Saturday, September 21, 2019

A Fluke Case Over The Wage Axis

Figure 1: Wage Curves and The Price of Corn for the Fluke Case

This post extends a previous post. I am basically introducing structural dynamics into an example, by Bidard and Klimovsky of fake switch points.

At a rate of profits of zero in the example, the price of corn is zero for Alpha, one of the two techniques that is cost-minimizing there and for somewhat higher rates of profits. At a time before the fluke case, only the Gamma technique is cost-minimizing at a rate of profits of zero. The price of corn, as calculated with the Alpha technique, is negative at a rate of profits of zero. Alpha prices become non-negative only for positive rates of profits. This possibility cannot arise in examples with only single production and the choice of technique analyzed by the construction of the wage frontier.

2.0 A Fluke Case

Technology and techniques are specified as in the previous post. I consider variations in labor coefficients with time. Two commodities can be produced jointly with each of three production process. In each process, workers produce outputs of the two commodities from smaller inputs of each commodities. Requirements of use are such that at least two processes must be operated. So each technique combines two processes.

A system of price equations is associated with each technique. The system, including an equation specifying the numeraire, can be taken to define the wage and the prices of both commodities, given an exogenous specification of the rates of profits. Table 1, at the head of this post, illustrates the solution prices at a given point of time. Linen is taken as the numeraire. The top half of the figure shows the wage, for each technique, as a function of the rate of profits. The bottom half of diagram shows the corresponding price of corn. Notice that, for the Alpha technique, the price of corn is zero when the rate of profits is zero.

A technique is only feasible, for the analysis of the choice of technique, when both the wage and prices are non-negative. In Figure 1, the rate of profits is partitioned into two roman-numbered regions. In Region II, both the Alpha and Gamma techniques are feasible. In Region III, only the Alpha technique is feasible.

At a switch point:

  • The wage curves for at least two techniques intersect at the switch point.
  • No extra profits can be made at the going rate of profits in any process.
  • No excess costs arise for any process that can be operated at the switch point.

No switch points exist in the example at the time illustrated in Figure 1. For the structure of the example, all three wage curves intersect at a (non-fake) switch point. Furthermore, the price of corn is the same for all three techniques at the switching rate of profits.

Not enough information has been given so far to determine which techniques are cost-minimizing at each feasible rate of profits in Figure 1. I like to plot extra profits for each process and each price system. I do not show such plots in the post. Nevertheless, Table 1 summarizes which techniques are cost minimizing.

Table 1: Cost-Minimizing Techniques
IGammab, c
IIAlpha and Gammaa, b, c
IIIAlphaa, c
3.0 Before the Fluke Case

Consider time before the fluke case illustrated in Figure 1. Labor coefficients are larger. Figure 2, below, illustrates the wage and price curves for a specified time before the fluke case described above. Notice the appearance of Region I, where Gamma is uniquely cost-minimizing. The fluke case is a knife-edge case where Region disappears. The wage axis becomes the boundary between Regions I and II. Of these two regions, only Region II exists for a positive rate of profits.

Figure 2: A Fluke Fake Switch Point?

Does Figure 2 illustrate another fluke case? At the fake switch point at a rate of profits of five percent, the price of corn is zero. But consider Figure 3 below. The only difference in the example between Figures 2 and 3 is the specification of the numeraire. With corn as numeraire, the fake switch points disappear, and a new fake switch point appears at a rate of profits of 13 1/3 percent. The wage and the price of linen approach an asymptote for the rate of profits at which the price of corn is zero when linen is the numeraire. Which techniques are cost-minimizing is unaffected by the choice of the numeraire.

Figure 3: Not A Fluke With Corn As Numeraire
4.0 After the Fluke Case

Consider some time after the fluke case illustrated in Figure 1. With the chosen parameters, labor coefficients have decreased less in the first production process than in the other two. Figure 4 shows the next qualitative change in the example, in which a switch point appears over the wage axis. I have already analyzed this case for this example.

Figure 4: A Switch Point On The Wage Axis

Between the times illustrated by Figures 1 and 4, Regions II and III continue to characterize the range of feasible non-negative rates of profits. The price of corn is positive, for all three techniques, is positive for feasible rates of profits for each technique. Region I has vanished.

The switch point continues to exist after the time illustrated in Figure 4, but at a positive rate of profits. A new region appears. For a rate of profits of zero and small positive rates of profits, the Beta technique is uniquely cost-minimizing.

5.0 Conclusion

This post has presented a fluke case only possible under joint production. In this example, the choice of technique cannot be determined by constructing the wage frontier.

This post has also presented a sort-of fluke case associated with a fake switch point. In this case, the fake switch point appears on the frontier at a rate of profits at which the price of corn is zero. The set of cost-minimizing techniques and processes varies at the fake switch point. But its existence depends on the choice of the numeraire.

I have been working on a taxonomy of fluke switch points for understanding structural economic dynamics. This post illustrates that my approach can extend to joint production. New phenomena and fluke cases can arise, and one must, perhaps, pay closer attention to what is and is not dependent on the choice of the numeraire.

Monday, September 16, 2019

A Pattern Over The Wage Axis In A Case Of Joint Production

Figure 1: Wage Curves with Corn as Numeraire
1.0 Introduction

This post presents an example of a fluke switch point in which the choice of technique cannot be analyzed by the construction of the wage frontier. Under joint production, the technique that is cost-minimizing, for a given rate of profits, does not necessarily maximize the wage. Nevertheless, one can still see what I call a pattern over the wage axis in this case. The example is a generalization of the numerical example in Bidard & Klimovsky (2004).

2.0 Technology

I postulate an economy in which two commodities, corn and linen, can be produced from inputs of corn, linen, and labor. Managers of firms know of three processes (Tables 1 and 2) to produce corn and linen. Each process produces net outputs of corn and linen as a joint product. Inputs and outputs are specified in physical units (say, bushels and square meters) per unit level of operation of the given process. Inputs are acquired at the start of the year, and outputs are available for sale at the end of the year.

Table 1: Inputs for The Technology
Laboreσ0,1(1 - t)eσ0,2(1 - t)eσ0,3(1 - t)

Table 2: Outputs for The Technology

I assume that requirements for use are such that two processes must be operated to satisfy those requirements. I need to investigate the implications of this assumption further. Apparently, for this example, it implies that the economy is not on a golden rule steady state growth path, with the rate of profits equal to the rate of growth. Anyway, with this assumption, three techniques - Alpha, Beta, and Gamma - can be operated. Table 3 specifies which processes are operated for each technique.

Table 3: Techniques
Alphaa, b
Betaa, c
Gammab, c

The technology, as I have defined it, is parameterized. I consider the following specification for the rate of decrease in labor coefficients.

σ0,1 = 2
σ0,2 = σ0,3 = 5/2

Bidard & Klimovsky's example arises when t is unity. I consider the following value for time:

t ≈ 0.91973

Structural economic dynamics arises as time varies.

3.0 Price System

Prices of production arise for each technique and each specification of the numeraire. For the Alpha technique, prices of production are characterized by the system of the following three equations:

(20 p1 + 20 p2)(1 + r) + [ eσ0,1(1 - t) ] w = 21 p1 + 27 p2
(20 p1 + 20 p2)(1 + r) + [ eσ0,2(1 - t) ] w = 23 p1 + 25 p2
p1 d1 + p2 d2 = 1


  • r is the rate of profits.
  • w is the wage.
  • p1 is the price of corn.
  • p2 is the price of linen.
  • d1 is the quantity of corn in the consumption basket serving as numeraire.
  • d2 is the quantity of linen in the consumption basket serving as numeraire.

Given one of the distributive variables, this system of equations can be solved. Figure 1, at the top of this post, graphs the wage curves for the three techniques, when d1 = 1 and d2 = 0. Figure 2 graphs the wage curves when linen is the numeraire.

Figure 2: Wage Curves with Linen as Numeraire

Notice that which technique lies on the outer envelope, as the rate of profit, varies with the choice of numeraire. In Figure 1, the Alpha technique maximizes the wage, for all feasible positive rates of profits. In Figure 2, the Gamma technique, then the Alpha technique, maximizes the wage, with an increasing rate of profits. This dependence of qualitative characteristics of the wage frontier cannot arise when all capital goods are circulating capital.

In the example, the two processes for a technique and the remaining process must all obtain the same rate of profits at a (genuine, non-fake) switch point. In the example, all three wage curves must intersect at a switch point. Another aspect of a switch point is that the prices of each good must be invariant across the price systems for the techniques entering the switch point. When corn is the numeraire, the price of linen must be the same for all three techniques at the switch point. This property is illustrated in Figure 3. The corresponding property for the price of corn, when linen is the numeraire, is illustrated in Figure 4. No sign of the fake switch points appears in Figures 3 and 4.

Figure 3: Price of Linen with Corn as Numeraire
Figure 4: Price of Corn with Linen as Numeraire

4.0 Choice of Technique

Wage curves can be misleading when analyzing the choice of technique under models of joint production. How then should the choice of technique be found?

First, suppose the Alpha technique has been adopted. One can cost up the outputs and inputs of each process, for the solution to the price system for the Alpha technique. Figure 5 shows results. No extra profits, sometimes called pure economic profits, are made in operating the processes comprising the Alpha technique. For positive rates of profits, operating process c will not obtain the going rate of profits. Clearly, the Alpha technique is cost-minimizing for the graphed range of the rate of profits.

Figure 5: Extra Profits with Alpha Prices

Second, suppose the Beta technique is chosen. Figure 6 graphs extra profits, for each process, as a function of the rate of profits, given Beta prices. For a positive rate of profits, the second process earns extra profits and will be adopted by managers of firms. Notice that one cannot tell from the diagram which process will be dropped. This issue does not arise without joint production. In the case of single production, only one process in the given technique produces the same commodity as that produced by the new process.

Figure 6: Extra Profits with Beta Prices

Finally, suppose the Gamma technique is chosen. Figure 7 graphs extra profits for this case. And the Gamma process is cost-minimizing for the full range of the rate of profits shown in the figure.

Figure 7: Extra Profits with Gamma Prices

The above has shown that, in this example, both the Alpha and Gamma techniques are cost-minimizing at feasible positive rates of profits. The Beta technique is cost-minimizing only at the switch point at a rate of profits of zero percent. The choice of technique is independent of the numeraire. Presumably, the choice between the Alpha and Gamma techniques is made based on requirements for use. At any rate, the chosen technique need not maximize the wage, given the rate rate of profits and the specification of the numeraire.

5.0 Conclusion

This example has illustrated that a specific fluke switch point, which I originally defined for cases with only circulating capital, can also arise in joint production. I except to find a need for new kinds of fluke switch points as I further examine joint production. I am hoping to be able to draw pattern diagrams in which qualitative properties are independent of the choice of the numeraire.

  • Bidard, Christian and Edith Klimovsky (2004). Switches and fake switches in methods of production. Cambridge Journal of Economics. 28 (1): 89-97.

Saturday, September 07, 2019

Martin Weitzman's The Share Economy

I happen to have one book by Marty Weitzman (1942 - 2019) on my bookshelf. So I thought I would write a bit about The Share Economy: Conquering Stagflation.

This is an ill-timed book. It proposes that firms negotiate with workers to pay them a percentage of revenues, instead of, say, an hourly money wage. It argues that such a change will address the widespread macroeconomic problem, throughout the 1970s, of simultaneously high unemployment and high inflation. But, by the time the book came out, stagflation had been "solved", in an extremely reactionary way. The countervailing power of organized labor was being abolished. Labor unions were being crushed, and workers would, by and large, no longer see their wages increase with productivity. Instead of unemployment being addressed, workers would just have to get used to long-lasting higher unemployment.

Maybe some day, we will get back to a setting where Weitzman's book is socially relevant. Even so, it is worth exploring how macroeconomic performance is affected by microeconomic structures.

Although I think of Weitzman as a mainstream economist, his view of the microeconomic setting at the time of his writing was not that far away from Post Keynesianism. He thinks of the "tone" of "modern industrial capitalism" as set by "a relatively small number of large-scale firms", such as those in the Fortune 500. These firms are described by the theory of monopolistic competition. (quotes on p. 11). These firms are characterized by constant costs over a wide range of levels of production below limits set by capacity. They set their prices at a markup over cost. The theory of profit maximization, under these assumptions, yields a markup based on elasticity of consumer demand.

Weitzman explicitly rejects a theory of monopsony for labor markets:

"...If your aim is to focus in on fine close-up details and you wish to do justice to the facts, you must rely on a heavily institutional approach. But I think the unique long-run substitutability of labor among different uses actually makes the competitive theory a rather good description of long-run tendencies in the labor market...

In this book I am primarily interested in the general theory of wage determination... least the labor market behaves 'as if' it is competitive, in the sense that countervailing power between buyers and sellers of labor is sufficiently balanced that neither party has a clear upper hand and both possess approximately equal bargaining strength. The economy-wide real wage is not very different from what would be determined by competitive forces in the labor market." (pp. 29-30.)

I am not sure that Weitzman's account of firms is consistent with firms operating multiple plants and producing multiple products. I think of Alfred Eichner's theory of the megacorp here. I also doubt that theories of full cost, markup, or administered prices should be developed based on markups determined by elasticities. Rather, the markup might be theorized as based on firm's plans for growth.

Weitzman sees that firms will respond to fluctuations of demand by adjusting quantities, not prices. He cites Janos Kornai's contrast of planned, socialist economies with capitalist economies. In the United States, firms must attend to making the consumer's shopping experience as pleasant as possible, while in the Soviet Union, establishments do not care and consumers wait in queue. On the other hand, establishments in the Soviet Union cater to the worker. Weitzman argues his share economy would change the dynamics of the labor market such that firms in the United States would also worry more about the worker's experience.

Wietzman sees the contemporary practice of firms awarding year-end bonuses as a start towards his share economy. He includes Eastman Kodak as an example. Kodak is now bankrupt, and Kodak Park in Rochester, NY, is mostly empty and decaying. In my anecdotal experience, bonuses are often experienced as a present that cannot be planned or depended on. Maybe it would be different with more transparency from your employer, as resulting from a union contract, representatives from the union sitting on the board of directors, an Employee Stock Ownership Plan (ESOP), or some such.

Overall, I find The Share Economy intriguing. It illustrates how good economists will not develop an universal theory, but will address problems of the economist's own time and place.

(A propos of nothing in particular, Branko Milanovic has a post coming close to an endorsement of Neo-Ricardianism.)

Sunday, September 01, 2019


This list is mostly a matter of aspirational reading.

Wednesday, August 28, 2019

Mass Publics Apathetic About Democratic Norms?

This post gestures to a worrisome argument that could be constructed by combining arguments from certain references. It is also more about current events than most posts on this blog.

Philip Converse's argument that most members of the mass public are ideologically innocent has long been influential among political scientists. Why should those who have families to raise, bills to pay, and jobs to take up their time pay much attention to the details of politics?

Barber and Pope (2018) provides recent empirical evidence, from something like a natural experiment, that conservative Republicans, especially, are unprincipled. Their results are based on a survey conducted in early 2017, before Trump had a record as governing. Since Trump does not care to know anything about anything, one can truthfully report statements of him supporting either side on almost any issue. The survey contained questions on minimum wages, taxes, abortion, immigration, gun control, Iran, health care, climate change, planned parenthood. Some surveys just asked the questions. Others reported Trump's opinion in a liberal direction. Others reported Trump's opinion in a conservative direction. "[L]ow knowledge respondents, strong Republicans, Trump-approving respondents, and self-described conservatives" generally just follow what their leader says.

It is difficult to construct an experiment like this for others. One might think that liberal Democrats might be swayed against a position by hearing that it is Trump's position. But one would like to find an authority that they accept that is equally inconsistent. Otherwise, one would have to assign views in a survey that are not truthful. As I understand it, the latter is what Jaydani and Chang (2019) do in demonstrating that mainstream economists are unprincipled. They show agreement with a statement among economists depends on whether it is assigned to a mainstream economist or to a heterodox economist.

Levitsky and Ziblatt (2018) argue that a democracy deteriorates into something like fascism when gate keepers fail to uphold democratic norms. I do not know if this is an example, but journalists are trained in an ethic in which one is supposed to disclose an interest in a story, if one has one. Sean Hannity, for example, violated this norm when he reported on Michael Cohen and Trump's violation of campaign finance laws; Cohen was Hannity's lawyer for certain real estate transactions. Calling the press "the enemy of the people" is a fascist slogan. American First is a slogan for pro-Nazis. Presidents do not accuse the Chairman of the Federal Reverse of playing politics. Whatever one may think of these norms, I do not expect many watchers of, say, Fox News to worry about this sort of rhetoric unless it is pointed out to them by authorities they trust.

Mark Tushnet's 2004 concept of constitutional hardball is another discussion of democratic norms in the United States. And he argued that they were being violated, partly in a tit-for-tat fashion. For example, how willing is Congress to give advise and consent to qualified appointees of the President when he is of the other party? Fishkin and Pozen argue that a willingness to throw out norms that uphold our system of government is not symmetrical.

Stanley (2018) can be read as suggesting that the effects of elites and gate keepers to fail to uphold democratic norms can be cumulative. Anti-intellectualism and a disrespect for truth leads followers to be unaware of norms being violated. Conspiracy theorizing and a sense of victimhood increases. Followers become less accepting of reasoned argument and more dismissive of those not in their hierarchy.

To summarize: members of mass publics cannot be expected to understand the risks of willful and blatant violation of democratic norms without leadership. In the give and take of politics, our leaders have been not upholding such norms and, in fact, have been discarding them. Perhaps a process of cumulative causation is underway that can lead to nowhere good.


Friday, August 23, 2019

Economists Insulting Me And Insulting Keynes

I happen to think the minimum wage in the United States should be raised. I'll go along with the consensus of $15 an hour.

I also happen to know that, even under ideal conditions, wages and employment cannot be explained by supply and demand.

Some economists, who I have no (other) reason to disrespect, seem to think my true statement about labor economics can be discredited by attacking my motivations. So they point out how, under (incoherent) neoclassical theory, higher minimum wages can be justified by, for example, the theory of monopsony. But my motivations are almost the opposite. I take the evidence that neoclassical economics is wrong about labor markets as a launching pad into the illogic of mainstream economics. (Is this the most recent meta-analysis on minimum wages?)

The attack, based on motive, is insulting. One might think a point of logic cannot be discarded by presuming that it was made because of a desired political conclusion. But enough about me. I want to talk about how John Maynard Keynes was attacked in a similar way.

Some may portray the Keynesian revolution as about policy. The point is to demonstrate that fiscal or monetary policy can be effective in the short run, while prices and quantities are adjusting to a long run equilibrium in which all markets, including the labor market, clear. But Keynes is clear that his book about is about theory, not policy:

"This book is chiefly addressed to my fellow economists. I hope that it will be intelligible to others. But its main purpose is to deal with difficult questions of theory, and only in the second place with the applications of this theory to practice." -- the first three sentences in (the preface to) The General Theory of Employment Interest and Money (Keynes, 1936).

And sticky prices is characteristic of the theory that he is rejecting:

"For 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 the rigidity the blame of maladjustment." -- Keynes, 1936: p. 257.

So, insofar as the Keynesian revolution was about, say, fiscal policy it was a counterrevolution against Keynes' ideas.

I realize that economics can have great practical effects, for good or ill. Some, perhaps, want to advocate policies which they deem good. Rather than trying to tilt at windmills, they may think it more worthwhile to show how one can argue for such policies within orthodox theory. I hope some who do this are not merely trying to ensure they retain access to levers of power. If one puts on a mask long enough, one risks becoming what one pretends to be. The understanding of capitalism is not advanced in any way at all. Suppose one thinks about policy with simple models. Then, when one has a conclusion, one bows to the orthodoxy and appends a superfluous shell of constrained maximization. (I haven't read the book in the link.) If this is typical among a population of mainstream economists, outsiders may wonder what is the point of all that mathematics and supposed science?

Saturday, August 17, 2019

Reswitching, Recurrence, And The Incoherence Of The Marginal Productivity Theory Of Distribution

Blair Fix argues that economists argue in a circle in putting forth the marginal productivity theory of distribution. I know that there is no such consistent theory anyways. It occurs to me that process recurrence, as well as the reswitching of techniques, can be used to demonstrate this inconsistency.

Suppose you completely know the technique being used in an economy to produce its output. And, which is even more impossible, you know all other possible techniques. I am thinking of a technique being specified with something like a Leontief input-output matrix, in physical terms. Assume, counterfactually, that all these techniques exhibit constant returns to scale. With these assumptions, you know the physical marginal product of each input into production, whether it is previously produced or not. (In my favorite way of specifying technology, marginal products are typically intervals, not derivatives.)

The reswitching of techniques shows that one cannot necessarily uniquely map from technology and the technique in use to the functional distribution of income. Wages, for example, are not determined by the marginal product of labor. With reswitching, the same technique is adopted for different (ranges of) wages, with other techniques being cost-minimizing in-between. For both ranges in which the technique is adopted, the same inputs are used in each industry, per unit output. Productivity and marginal products are the same, in physical terms. Yet the value of marginal products, in price terms, can be vastly different. How then can the price of factors of production be said to be determined by marginal productivity?

The same argument applies at the level of a single industry. Suppose the process in use to provide the output of an industry is known. Likewise, all other processes that may be used in that industry, at the given level of technology, is assumed known. With process recurrence, the process in use is adopted at different levels of wages, with other processes being cost-minimizing in-between. Once again, one can see that the prices of factor inputs are not determined by marginal productivity.

Process recurrence is more general than the reswitching of techniques. Reswitching implies recurrence, but recurrence can happen without reswitching. Arrigo Opocher and Ian Steedman have further generalized recurrence to individual coefficients of production. As I understand it, he amount of iron ore required as input per ton steel produced by the steel industry can recur without the whole process of production recurring in the steel industry.

Anyways, no competent economist nowadays accepts the marginal productivity theory of distribution. But many economists might teach incoherent nonsense to students, all the same.

Tuesday, August 06, 2019

Structural Economic Dynamics And Reswitching In A One-Good Model

This post, as suggested, extends this one-good example. I assume a constant returns-to-scale technology, as specified in Tables 1 and 2. Labor is advanced to the capitalists, and wages are paid out of the surplus at the end of the year (period of production). The capitalists (incorrectly) expect the technology in existence at the start of the year to continue to exist. I assume prices of (re)production prevail.

Table 1: Inputs for The Technology
Labor30 eσ0,1(1 - t)180 eσ0,2(1 - t)(39/2) eσ0,3(1 - t)
New Widgets100
One-Year Old Widgets010
Two-Year Old Widgets001

Table 2: Outputs for The Technology
New Widgets3 eσ1,1(t - 1)(7/4) eσ1,2(t - 1)(237/20) eσ1,3(t - 1)
One-Year Old Widgets100
Two-Year Old Widgets010

Only a newly produced widget is a consumer good. Old widgets can be used in production for two more years. The economic lifetime of a widget (machine) may be less than its physical life. Free disposal is assumed. I define techniques:

  • Alpha: The widget is discarded after one year.
  • Beta: The widget is discarded after two years.
  • Gamma: The widget is discarded after three years.

The specification of technology allows for productivity to increase in each process, both because labor is saved and because more output is produced with a unit input of widgets. Figure 1 shows one of my pattern diagrams, in which the specification of increased productivity results from reducing the parameter space to three dimensions.

I identify two of my patterns in this diagram, a pattern over the wage axis and a reswitching pattern. In Region 2, reswitching occurs. Around the switch point at the lower rate of profits, a higher rate of profits is associated with a truncation of the economic life of a machine to one years. This logical possibility contradicts Austrian capital theory, in which a scarcity of capital results in a higher rate of profits and a longer period of production. In circulating capital models, the switch point at the lowest rate of profits is 'non-perverse', unlike here. I thing Ian Steedman made the same observation decades ago.

Tuesday, July 30, 2019

Structural Economic Dynamics, Markups, Real Wicksell Effects, And The Reverse Substitution Of Labor

I am being published in Structural Change and Economic Dynamics. Currently, this link is without my corrections to proofs, I guess.

Research highlights:

  • Technical progress and variations in industry markups can change characteristics of the labor markets.
  • A numeric example illustrates the theory of the choice of technique.
  • In the example, switch points are created and destroyed with varying coefficients of production and varying markups.
  • Around some switch points, higher wages are associated with greater employment, given the level of net or gross output
  • Graphical displays are provided for visualizing these results.

Abstract: This article presents an example in which perturbations in relative markups and technical progress result in variations in characteristics of the labor market. Around a switch point with a positive real Wicksell effect, a higher wage is associated with firms wanting to employ more labor per unit output of net product. Around a switch point with a reverse substitution of labor, firms in a particular industry want to hire more labor per unit output of gross product. Technical progress and variations in markups can bring about and take away circumstances favorable for workers wanting to press claims for higher wages. This article presents specific fluke switch points in which variations in technology and markups change these circumstances, as well as novel diagrams for visualizing the effects of such variations.

Tuesday, July 23, 2019

No Such Thing As The Natural Rate Of Unemployment

I know that the idea of a "natural rate" of unemployment or a non-accelerating inflation rate of unemployment (NAIRU) makes no sense. I cite, for example, James Galbraith's 1998 book, Created Unequal: The Crisis in American Pay. I think Colin Rogers' 1989 book is related.

Jared Bernstein gives the idea of a natural rate of unemployment at the first of four examples of ideas that [mainstream] economists have gotten wrong for decades. This is not the first example of a case where Post Keynesians (and only Post Keynesians(?)) could explain an empirical phenomenon decades in advance.

Friday, July 19, 2019

Harrod-Neutral Technical Progress and Fluke Switch Points

Figure 1: A Pattern Diagram

I have put up a working paper with the post title.

Abstract: This article considers Harrod-neutral technical progress in the context of an analysis of the choice of technique. In a model of the production of commodities by means of commodities, neutral technical change is compatible with the reswitching of techniques, capital reversing, process recurrence, and the reverse substitution of labor. A taxonomy of fluke switch points is applied to an example, illustrating how these phenomena can arise and vanish in the course of neutral technical progress.

I get various fluke switch points, as is typical of my examples. By assuming Harrod-neutral technical change, I end up with the structure in Figure 2, in one slice of the parameter space.

Figure 2: A Two-Dimensional Pattern Diagram

Tuesday, July 16, 2019

Children, Dialectics, and Topology

"One of the curious things about our educational system, I would note, is that the better trained you are in a discipline, the less used to dialectical method you're likely to be. In fact, young children are very dialectical; they see everything in motion, in contradictions and transformations. We have to put an immense effort into training kids out of being dialecticians." -- David Harvey, Companion to Marx's Capital: The Complete Edition. Verso (2018).

I do not have children, and I am not sure I understand Harvey's claim. But one writer I liked was Jean Piaget. (I also want to mention Seymour Papert.)

I take from him that children think in a way that can be described by advanced mathematics. I think, in particular, of topology and modern algebra. The idea is children take time to learn certain invariants and conservation laws that many of us now take for granted. In topology, one asks what can be said about sets and functions when one does not have a distance function? If you rotate a disk, suppose, for example, the distance between two points cannot be assumed the same when you look in the east-west and north-south direction. Algebra investigates certain abstract structures, with as little as possible assumed about the properties of operations. A difference between mathematicians and children, however, is that the mathematicians (better than me) learn how to articulate and characterize such structures.

I do not think I am necessarily contradicting Harvey. J. Barkley Rosser, Jr. has a paper that perhaps can be used to draw connections between Piaget and Harvey's ideas about how children think.

Thursday, July 04, 2019

On Milana's Purported Solution To The Reswitching Paradox

Carlo Milana has posted a paper on arXiv. I was prepared to accept this paper's claims. Economists have developed price theory. Referring to Sraffian "paradoxes" and "perverse" switch points is a matter of speaking. There does not exist separate Sraffian and neoclassical versions of price theory. For a result to be "perverse", it need only contradict outdated neoclassical intuition. But it is as much a part of the mathematical economics as any other result. (It is another matter that much teaching in microeconomics is inconsistent with the mathematics.)

In equilibrium, the price of the services of each capital good in use is equal to the value of the marginal product of that good, with all prices discounted to the same moment in time. This discounting implies that the interest rate appears in a formal statement of these equations. These equalities are very different from the claim that the interest rate equals the marginal product of (financial) capital. In limited cases, one can prove something like the aggregate equality. No such thing as a marginal productivity theory of distribution, however, is restored. Milana might cite Hahn (1982) on this background.

But Milana goes further. He claims that reswitching is impossible or, at least, examples up to now are erroneous.

I think Milana's basic mistake is exposed in Salvadori and Steedman (1988). (I go through one of their examples here.) The Samuelson-Garegnani model is not a model of two-(produced) goods. The model contains as many capital goods as there are techniques. Potentially, there can be a continuum of capital goods in the model. As such, it is meaningless to require the price of the capital goods used in each technique that is cost-minimizing at a switch point to be equal to one another. That is analogous to requiring the price of a ton of iron be equal to the price of a ton of tin.

For some reason, Milana does not discuss examples of reswitching in flow-input, point output models, such as in Samuelson (1966). Nor does he acknowledge, as I read him, valid examples in which the same n commodities are produced in all techniques, and all commodities are basic in all techniques. (Does he say anything at all about the distinction between basic and non-basic commodities?) At a non-fluke or generic switch point, in such a framework, the two techniques that are cost-minimizing differ in a process in exactly one industry.

Milana should read and reference Bharadwaj (1970), as well as Bidard and Klimovsky (2004) on fake switches in models of joint production. Other Linear Programming formulations are available for considering the choice of technique. Vienneau (2005) presents one. What does Milana have to say about the direct method for analyzing the choice of technique in Kurz and Salvadori (1995)? I briefly provide a survey of different analysis in Vienneau (2017), as well as an algorithm for finding the cost-minimizing technique? Are all these approaches in error?

  • Khrishna Bharadwaj. 1970. On the maximum number of switches between two production systems. Schweizerische Zeitschrift fur Volkswortschaft and Statistik (4): 401-428. Reprinted in Bharadwaj 1989. Themes in Value and Distribution: Classical Theory Reappraised, Unwin-Hyman.
  • Christian Bidard and Edith Klimovsky. 2004. Switches and fake switches in methods of production. Cambridge Journal of Economics 28:89-97
  • Frank Hahn. 1982. The neo-Ricardians Cambridge Journal of Economics 6:353-374.
  • H. D. Kurz and N. Salvadori. 1995. Theory of Production: A Long-Period Analysis. Cambridge University Press.
  • Carlo Milano. 2019. Solving the Reswitching Paradox in the Sraffian Theory of Capital. arXiv:1907.01189
  • Neri Salvadori and Ian Steedman. 1988. No reswitching? No switching! Cambridge Journal of Economics 12: 481-486.
  • Paul A. Samuelson. 1966. A Summing Up. The Quarterly Journal of Economics 80 (4): 568–583.
  • Robert Vienneau. 2005. On labour demand and equilibria of the firm. The Manchester School 73(5): 612-619.
  • Robert Vienneau. 2017. The choice of technique with multiple and complex interest rates. Review of Political Economy 29(3): 440-453.

Saturday, June 22, 2019

Easy To Be Hard

Young Children Policing Group Members

This post presents examples of psychologists inducing stress in experimental subjects, some showing why we need Institutional Review Boards (IRBs). Some of the older studies involved so much suffering that experimental subjects suffered Post-Traumatic Stress Disorder (PTSD). I recall that at the end of the 1976 movie, The Tenth Level, about the Milgram experiment, starring William Shatner, the scientists are discussing what they would do if they were experimental subjects. Would they refuse to torture others? And one says to Shatner/Milgram something like, "It seems to me, you have already been tested and failed."

  • Yudkin, Van Bavel, and Rhodes: Almost the only somewhat happy story here. Toddlers are willing to close a fun slide, for themselves, to punish another child for misbehavior. The experiment illustrates costly third-party punishment.
  • Stanford prison experiment: A sample of college students are randomly divided up into pretend guards and prisoners. The guards quickly begin abusing the prisoners.
  • Jane Ellliot experiments: In order to understand segregation and prejudice, divides a class of school children into blue eyes and brown eyes. The blue eyes sit at the front and treated well; the brown eyes sit at the back and are badly treated. The next Monday, the situation is reversed. Quickly, the well-treated act as if they believe they are superior and the others inferior.
  • Robber's Cave experiment: A somewhat happy ending, I guess. Boys divided up into two competitive groups at summer camp quickly disdain one another. Given a problem that requires cooperation with the other group, they will work together.
  • Milgram experiment: Given an authority figure telling them that this is experiment on negative re-inforcement for learning, people are willing to increase electric shocks past the point of torture. Some refused.
  • Gibson and Walk experiment: As far as the baby is concerned, they are crawling over the edge of a cliff on air. Tests whether caution about heights is inherent. More about individual psychology than most of the rest in this list.
  • Asch experiment: On conformity. Subject goes last in a group noting which line was the same length as the a standard. The subject does not realize the rest are part of the experiment. Many were willing to go along with the obvious falsehood all the others said.
  • Little Albert experiment: A baby is conditioned, as with Pavlov's dogs, to be terrified of a white rat, rabbit, dog, and a sealskin coat. More about individual psychology than most of the rest in this list.

Randomized Control Trials (RCTs) provide a rigorous methodology, albeit they can present problems of generalization and external validity. Not all of the above are RCTs. They do illustrate that designing ethical RCTs can be difficult. I expect the above list of amazingly mostly abusive studies, even in psychology can be extended.

  • Yudkin, Danial A., Jay J. Van Bavel, and Marjorie Rhodes (2019). Young children police group members at personal cost. Journal of Experimental Psychology.
  • Haney, C., W. C. Banks, and P. G. Zimbardo (1973). A study of prisoners and guards in a simulated prison. Naval Research Review 30: 4-17.
  • Muzafer Sherif (1966). In Common Predicament: Social Psychology of Intergroup Conflict and Cooperation Houghton Miffin.
  • Milgram, Stanley (1963). Behavioral study of obedience. Journal of Abnormal Social Psychology 67: 371-378.
  • Gibson, E. J. and R. D. Walk (1960).Visual Cliff. Scientific American April.
  • Asch, Solomon E. (1955). Opinions and social pressure. Scientific American November.
  • Watson, John B. and Rosalie Rayner (1920). Conditioned emotional reactions. Journal of Experimental Psychology 3(1): 1-14.

Monday, June 17, 2019

Lewin and Cachanosky on Neo-Ricardian Economics [Citation Needed]

This post is about the misrepresentation of Sraffian capital theory in Lewin and Cachanosky (2019). I cannot recommend this short book. Presumably, it is meant as an introduction. But I do not see it as succeeding. I do not see what a more advanced audience would get out of it that is not available in a few recent papers by Lewin and Cachanosky.

Before proceeding to my main theme, let me note that I agree with some parts of this book, mainly where Lewin and Cachanosky draw on Ludwig Lachmann, to parallel themes in Joan Robinson's emphasis on historical time. They state that no physical measurement of capital exists and that capital is not a factor of production, with a demand function. They state, probably as influenced by Jack Birner, that Hayek never set out a coherent and internally valid theory of capital. His triangles are only useful as an expository device. I am also ignoring certain gaps. For example, the text at the bottom of page 30 suggests, incorrectly, that the economic life of a machine would be the same as its physical life in equibrium, where such disequilibrium phenomena as the introduction of new and better vintages and changes in tastes and technology do not arise.

Citations are needed for these passages:

"Lachmann's capital theory provides the definitive understanding of the nature and working of the capital structure for Austrians today. Rather than conceiving of production as involving a homogeneous mass of 'capital' as a stock (as in both the neoclassical and modern Ricardian conceptions), Lachmann sees it as involving an ordered structure of heterogeneous multispecific complementary production goods. This structure is ever changing as entrepreneurs combine and recombine productive resources in accordance with their assessments of profitability." -- Lewin and Cachanoksy, p. 35.

Where do the neo-Ricardians reject the analysis in Sraffa's book?

"The Keynesian revolution established macroeconomics as [a] legitmate sub-branch of economic inquiry focusing on the relationship betwenn aggregates... [The] neoclassical production function is the workhorse of much of modern literature...

"...its ability, using the marginal productivity theory, to explain the distribution of output (income) between capital and labor... During the 1960s and following, the neoclassical production function was the object of attack by the 'Cambridge Marxists' UK (neo-Ricardians) against the 'Cambridge Massachusetts' neoclassicals, on the presumption that it was essential to the validity of the marginal productivity explanation of the distribution of income ... and that demolishing the notion of capital upon which the aggregate production function depended, they would, at the same time, demolish the marginal productivity theory of distribution." -- Lewin and Cachanoksy, p. 46-47.

Where do the neo-Ricardians assert the non-existence of disaggregated, microeconomic neoclassical theory?

"These paradoxes consist of cases in which it is alleged, for example, ... a fall in the interest rate may first lead to the adoption [of] a more 'capital-intensive' productive technique, and then switch, paradoxically, to a less 'capital-intensive' technique, and then switch back again as the interest rate continues to fall. These are alternative techniques, characterized by their physical capital labor ratios. In other words, switches may occur, as well as reswitches and reversals..." -- Lewin and Cachanoksy, p. 68.

Even Joan Robinson's "real capital" is measured for a given interest rate. Techniques of production are characterized by a complete list of inputs and outputs. These inputs can include produced means of production, unproduced natural resources, and various kinds of labor. When deciding on which technique to adopt, managers of firms, in Sraffian and in any other reasonable analysis of a capitalist system, coompare costs and revenues, with inputs and outputs evaluated at prices.

"The neo-Ricardians identify all 'capital' as intermediate goods, such as machines, tools, or raw materials. They are goods-in-process from the original labor that constructed them, to the emergence of the final consumer good. So all capital goods (can be and) are reduced to dated labor. In this way, we get a purely physical measure of 'capital', one that, by construction, does not vary with the interest rate." -- Lewin and Cachanoksy, p. 69, footnote 3.

Where do the neo-Ricardians assert that, in all interesting cases of joint production, all intermediate goods can be expressed as produced by inputs consisting only of a stream of dated labor? Where do they put forth a measure of capital that does not vary with the interest rate?

"Also important, the neo-Ricardians identify the price of capital as the rate-of-interest which they regard as synonymous with the rate of profit. But neither is correct... The market interest rate is, indeed, the price of capital as we understand it. It is the cost of borrowing 'capital' for the employment of any valuable resource or for any other reason. It is the price of credit and is determined by the time prefernces of borrowers and lenders and the production possibilities available. (The neo-Ricardians have no discussion of what determines interest rates.)" -- Lewin and Cachanoksy, p. 72.

Post Keynesians have considered a theory of growth and distribution in which the interest rate is set by the monetary authorities and the rate of profits exceeds the interest rate by a conventional markup. They have considered other theories in which the wage is given by forces outside the theory of value. They have developed theories of inflation in which conventions on both the rate of profits and wages conflict. In the late 1950s and early 1960s, Richard Kahn, Nickolas Kaldor, Luigi Pasinetti, and Joan Robinson pointed out that savings propensities out of wages and profits constrained functional income distribution along a steady state growth path. Kaldor (1966), in this tradition, developed a model in which the interest rate and the rate of profits are distinguished. I provide two textbooks, in the references, that survey this large body of work.

  • Duncan K. Foley, Thomas R. Micl, Daniele Tavani (2019). Growth and Distribution, Second edition. Harvard University Press.
  • Peter Lewin and Nicolas Cachanosky (2019). Austrian Capital Theory. Cambridge University Press.
  • Stephen A. Marglin (1984). Growth, Distribution, and Prices, Harvard University Press.

Saturday, June 08, 2019

On Hicks' Average Period of Production

Figure 1: APP Around Switch Points
1.0 Introduction

I take it that the Austrian theory of the business cycle builds on Austrian capital theory. The following two claims are central to Austrian capital theory:

  • Given technology, profit maximizing firms adopt a more capital-intensive, more roundabout technique at a lower interest rate.
  • The adoption of a more roundabout technique increases output per worker.

Originally, Eugen von Böhm-Bawerk proposed a physical measure of the average period of production, but economists of the Austrian school have been distancing themselves from this position for well over half a century. I have argued that the first claim fails, even in a framework without any scalar measure of capital-intensity or the average period of production.

Recently, Nicholas Cachanosky and Peter Lewin, in a series of articles, have championed J. R. Hicks' measure of the Average Period of Production (APP), as a justification of the first claim. They note that the APP, as defined here, is a function of the interest rate. Hence, it cannot fully support Böhm-Bawerk's theory. Saverio Fratini has argued this justification does not work, since the second claim above fails, when this APP is used as a measure of capital-intensity. Lewin and Cachanosky, in reply, argue that Fratini does not properly calculate the APP, since it should be forward looking and apply in disequilibria.

This post re-iterates Fratini's argument, with his example. I more closely follow Cachanosky and Lewin's approach, though.

2.0 Technology

Fratini considers a technology consisting of two techniques of production, Alpha and Beta (Table 1). Each technique requires three years of unassisted labor inputs, per bushel wheat produced at the end of the third year. Labor is advanced and paid at the end of the year. Labor is taken as numeraire. That is, the wage is assumed to be $1 per person-year. The price of a bushel wheat, p, is taken to be $12 dollars per bushel. As I hope becomes apparent, these assumptions generally characterize a disequilibrium.

Table 1: Inputs for Producing A Bushel Wheat
13a3 = 1 Person-Yr.b3 = 2 Person-Yrs.
22a2 = 7 Person-Yrs.b2 = 2 Person-Yrs.
31a1 = 2 Person-Yrs.b1 = 8 Person-Yrs.

The output per worker, in a stationary state, is determined by the chosen technique. Suppose the Alpha technique is adopted. In any given year, 10 person-years are employed per bushel wheat produced. Two person-years are being expended to produce each bushel of wheat harvested at the end of the year, seven person-years are being employed to produce each bushel of wheat available at the end of the next year, and one person-year is employed per bushel wheat harvested even a year later. That is, output per worker, under the alpha technique, yα, is (1/10) bushels per person-year. Similarly, output per worker for the beta technique, yβ, is (1/12) bushels per person-year.

3.0 Net Present Value and the Choice of Technique

Suppose a wheat-producing firm faces a given annual interest rate, r. For convenience, define:

R = 1 + r

The discount factor, f, is defined to be:

f = 1/R = 1/(1 + r)

Consider a decision to choose a technique to adopt for next three years in producing wheat. Powers of the discount factor are used to evaluate the costs and revenues for each technique at the start of the given year. For example, the NPV of the alpha technique is:

NPV(α, f) = -a3 f - a2 f2 + (p - a1) f3

I have assumed that firms expect the given interest rate to remain unchanged for the decision period - a common convention. Revenues are positive, and costs (or outgoes) are negative.

Figure 2 graphs the difference between the NPV for the two techniques. A positive difference indicates that the alpha technique maximizes the NPV, while a negative difference arises when the beta technique is preferred. Which technique is chosen by cost-minimizing firm for each interest rate is shown. At switch points, firms are indifferent between the two techniques.

Figure 2: Difference in NPVs

Under the assumptions, NPV is always positive. (If the beta technique were adopted at an interest rate of zero, its NPV would be zero then.) If markets were competitive, the price of wheat would vary until the NPV was zero, given the interest rate. Fratini does indeed assume equilibrium and analyzes the choice of technique with backwards-looking calculations of costs, as Lewin and Cachanosky claim. But this makes no difference to his argument, so far.

4.0 The Average Period of Production

One might be interested in how NPV varies with the discount factor. The elasticity of the NPV, with respect to the discount factor, is a dimension-less number for assessing such sensitivity. Somewhat arbitrarily, I discount elasticity one period:

APP(α, f) = f [1/NPV(α, f)] [d NPV(α, f)/df]

Elasticity is the variation of NPV with variation of the discount factor, as a proportion of NPV.

APP(α, f) = [-a3 f/NPV(α, f)] x 1
+ [- a2 f2/NPV(α, f)] x 2
+ [(p - a1) f3/NPV(α, f)] x 3

The APP for a technique, at a given discount factor, is the weighted average of the time indices, looking forward, for a given income stream. The weights are the proportion of the income stream received in each period. All income is discounted to the start of the first year.

So the elasticity of the NPV of an income stream, with respect to the discount factor can also be expressed as the average period of production.

Notice that the APP is not defined in equilibrium. The denominators in the above terms are zero, and the APP could be said to be infinite. If only costs are used in the above calculations (thus, no longer of a NPV), the APP is well-defined, at least in the flow-input, point output case. Fratini (2019) does this.

One could also express the APP as a function of the interest rate:

APP(α, r) = [-a3 R2/NPV(α, r)] x 1
+ [- a2 R/NPV(α, r)] x 2
+ [(p - a1)/NPV(α, r)] x 3


NPV(α, r) = -a3 R2 - a2 R + (p - a1)

I skip over some some algebraic manipulations above.

The above is not the definition of the APP in Fratini (2019), for example, in Equation 7. Where I have time indices of 1, 2, and 3, Fratini has indices of 3, 2, 1. I guess one can say that his definition of the APP is backwards-looking.

Fratini's argument still goes forward with Cachanosky and Lewin's (or Hicks') definition. One could present a mathematical proof that the APP is always increased around a switch point with a fall in the interest rate. But here I'll just graph it for the example. See Figure 1, at the top of this post. Around each switch point a lower interest rate is indeed associated with the adoption of a technique with a larger APP. But consider the switch point at an interest rate of 200 percent. The beta technique, adopted at a notionally lower interest rate, has a lower value of output per head.

4.0 Conclusion

The example illustrates that, around a switch point, a lower interest rate is associated with the adoption of a more roundabout technique, where roundaboutness is measured by Hicks' Average Period of Production. Incidentally, the example demonstrates that in a region where one technique is cost-minimizing the APP may decrease with the interest rate. But the adoption of a more roundabout technique can be associated with a decrease in output per worker. So much for Austrian capital theory and the Austrian theory of the business cycle.

Update (14 June 2019): Re-order numbers in table, as they are used in the calculations. References

Thursday, June 06, 2019

Refutation Of Austrian Business Cycle Theory

Those who understand price theory reject the theory of the Austrian Business Cycle (ABC). I am thinking here that its logical invalidity follows from post-Sraffian capital theory. It is also wrong because of its reliance on the concept of the natural rate of interest.

Some years ago, I tried to get published a demonstration that ABC theory was in error. I forget how many journals rejected it. Four or five articles here are from this series of revisions. The rejections from the journals more sympathetic to Post Keynesians generally said that everybody knows that ABC theory is wrong. The rejections from the journals more sympathetic to the Austrian school said that I ought to read more and more obscure literature. Some of this was helpful for my understanding of the history of ABC theory, but none really addressed my points.

Anyways, my favorite revision is the last. I think this is fairly good, but, as of now, do not intend to resubmit it anywhere. I find that recently some articles on the Cambridge Capital Controversies have been published in the Review of Austrian Economics.


Friday, May 31, 2019

Some Reviews of Quiggin's Economics in Two Lessons

I have been thinking of posting a review of Quiggin's book, but this is not it. I suppose I should mention that I am in the acknowledgements.

Quiggin has a response to a couple of the above. By the way, he had a paper, in 1987, on public choice.

I think any reviewer should note that Quiggin is extremely generous to Hazlitt's Economics in One Lesson. Hazlitt does not mention "opportunity cost". By focusing on this concept, Quiggin makes Hazlitt seem more coherent than he is. I agree with Quiggin that this coherence does not require Hazlitt to think the economy is always in equilibrium. It is consistent with prices providing signals, that, when entrepreneurs act on them, move the economy towards equilibrium. It is not consistent, as Quiggin notes in his book, with the economy persisting for a long time within the production possibility frontier, without any tendency to more towards the frontier.

It is no answer to or review of Quiggin's book to rattle on about Keynesianism or the logically incorrect AustrianBusiness Cycle theory. One has to also address Quiggin's points about externalities, information asymmetries, and the continual redefinition of property rights.

Furthermore, a fair reviewer would note that Quiggin does not recommend a mechanical calculation of, say, taxes and subsidies to correct market failures. Although, I guess, he does not mention "government failure" in his book, his consideration of policies is a lot more nuanced than that.

Furthermore, if one thinks the theory of public choice provides an answer to Quiggin, one should note that Hazlitt does not discuss these matters. Hazlitt was a propagandist and, for decades, should have not been taken seriously.

As far as I know, public choice is an application of neoclassical economics. Gloria-Palermo and Palermo (2005), as I recall this paper, argues that the Hayekian argument about the coordinating function of market prices does not provide a welfare criterion alternative to Pareto efficiency. I think I have such criteria in focusing on conditions for the continued reproduction of society, as opposed to the efficient allocation of given resources. One can also point to the Veblenian dichotomy, between instrumental and ceremonial aspects of institutions, as well as to the pragmatism of John Dewey. If I do review Quiggin's book, I want to point out how it is too accepting of Neoclassicism, as well as where it points beyond.

  • Sandy Gloria-Palermo and Giulio Palermo (2005). Austrian economics and value judgements: A critical comparison with Neoclassical Economics. Review of Political Economy 17(1): 63-78.

Saturday, May 25, 2019

All Combinations of Real Wicksell Effects, Substitution of Labor

Figure 1: A Pattern Diagram

Consider an example of the production of commodities, in which many commodities are produced within capitalist firms. Suppose two techniques are available to produce a given net output. These techniques use the same set of capital goods, albeit in different proportions. They differ in process in use for only one industry. Given the qualification about the same capital goods, generic (non-fluke) switch points are the intersection of the intersection of the wage curves for two techniques that differ in exactly one process.

Suppose that, due to technological progress, some coefficients of production decrease in the process unique to the Alpha technique. Figure 1 shows a possible pattern diagram for this generalization of a previous example. Here, switch points and the maximum rate of profits are plotted against the rate of profits. As time goes by, a reswitching pattern leads to a reswitching example. The switch point created at the larger rate of profits exhibits, after t = 1/2, a negative real Wicksell effect and a reverse substitution of labor. A pattern over the axis for the rate of profits then results in the existence of another switch point at an even higher rate of profits. Technological progress can bring about, in a single example, the combination of both non-zero directions of real Wicksell effects with both non-zero directions of the substitution of labor.

The regions in Figure 1 in which reswitching occurs also illustrate process recurrence. Process recurrence is more general, inasmuch as it can arise even without reswitching.

Since all four possible combinations, of nonzero-real Wicksell effects and the substitution of labor, are possible, the direction of real Wicksell effects and the direction of the substitution of labor are independent of one another. The choice of technique results in variation in gross outputs in multiple industries, for given net outputs. (The question of returns to scale is of interest in this context.) These variations in gross outputs also result in variation in the amount of labor firms want to employ. Around a switch point with a positive real Wicksell effect, firms want to employ more labor, per unit of net output, in the aggregate across all industries. A necessary consequence is that they want to employ more labor in at least one industry. This variation in aggregate employment is consistent with any direction in the variation in the labor coefficient of production in the industry with the varying process.

Friday, May 24, 2019

Alfred Eichner's Microfoundations, Or An Open Letter To Marco Rubio

The Growing Importance of Finance in the Post-War U.S. Economy

As I understand it, Marco Rubio takes from Post Keynesians the idea that, during the post-war golden age, investment decisions were dominated by industrial firms. But now, they are dominated by financial corporations. This change has been accompanied by deleterious effects on economic growth, stagnant wages, and an upward shift in the distribution of income and wealth. The increasing importance of finance in the economy in the United States, at least, is illustrated by the above graph. The impact of the global financial crisis is immediately apparent in 2008.

The distinction between having investment directed by finance or by industry might not make any sense to you if you think of every investment as like purchasing a bond. In this sort of way of looking at things, every investment can be evaluated by a Return On Investment, taking suitable account of risk, the payback period, and so on. It does not matter if one is talking about a college degree; research and development in, say, clean energy; a painting by Monet; or a stock option. To the financier, it is all one.

I take some of the most notable work of Alfred Eichner (1937-1988) as a description of the previous era. Eichner learned a lot about how corporations set prices by looking at the results of Senate Committee on the Judiciary, Subcommittee on Antitrust and Monopoly, as chaired by Estes Kefauver. Various corporate executives from the steel industry testified. Rubio, as I understand it, could similarly investigate how American businesses operate now.

Eichner theorized megacorporations. These are corporations that operate multiple plants and produce multiple products and that try to maintain market power. Eichner took aboard the idea, as developed by Gardiner Means and Adolfe Berle (1932), that ownership and control are separate in the modern corporation. In a sense recently explained by Dan Davies, Eichner's approach is microfounded. His theory is consistent with recognizing the principal agent problems that come about when a corporate board is somewhat independent of stock owners, when corporate executives are another group of personnel, and so one. According to Eichner, managers in the megacorp are interested in pursuing a satisfactory rate of growth, not in maximizing economic profits.

Eichner recognizes that corporations set prices as a markup on costs. He builds on the survey findings of R. L. Hall and C. J. Hitch. Eichner's ideas relate to theories of administered or full cost pricing. I guess they are consistent with Robin Marris's managerial theory of the firm.

Markups vary among industries and within an industry over time. How is the markup set? According to Eichner, the markup, at least for industry leaders in price-setting, are put at the level needed to finance investment for planned growth targets. Eichner draws an analogy to a tax, in the Soviet Union, on turnover. This tax was used to finance planned investment.

Eichner had some correspondence with Joan Robinson. He saw his theory of the megacorp as compatible with Post Keynesian theories of growth.

I explicitly do not claim that this theory is descriptive of how investment is determined nowadays in the United States. But I find lots of interesting ideas here.

  • Alfred S. Eichner. 1973. A Theory of the Determination of the Mark-up Under Oligopoly pp. 1184-1200.
  • William Milberg (ed.) 1992. The Megacorp & Macrodynamics: Essays in memory of Alfred Eichner M. E. Sharpe.

Saturday, May 18, 2019


Thursday, May 16, 2019

How To Defend Capitalism?

1.0 Summary of Defense

Last month, Mike Munger purports to "summarize the basic argument for capitalism" (emphasis added). He acknowledges his argument is superficial. I find it excessively so. Munger argues that capitalism:

  • Supports the division of labor
  • Provides price signals so as to direct production appropriately
  • Promotes economies to scale

Ultimately, this defense is that capitalism delivers the goods. Here's a well-expressed, simple defense that, partially, argues along these lines:

It is possible to defend our economic system on the ground that, patched up with Keynesian correctives, it is, as he put it, the 'best in sight'. Or at any rate that it is not too bad, and change is painful. In short, that our system is the best system that we have got.

Or it is possible to take the tough-minded line that Schumpeter derived from Marx. The system is cruel, unjust, turbulent, but it does deliver the goods, and, damn it all, it's the goods that you want.

Or, conceding its defects, to defend it on political grounds - that democracy as we know it could not have grown up under any other system and cannot survive without it.

What is not possible, at this time of day, is to defend it, in the neoclassical style, as a delicate self-regulating mechanism, that has only to be left to itself to produce the greatest satisfaction for all.

But none of the alternative defences really sound very well. Nowadays, to support the status quo, the best course is just to leave all these awkward problems alone." -- Joan Robinson (1962). Economic Philosophy, p. 130

2.0 Division of Labor and Efficiencies of Scale

I am not sure that Munger has three principles. I think of the division of labor and efficiencies of scale as closely related. But are either specific to capitalism, as opposed to any society with large scale production? In some sense, Munger is not necessarily attacking a strawperson. Here's an expression of a wish for a post-capitalist society that is arguably not consistent with large-scale production:

" communist society, where nobody has one exclusive sphere of activity but each can become accomplished in any branch he wishes, society regulates the general production and thus makes it possible for me to do one thing today and another tomorrow, to hunt in the morning, fish in the afternoon, rear cattle in the evening, criticise after dinner, just as I have a mind, without ever becoming hunter, fisherman, herdsman or critic." -- Karl Marx, The German Ideology.

But, maybe with enough automation, such a society would be possible.

I find it of interest that Marx, in The Communist Manifesto and in Capital describes how capitalism brought about a remarkable increase in productivity. I find Marx, on the division of labor, much more concrete and extensive than Adam Smith, even though he is writing about the abstraction of capital in general. How much has been written about what Marx took from Charles Babbage's On the Economy of Machinery and Manufactures? This book has a lot to say about what would now be called Command, Control, Communications, and Intelligence (C3I)?

Anyways, questions arise when a defense of capitalism echoes capitalism's greatest critic.

3.0 Price Signals Consistent with Market Socialism

Munger's second principle, about price signals, draws, I assume, on Friedrich Hayek. I do not see how this is a defense of capitalism, as opposed to markets. Whatever you think of it, a large literature on market socialism exists. Private ownership of capitalist enterprises is not necessary for the existence of price signals. I suppose one could argue about incentives in this context, which I do not think Munger does.

4.0 Other Arguments

I think interesting that Munger does not say anything about the efficient static allocation of resources or the first and second welfare theorems. In some sense, he is correct to put these ideas aside, since a good apologetic argument for capitalism cannot be fashioned in these terms.

On the other hand, Munger avoids all of the issues that John Quiggin brings up in his recent Economics in Two Lessons. Issues with unregulated capitalism include externalities, the assignment and distribution of property rights, and periodic bouts of widespread unemployment. (I find unpersuasive talk of "government failure" as a response to the demonstration that unregulated capitalism is bound to misallocate resources. Is a claim being made that anybody can calculate a closed-form optimal allocation at any point in time?)

5.0 What is Capitalism?

I suspect that Munger supports a fairly hierarchical version of capitalism, with widespread private, brutal, and authoritarian institutions (for example, corporations). Inspired by Chapter 9, "Security and Freedom", of Hayek's The Road to Serfdom, I would ask what is compatible with Munger's apologetics for capitalism? Widespread co-operative, syndicates, and and factory councils? Co-determination, in which union representatives are on corpation boards? Sovereign Wealth Funds, Employee Stock Ownership Plans, Universal basic income, government insurance, and social security?

So Munger's three principles do not seem to rule out either an extensive social democracy or even democratic socialism.