an eligible technique are uniquely determined by the given rate of profits. If the rate of profits is in a range where such prices are non-negative for at least one technique, one of the techniques is uniquely cost-minimizing, except at switch points. This property does not necessarily hold in models of general joint production. The first subsection of the first non-introductory chapter on joint production in Bidard (2004) has the title "Not amused". An examination of local perturbations in an example of intensive rent illustrates surprising possibilities.

Table 1 presents coefficients of production, in which an example from D'Agata (1983) has been extended to include structural economic dynamics. Only one type of land exists, and three processes are known for producing corn on it. The scarcity of land is shown by the possibility of two corn-producing processes being operated side-by-side in the cost-minimizing technique.

Table 1: The Coefficients of Production
Labor111(11/5) e1-σ te1-φ t
Land001 e1-σ te1-φ t
Iron001/10 (1/10) e1-σ t(1/10) e1-φ t
Steel002/5 (1/10) e1-σ t(1/10) e1-φ t
Corn1/103/51/10 (3/10) e1-σ t(2/5) e1-φ t

Following D'Agata, assume that one hundred acres of land are available and that net output consists of 90 tons iron, 60 tons steel, and 19 bushels corn. The net output is also the numeraire. All three commodities must be produced for any composition of net output. Table 2 lists the available techniques. Only Alpha, Delta, and Epsilon are feasible for the parameter ranges considered. Not all land is farmed and only one corn-producing process is operated under Alpha. Two corn-producing processes are operated together under Delta and Epsilon.

Table 2: Techniques
AlphaI, II, III
BetaI, II, IV
GammaI, II, V
DeltaI, II, III, IV
EpsilonI, II, III, V
ZetaI, II, IV, V

Figure 1 shows the wage curves for feasible techniques at a selected parametrization. I take the wage curve for a technique to be defined only for non-negative rates of profits at which the wage, rent per acre, and the prices of produced commodities are non-negative. The wage is negative for Delta for rates of profits below that at the switch point, and rent is negative for rates of profits greater than that at the switch point. Rent is negative for Epsilon for rates of profits less than at the switch point, and the wage is negative for greater rates of profits. Thus, the switch point is the only point on the wage curves for Delta and Epsilon. The switch point is a fluke in two ways. It is a switch point for three techniques, not two. And it is on the axis for the rate of profits.

Figure 2 shows a partition of the parameter space around this fluke case. An intersection of three wage curves over the axis for the rate of profits is a combination of three pairs of wage curves intersecting over the axis for the rate of profits. These three fluke cases are the partitions between regions 1 and 2, regions 1 and 3, and regions 3 and 4. The partition between regions 2 and 5 is associated with the fluke case of three wage curves intersecting at a non-negative rate of profits. The partition between regions 4 and 5 illustrates a fluke switch point specific to models of rent.

Figure 2: A Part of Parameter Space

Regions 2, 4, and 5 illustrate the possible non-uniqueness and non-existence of a cost-minimizing technique. For concreteness, consider the point in region 4 with the wage curves and variation in rent per acre illustrated in Figure 3. For rates of profits up to the first switch point, Alpha is cost-minimizing. Epsilon is cost-minimizing between the switch points, and Delta is also cost-minimizing for high rates of profits in this range. Beyond the second switch point, no technique is cost-minimizing. Whether or not land is scarce depends on the distribution of income.

Figure 3: Wage Curves and Rent for Region 4

How can one determine which techniques are cost-minimizing for a given rate of profits? Given the technique and the rate of profits, the costs of the capital goods, the rent on land, and wages can be summed for a unit level for each process. Iron, steel, and corn inputs incur the going rate of profits in this sum. The difference between the revenues and this sum is the extra profits obtained in operating a process. By definition, no process comprising the technique yields extra profits. The technique is cost-minimizing if extra profits cannot be obtained by operating any other process.

For the parameters illustrated in Figure 3, extra profits are obtained by operating process IV or V at Alpha prices for a rate of profits greater than that at the first switch point. Alpha is only cost minimizing at a lower rate of profits. Figure 4 depicts the extra profits available from each corn-producing process at Delta and Epsilon prices. The range of rates of profits in which each technique is cost-minimizing is indicated, and these ranges overlap. For some rates of profits greater than the rate of profits at the second switch point, prices of production indicate that Epsilon should be adopted when prices of production for Delta prevail and that Delta should be adopted when prices of production for Epsilon prevail. This circuit is a manifestation of the non-existence of a cost-minimizing technique.

Figure 4: Extra Profits for the Delta and Epsilon Techniques

The cost-minimizing technique is not unique for some rates of profits in regions 2 and 5, as well as in region 4. Even though prices of production are positive for some feasible techniques, no cost-minimizing technique may exist. Table 3 summarizes how cost-minimizing techniques vary with the rate of profits in each of these five numbered regions.

Table 3: Properties of Regions in the Parameter Space
10 ≤ rrmax, αAlphaNo rent is paid.
20 ≤ rrmin, δAlphaNo rent is paid.
rmin, δrr1Alpha, DeltaThe wage curve for Delta slopes up, and rent decreases with the rate of profits.
30 ≤ rr1AlphaNo rent is paid.
r1rrmax, εEpsilonRent increases with the rate of profits.
40 ≤ rr1AlphaNo rent is paid.
r1rrmin, δEpsilonRent increases with the rate of profits.
rmin, δrr2Delta, EpsilonThe wage curve for Delta slopes up. Rent decreases with the rate of profits for Delta and increases for Epsilon.
50 ≤ rrmin, δAlphaNo rent is paid.
rmin, δrr1Alpha, DeltaThe wage curve for Delta slopes up, and rent decreases with the rate of profits.
r1rr2Delta, EpsilonThe wage curve for Delta slopes up. Rent decreases with the rate of profits for Delta and increases for Epsilon.

Whether or not land obtains a rent can depend on the distribution of income. For a low-enough rate of profits in regions 2, 3, 4, and 5, the first three processes are operated. Iron, steel, and corn are each produced with one process, and land obtains no rent. For a higher rate of profits, the Delta or Epsilon technique can be cost-minimizing. Corn is produced by two processes, and scarce land obtains a rent. Even if the requirements for use can feasibly be satisfied with some land not farmed, the cost-minimizing technique may be such that two processes are operated side-by-side on land, with no land lying fallow.

The reverse substitution of labor, reswitching, capital reversing, the association of the truncation of the economic life of machine with a more capital-intensive technique, a divergence between the order of fertility and the order of rentability, the variation in the existence of rent with the rate of profits or the wage, and the non-uniqueness and the non-existence of a cost-minimizing technique are not fluke cases. These posts demonstrate this conclusion by contrasting these possibilities with genuine fluke cases.

Friday, July 22, 2022

An Extensive Rent Example

Figure 1: Wage Curves and Rent for an Example of Extensive Rent

The analysis of the choice of technique in models of extensive rent can be based on the construction of wage curves, even though the outer envelope does not represent the cost-minimizing technique. The orders of fertility and rentability are emphasized here. The order of fertility is the order in which different qualities of land are introduced into production as requirements for use expand. The order of rentability specifies the sequence of different qualities of lands from high rent per acre to low rent per acre. Both orders may vary with the distribution of income. Table 1 presents coefficients of production for an example. Technical progress is assumed to reduce coefficients of production in each of the corn-producing processes, at different rates.

Table 1: The Coefficients of Production
InputIron IndustryCorn Industry
Labor1(5191/5770)e1-φ t(305/494) e1-θ t(3/2)e1-σ t
Type 1 Land0e1-φ t00
Type 2 Land00e1-θ t0
Type 3 Land000e1-σ t
Iron9/20(1/40)e1-φ t(3/1976) e1-θ t(3/20)e1-σ t
Corn2(1/10)e1-φ t(229/494)e1-θ t(1/3)e1-σ t

The quantity of produced corn is constrained by the available quantities of each type of land. Suppose endowments include one hundred acres of each type of land, a stationary state prevails, and net output is somewhere between 322 and 444 bushels of corn. Then all three types of land must be farmed with the parameters specified in Figure 1. One type will be only partially farmed. The iron-producing process must be operated in each of the three economically viable techniques sustaining such a stationary state. Table 2 describes which type of lands are fully cultivated and which type of land is left partially farrow in each of the Alpha, Beta, and Gamma techniques.

Table 2:
Type 1Type 2Type 3
AlphaFully farmedFully farmedPartially farmed
BetaPartially farmedFully farmedFully farmed
GammaFully farmedPartially farmedFully farmed

For a given technique, the rent on a type of land only partially farmed is zero since it is not scarce. The wage curves in the left pane in Figure 1 are constructed from the price equations provided by the iron-producing process and the corn-producing process for the land that pays no rent in each technique. The choice of technique depends on both income distribution and requirements for use (Quadrio-Curzio 1980). Suppose the rate of profits is taken as given. Then the r-order of efficiency or fertility is the order of the wage curves downwards, until requirements for use are satisfied. Since all three types of land must be somewhat cultivated in the example, the wage frontier is the inner envelope of the wage curves. For the illustrated parameters, Alpha is cost-minimizing, and the order of fertility between the switch points is Type 1, Type 2, and Type 3 lands.

One can calculate the cost of capital goods at the given rate of profits and the cost of labor inputs for corn-producing processes on each of Type 1 and Type 2 lands. Since coefficients of production are specified per bushel corn produced, the revenues from each of these processes, at a unit level, are the same as the process operated on Type 1 land. Rent is the difference between revenues and non-land costs on Type 1 and Type 2 lands. Rent per acre is plotted in the right pane for Figure 1. The order of rentability is the order of lands by rent per acres. The order of rentability is the same as the order of fertility between switch points for the given parameters.

The two fluke switch points in Figure 5 do not lie on the wage frontier. The maximum rate of profits for the wage curve for Alpha is the maximum rate of profits for this example. One of the switch point for the wage curves for the Beta and Gamma techniques is at this maximum rate of profits. As seen in Figure 2, this is another edge case, a fluke that arises in models of extensive rent. By the way, at other parameter ranges the curves for rent as a function of the rate of profits in the right pane in Figure 1 can intersect. The order of rentability can vary with distribution, and fluke cases in which these curves intersect at a maximum rate of profits or a rate of profits of zero can arise.

Figure 2: The Parameter Space

Figure 2 illustrates a region of the parameter space around this fluke case. To the northwest, one switch point between the wage curves for Beta and Gamma has vanished over the wage axis, and the other is at a rate of profits exceeding the maximum rate of profits for Alpha. The order of fertility matches the order of rentability. The southwest is of a reswitching example. For such small perturbations, the order of rentability does not change in this example. Thus, the order of fertility matches the order of rentability only at intermediate rates of profits with reswitching here. The northeast and southwest also illustrate parameters for which the order of fertility varies with the rate of profits. The order of fertility varies from the order of rentability at one or the other extreme, as indicated.

The reverse substitution of labor, reswitching, capital reversing, the association of the truncation of the economic life of machine with a more capital-intensive technique, and a divergence between the order of fertility and the order of rentability are not fluke cases. These posts demonstrate this conclusion by contrasting these possibilities with genuine fluke cases.

Saturday, July 16, 2022

Fixed Capital And The Emergence Of Reswitching

Figure 1: A Wage Frontier With A Fluke Switch Point

A fluke example with fixed capital illustrates the emergence of the reswitching of techniques. Table 1 presents coefficients of production in a perturbation of an example from Schefold (1980). With the first process, workers, under the direction of mangers of firms, manufacture new machines. The remaining two processes are used to produce corn. The last process requires an input of an old machine, which is jointly produced with corn by the second process. Corn is both a consumption good and a capital good, insofar as it is an input into all three processes. Technology improves in this example, as usual, with an exponential decline in specified coefficients of production.

Table 1: The Coefficients of Production
InputMachine IndustryCorn Industry
One ProcessAnother Process
Labor(1/10)e1-σ t(43/40) e1-φ te1-φ t
Corn(1/16)e1-σ t(1/16) e1-φ t(1/4)e1-φ t
New Machines010
Old Machines001
New Machines100
Old Machines010

The choice of technique corresponds here to the choice of the economic life of the machine. This lifetime is truncated to one year for the Alpha technique, while the machine is operated for its full physical life of two years under the Beta technique. In a pure fixed capital model, the choice of technique can be analyzed by the construction of the wage frontier. The cost-minimizing technique at a given rate of profits has a wage curve on the outer frontier, as illustrated by Figure 1 for a specified parametrization. Managers of firms are willing to operate the machine for two years for any feasible rate of profits. At the maximum wage or a rate of profits of zero, the Alpha technique is also cost-minimizing. The single switch point is a fluke in two ways. First, it lies on the wage axis. Second, the wage curves are tangent at the switch point.

The left pane in Figure 2 depicts a part of the parameter space for this example. Although not apparent to the eye, a thin wedge between two partitions extends to the northeast of the point for the parameters corresponding to Figure 1. At the upper edge of this wedge, the two wage curves for the techniques are tangent at a switch point. The example is of reswitching below this partition and within this wedge. Schefold's example lies to the northeast off the graph, when σ t and φ t are both unity. At the lower edge of this wedge, the switch point with the lower rate of profits is on the wage curve. The pane on the right in Figure 2 shows the vertical difference between these two partitions so as to convince the reader of the existence of this region with reswitching.

Figure 2: A Part of a Parameter Space

Reswitching demonstrates the well-known conclusion that no coherent marginal productivity theory of distribution exists. The economic life of the machine is the full two years here for a low and high rate of profits. Truncation occurs for a range of intermediate rates of profits. The specification of which technique is cost-minimizing can be consistent with vastly different functional distributions of income, with other techniques being cost-minimizing for less extreme distributions. Marginal productivity is, at best, an analysis of the choice of technique within a more general framework.

The switch point at the higher rate of profits in the reswitching region of the parameter space illustrates capital-reversing. Around this switch point, a lower rate of profits is associated with the adoption of a less capital-intensive, cost-minimizing technique. At any rate of profits, inputs into production in a stationary state can be evaluated and these evaluations summed for each technique. The ratio of capital per worker, for example, is an index of the capital intensity of a technique. A more capital-intensive technique produces more output per worker, but its adoption is not necessarily encouraged by a lower rate of profits or interest rate. In other words, A higher wage is associated with the adoption of a technique that requires a greater input of labor per bushel corn produced net throughout the economy. Capital-reversing has been shown to occur in other examples without reswitching on the wage frontier. Harcourt (1972) surveys the controversy in which economists, such as Paul Samuelson and Robert Solow, in Cambridge, Massachusetts, struggled to accept these conclusions drawn by other economists, such as Joan Robinson and Piero Sraffa, at the University of Cambridge.

Consider the region to the southeast in the part of the parameter space illustrated in the left pane of Figure 2. A single switch point exists on the wage frontier. Around this switch point, a lower rate of profits is associated with the adoption of a technique with a greater value of capital per person-year and a greater output per worker. Nevertheless, truncating the operation of the machine for one year is associated with a more capital-intensive technique. The invalidity of Austrian capital theory does not even need the phenomena of reswitching and capital-reversing for its demonstration.

No switch points exist in the northwest of the part of the parameter space graphed in Figure 2, and the machine is operated for its full physical life of two years for any feasible distribution of income.

The reverse substitution of labor, reswitching, capital reversing, the association of the truncation of the economic life of machine with a more capital-intensive technique are not fluke cases. These posts demonstrate this conclusion by contrasting these possibilities with genuine fluke cases.