A Fixed Capital System That Is Or Is Not Interlocked

I have defined patterns of switch points in considering perturbations of examples of the choice of technique. For example, I have defined three-technique and four-technique patterns. An obvious extension is to consider how these patterns arise in models of joint production. A simplification is to only consider models of fixed capital without superimposed joint production.

This post lays out an example in which, maybe, some parameter values can lead to a three-technique pattern. I am trying to consider whether I want to allow it to be an interlocked system. The question arises when I lay out a simple example in which a machine can be used for one or two years.

Accordingly, consider an example with the coefficients of production in Table 1. Corn and new machines are finished goods. An old machine is an intermediate good. Intermediate goods cannot be sold for consumption. Processes I and II constitute the machine-producing or machine sector. Processes III and IV are in the corn sector. In each sector, there is one and only one primary process, in which the only inputs are finished goods. Processes I and III are the primary processes in the two sectors. Processes II and IV are secondary processes.

Table 1: Coefficients of Production for The Technology

Input	Process
	(I)	(II)	(III)	(IV)
Labor	a0,1	a0,2	a0,3	a0,4
Corn	a1,1	a1,2	a1,3	a1,4
New Machines	1	0	1	0
Old Machines	0	1	0	1
Outputs
Corn	0	0	b1,3	b1,4
New Machines	b2,1	b2,2	0	0
Old Machines	1	0	1	0

I make the usual assumption, inappropriate for environmental economics, of free disposal. A machine can be discarded without cost after used for only one year; managers of firms can choose not to operate the secondary processes in either sector. I also make the assumption that old machines cannot be transferred between sectors. An old machine jointly produced by the first process can be either discarded or used to operate process II. It cannot be used as an input in process IV. With these assumptions, this is a pure fixed capital system without superimposed joint production. An analysis of the choice of technique must consider the four techniques in Table 2. The cost-minimizing technique can be found by constructing the wage frontier. Demand does not matter except inasmuch as coefficients of production are affected by the scale at which processes are operated.

Table 2: Techniques

Technique	Processes
Alpha	I, III
Beta	I, II, III
Gamma	I, III, IV
Delta	I, II, III, IV

Table 3: Variables with Corn as Numeraire

Variable	Definition
w	Wage, in units of bushels per person-year
r	The rate of profits
p1	Price of a new machine, in units of bushels per machine
p2	Price of an old machine in the machine sector, in units of bushels per machine
p3	Price of an old machine in the corn sector, in units of bushels per machine

Suppose, on the other hand, that an old machine can be transferred between sectors. For example, the old machine jointly produced in the first process can be used in process IV to produce corn. Its history in being used to produce new machines has no effect on its efficiency in then being used to produce corn. Then only thee techniques, Alpha, Beta, and Gamma, would exist. Delta could only arise as a switch point between Beta and Gamma. Only two types of machines would exist. And p₂ would be redefined to be the price an old machine, whatever sector it would be in. This is then an example of an interlocked system. One might think reducing the number of techniques and the number of variables would simplify the model. But a simplification of the price system is available in the non-interlocked system that I do not think is possible for the interlocked system.

I think I am convincing myself that the assumption a system cannot be interlocked is a reasonable assumption.

A Bowles Taxonomy For Economists

Katzner, Bowles, and Resnick on UMass Amherst

Shortly after about 32:30 minutes, Sam Bowles, to laughter, draws a Venn diagram on the board. This is a light talk, and Bowles is explicitly describing economics from his own experience at the University of Massachusetts at Amherst. Bowles places various economists in various subsets. I have varied the names a bit in my reproduction below.

Bowles' Taxonomy

I take the universe to be the set of all economists. Or, maybe, given Bowles includes John Rawls, it is a set of academics concerned with topics Bowles thinks economists should be concerned with. I take it that this taxonomy is not to apply to all time and space, but maybe only to academics from about 1970 to now. I explicitly added Kenneth Arrow, Milton Friedman, and Paul Samuelson as examples of economists that do not fall into any of the three numbered subsets. One might think Arrow extended the domain of economics to include voting, social choice, and health economics. So he illustrates my point about this taxonomy being time-bound. For all its originality, I do not think Samuelson's work on revealed preferences, the Heckscher-Ohlin-Samuelson model of international trade, or a model of overlapping generations, for example, can be said to have extended the domain of topics covered by economics.

Anyways, the three sets are those economists:

1. Who are critical of neoclassical economics.
2. Who want to extend the fields or topics to which economics applies.
3. Who are critical of capitalism.

Bowles talks about the intersection of the three sets as "us". I expanded that to label the intersection of four who I think exemplify radical political economics, as developed at UMass. In the talk, Bowles names more for some of the intersections, and, of course, the UMass economics department included more radicals.

By the way, I think the contrast about what they have to say in these talks at UMass about (Neo) Walrasian General Equilibrium Theory (GET) with what John Eatwell has to say of interest. Bowles and Resnick say that economists have now rid themselves of GET, but they have replaced it with "nothing". Mainstream economics, in some sense, have nothing to say nowadays about how the system works as a whole. And they continue to teach the old, outdated stuff to students.

Economics Of Race And Other Economics For Others

Do economists have anything to say about racism in the United States? Some do. The Review of Black Political Economy, for example, exists.

Other groups in the United States are often thought of as marginalized. I have written about women in economics before. As usual, I want to mention the existence of the International Association for Feminist Economics and their journal Feminist Economics. I also note the existence of Queer Economics: A Reader for those economists that might be of a questioning bent.

Discourse in many academic disciplines about the Other often draw on post-modernism, post-structuralism, and other scary stuff. Some economists have attempted to extend Marxism to engage with postmodernism. Although I have read a bit of David Ruccio and Jack Amariglio, I do not know much about this. I suppose the journal Rethinking Marxism would be worth exploring if you want to know more.

I also do not know much about certain fields, such as development economics, economics of education, labor economics, and urban economics. But I would expect to find much more in their journals relevant to our current sad times than I would in the American Economic Review or the so-called Journal of Political Economy.

None of this has anything to say about whether or not some tenured economists at Chicago are ignorant, reactionary, and full of ressentiment.

Some Positions Some Take On Sraffa's Book

This post lists some views on Production of Commodities by Means of Commodities: A Prelude to a Critique of Economic Theory.

• The quantity flows Sraffa takes as given are those observable in an actual economy at a given time, as with a snapshot (Roncaglia 1978).
• These quantity flows, on the contrary, are at the level of effectual demand (Garegnani 1990).
• These quantity flows are for an economy in a self-replacing state.
• The assumption of constant returns to scale is necessary for drawing any interesting conclusions from Sraffa's work (Samuelson 1990, Samuelson 2000).
• Market prices tend towards or orbit around Sraffa's prices of production in a process akin to gravitational attraction (Garegnani 1990).
• Sraffa's book is an investigation of logical consequences in a system of prices of production, akin to reasoning in geometry; no claims are put forth about tendencies or paths of market prices (Sinha 2012).
• Sraffa started, in the 1920s, in his research for his 1960 book from labor values and Marx's schemes of reproduction in Volume 2 of Capital (De Vivo 2003 and Gilibert 2003).
• Sraffa began, on the contrary, with a formalization of prices in terms of physical real cost; labor values are a corruption of this notion of real costs and Sraffa was not originally inspired by Marx in his economics (Gehrke and Kurz 2006).
• Sraffa showed that labor values are unnecessary and redundant for defining prices of production (Steedman 1981).
• Sraffa, on the contrary, vindicated Marx in his work (Porta 2012 and Bellofiore 2014).
• Sraffa's work cannot be set in historical time (Robinson 1985).
• Sraffa, for methodological reasons, rejected counterfactual reasoning and thus the marginal revolution (Sen 2003).

Some of the above statements are probably stated more strongly than the referenced scholars might endorse. I am also not at all sure those are the best references. They certainly are not the most up-to-date. It is clear at any rate that the Cambridge Capital Controversy was not solely about difficulties in aggregating capital and that Sraffa's approach to economics cannot be subsumed by general equilibrium theory (Hahn 1982).

References

• Bellofiore, Riccardo. 2014. The loneliness of the long distance thinker: Sraffa, Marx, and the critique of economic theory. In Bellofiore and Carter (2014).
• Bellofiore, Riccardo and Scott Carter. 2014. Towards a New Understanding of Sraffa: Insights from Archival Research. New York: Palgrave Macmillan.
• Bharadwaj, Krishna and Bertram Schefold (eds.). 1990. Essays on Piero Sraffa: Critical Perspectives on the Revival of Classical Theory. London: Unwin Hyman.
• de Vivo, Giancarlo. 2003. Sraffa's path to Production of Commodities by Means of Commodities. An interpretation. Contributions to Political Economy 22 (1): 1-25.
• Garegnani, Pierangelo. 1990. Classical versus Marginalist Analysis. In Bharadwaj and Schefold (1990).
• Gehrke, Christian & Heinz D. Kurz. 2006. Sraffa on von Bortkiewicz: Reconstructing the classical theory of value and distribution. History of Political Economy 38 (1): 91-149.
• Gilibert, Giorgio. 2003. The equations unveiled: Sraffa's price equations in the making. Contributions to Political Economy 22 (1): 27-40.
• Hahn, Frank H. 1982. The neo-Ricardians. Cambridge Journal of Economics 6: 352-374.
• Kurz, Heinz D. (ed.). 2000. Critical Essays on Piero Sraffa's Legacy in Economics. Cambridge: Cambridge University Press.
• Porta, Pier Luigi. 2012. Piero Sraffa's early views on classical political economy. Cambridge Journal of Economics 36: 1357-1383.
• Robinson, Joan. 1985. The theory of normal prices and the reconstruction of economic theory.
• Roncaglia, Alessandro. 1978. Sraffa and the Theory of Prices (trans. by J. A. Kregel). New York: John Wiley & Sons.
• Samuelson, Paul A. 1990. Revisionist findings on Sraffa. In Bharadwaj and Schefold (1990) and reprinted in Kurz (2000).
• Samuelson, Paul A. 2000. Sraffa's hits and misses. In Kurz 2000.
• Sen, Amartya. 2003. Sraffa, Wittgenstein, and Gramsci. Journal of Economic Literature 41: 1240-1255.
• Sinha, Ajit. 2012. Listen to Sraffa's silences: a new interpretation of Sraffa's Production of Commodities. Cambridge Journal of Economics 36 (6): 1323-1339.
• Steedman, Ian. 1981. Marx after Sraffa. London: Verso.

A John Eatwell Lecture

John Eatwell On Why Economists Disagee

I like the above lecture by John Eatwell. He concludes by talking about the partial equilibrium model of supply and demand "that we teach, and we justify it by the general equilibrium model". He notes that lots of economists put imperfections in. The Arrow-Debreu is currently the fundamental model of price theory among mainstream economists. According to Eatwell, economists fall into at least five groups.

• Those who think revisions are important to retain market rationality and try to find ways to make the model work, for example, with representative agents in Dynamic Stochastic General Equilibrium models.
• Those who think reasonable, empirically-based imperfections can be used to produce practical models.
• Those who find things that fit empirically and don't worry too much about the explanation. For example, consider the Solow growth model.
• Those, the top econometricians, who simply study economic variables, without a lot of theory.
• In despair, those who are trying to analyze economic variables in entirely new ways, for example, behavioral economists, Colin Cameron.

Economics today is a catalogue of results and models built around a core, the Arrow-Debreu model, the results of which nobody believes. "And we ignore the long run. Economists have a theoretical core, which we don't use, or we modify to take away from its essence, or we don't believe it."

I think that many mainstream economists will refuse to tell an outsider that that is the state of mainstream economics today.

A Letter To Sraffa Long Before Google

At this time, the book had long ago been published by Cambridge University Press. I suppose I ought to review whatever conditions exist on transcribing stuff in the archives. The following is D3/12/111:9.

Routledge & Kegan Paul Ltd.

October 15th 1969

Professor Piero Sraffa,
Trinity College,
CAMBRIDGE

Dear Professor Sraffa,

At the Frankfurt Book Fair last week, Einaudi told me about your "Produzione di merci a mezzo di merci".

I don't know whether this has been published in English, but if not, we would be very interested in publishing it.

Yours sincerely,

Norman Franklin

Extracts From LBJ Announcement Of The Appointment Of The Kerner Commission

My fellow Americans:

We have endured a week such as no Nation should live through: a time of violence and tragedy.

For a few minutes tonight, I want to talk about that tragedy - and I want to talk about the deeper questions it raises for us all.

I am appointing a special Advisory Commission on Civil Disorders.

Governor Otto Kerner, of Illinois, has agreed to serve as Chairman, Mayor John Lindsay, of New York, will serve as Vice Chairman...

The Commission will investigate the origins of the recent disorders in our cities. It will make recommendations - to me, to the Congress, to the State Governors, and to the Mayors - for measures to prevent or contain such disasters in the future.

But even before the Commission begins its work; and before all the evidence is in, there are some things that we can tell about the outbreaks of this summer.

First - let there be no mistake about it - the looting, arson, plunder and pillage which have occurred are not part of a civil rights protest. There is no American right to loot stores, or to burn buildings, or to fire rifles from the rooftops. That is crime - and crime must be dealt with forcefully, and swiftly, and certainty - under law...

Those charged with the responsibility of law enforcement should, and must, be respected by all of our people. The violence must be stopped: quickly, finally, and permanently.

It would compound the tragedy, however, if we should settle for order that is imposed by the muzzle of a gun.

In America, we seek more than the uneasy calm of martial law. We seek peace based on one man's respect for another man - and upon mutual respect for law. We seek a public order that is built on steady progress in meeting the needs of all our people.

Not even the sternest police action, nor the most effective Federal Troops, can create lasting peace in our cities.

The only genuine, long-range solution for what has happened lies in an attack - mounted at every level - upon the conditions that breed despair and violence. All of us know what those conditions are: ignorance, discrimination, slums, poverty, disease, not enough jobs. We should attack these conditions - not because we are frightened by conflict, but because we are fired by conscience. We should attack them because there is simply no other way to achieve a decent and orderly society in America...

This is not a time for angry reaction. It is a time for action: starting with legislative action to improve the life in our cities. The strength and promise of the law are the surest remedies for tragedy in the street.

But laws are only one answer. Another answer lies in the way our people will respond to these disturbances.

There is a danger that the worst toll of this tragedy will be counted in the hearts of Americans; in hatred, in insecurity, in fear, in heated words which will not end the conflict, but prolong it.

So let us acknowledge the tragedy; but let us not exaggerate it...

-- Lyndon Baines Johnson, 27 July 1967

The Kerner Commission concluded, among many other things, "Our nation is moving toward two societies, one black, one white - separate and unequal."

More On A Fixed Capital Example

Figure 1: A Partition of a Parameter Space for the Schefold Example

1.0 Introduction

I want to revisit a perturbation analysis of an example, from Bertram Schefold, of reswitching with fixed capital.

Suppose workers use a machine to produce something or other, where the machine lasts several production periods. It is a possible choice to run the machine for less than its full physical life. One might think that choosing to adopt a technique with a longer economic life of the machine is, in some sense, more capital-intensive than choosing to junk it sooner. And this will lead to more output per worker. But, I am surprised to say, this is just not so. The underlying vision of Austrian-school economists is wrong even here.

If I worked through all the problems, with full understanding of their implications, in Kurz and Salvadori (1995), I would probably already know this. But, at least, I can make this point by examining perturbations of a single numeric example.

2. Technology

Table 1 shows the coefficients of production for the three processes comprising the available technology. Inputs must be available at the beginning of the year, and outputs become available at the harvest at the end. In the first process, labor uses inputs of corn to produce a new machine. That machine is used by labor in the second process, with inputs of seed corn, to produce more corn and a one-year old machine. In the third process, labor uses inputs of seed corn and the one-year old machine to produce corn. (I did think of calling the machine a "tractor".) The machine varies in physical efficiency over the course of its lifetime. In its second year, it requires less labor to tend it, but more inputs of corn.

Table 1: Coefficients of Production for The Technology

Input	Process
	(I)	(II)	(III)
Labor	(1/10) e1 - σ t	(43/40) e1 - φ t	e1 - φ t
Corn	(1/16) e1 - σ t	(1/16) e1 - φ t	(1/4) e1 - φ t
New Machines	0	1	0
Old Machines	0	0	1
Outputs
Corn	0	1	1
New Machines	1	0	0
Old Machines	0	1	0

I postulate the possibility of technical progress. The parameter σ specifies the rate of technical progress in producing machines, while φ specifies the rate of technical progress in using machines to produce corn. When (σ t) and (φ t) are unity, this is a reswitching example from Bertram Schefold (1980: 179). Corn is assumed to be the only consumer good, and it also is used as circulating capital. I also take a unit of corn as the numeraire.

A choice of technique arises. I call Alpha the technique in which the machine is operated only one year, and I assume free disposal. Beta is the technique in which the machine is operated for its full physical life time.

3.0 Price Equations

I take corn as numeraire. Although I do not make use of this generality in this post, I formulate systems of equalities and inequalities for prices of production with the possibility of persistent differences in the rate of profits among processes. p₁ is the price of a new machine, p₂ is the price of an old machine, w is the wage, and r is the scale factor for the rate of profits. The relative rates of profits are specified by given ratios s₁, s₂, and s₃ for the processes, which I take to be unity throughout. Coefficients of production are taken as given; one might think of the parameter t as expressing a very slow, secular time. With these parameters, and either the wage or the scale factor for the rate of profits taken as given, one solves for the prices of new and old machines, the other distributive variable, and the choice of technique.

3.1 Price Equations for the Alpha Technique

Suppose the Alpha technique is cost-minimizing, and the machine is discarded after being used for one year. The price of a new machine, the wage, and the scale factor for the rate of profits are related by the following two equations:

[(1/16) e^{1 - σ t}](1 + s₁ r) + [(1/10) e^{1 - σ t}] w = p₁

[(1/16) e^{1 - φ t} + p₁](1 + s₂ r) + [(43/40) e^{1 - φ t}] w = 1

The first equations comes from the process for producing a new machine. The second equation comes from the process for producing corn with a new machine. The price of an old machine is zero:

p₂ = 0

For the Alpha technique to be cost-minimizing, extra profits must not be available from operating the process that produces corn with an old machine. That is, the cost of a unit level operation of that process must not fall below revenues:

[(1/4) e^{1 - φ t}](1 + s₃ r) + [e^{1 - φ t}] w ≥ 1

A switch point exists when the above equation is met with equality.

3.2 Price Equations for the Beta Technique

Now suppose the Beta technique is cost-minimizing. The prices of a new and old machine, the wage, and the scale factor for the rate of profits are related by three equations:

[(1/16) e^{1 - σ t}](1 + s₁ r) + [(1/10) e^{1 - σ t}] w = p₁

[(1/16) e^{1 - φ t} + p₁](1 + s₂ r) + [(43/40) e^{1 - φ t}] w = 1 + p₂

[(1/4) e^{1 - φ t} + p₂](1 + s₃ r) + [e^{1 - φ t}] w = 1

For the Beta technique to be cost-minimizing, the price of an old machine must not be negative.

p₂ ≥ 0

Here, too, a switch point exists when the above equation is met with equality. Suppose prices of production for the Beta technique yield a negative price for an old machine. This is a signal to firms that they should truncate the economic life of the machine. They should only operate it for one year.

4.0 Perturbations

I do my usual thing of analyzing how the choice of technique varies with technical progress along a secular path, given values of parameters that specify the rate of decrease in specified coefficients of production. Technical progress in the example reduces the inputs of labor and circulating capital needed to produce a given output. The notation allows the rate of technical progress to differ between the machine and corn industries. The rate of technical progress is assumed to affect both processes that produce corn in the same way, whether or not the machine the workers use is new or old.

4.1 A Temporal Path

The choice of technique varies with distribution and technical progress. Figure 2 illustrates one particular ratio of the rate of technical progress in producing machines to the rate in using machines. Changes in the number and characteristics of switch points occur with patterns already described in previous blog posts. Switch points appear over the axis for the rate of profits and over the wage axis. Schefold's particular parameterization occurs just before switch points vanish in a reswitching pattern.

Figure 2: A Case of Variation in Switch Points with Technical Progress

4.2 Another Temporal Path

Figure 3 illustrates another particular ratio of the rate of technical progress in producing machines to the rate in using machines. Here too, the technical progress in using machines overwhelms technical progress in producing machines, and this is manifested by a transition ultimately from a region in which the economic life of a machine is one year to a region in which its economic life is its whole physical life, whatever the distribution of income. In this example of technical progress, a pattern over the wage axis precedes a pattern over the axis for the rate of profits. A reswitching example arises and disappears. It is then cost-minimizing to run the machine for its full physical life at high and low wages, but at intermediate wages cost-minimizing firms will truncate the economic life of the machine.

Figure 3: Another Case of Variation in Switch Points with Technical Progress

4.3 A Partition of the Parameter Space

At each point on the two paths through logical time characterized by Figures 2 and 3, the amount of technical progress in producing machines and in using machines is specified. Figure 1 partitions the resulting parameter space, based, as usual, on the number and characteristics of switch points in the choice of technique. Table 2 notes the switch points and lists the cost-minimizing technique, from a low to a high wage, for each numbered region. The locii separating Regions 1 and 2 and Regions 3 and 4 are parallel affine functions. The locus for the reswitching pattern is tangent to the locus for the pattern over the wage axis at the intersection of Regions 2, 3, and 4. Figure 1 demonstrates the applicability of the taxonomy of fluke switch points to the case of fixed capital.

Table 2: The Wage Frontier in Selected Regions in Parameter Space

Region	Switch Points	Cost-Minimizing Techniques
1	None	Alpha
2	One	Beta, Alpha
3	Two	Beta, Alpha, Beta
4	None	Beta
5	One	Alpha, Beta

The Schefold example is in narrow edge at the left of Region 3, along the dotted line corresponding to Figure 2. Just as this approach of partitioning (projections of) parameter spaces can be used to construct fluke switch points, it can also be used to improve examples of non-fluke switch points. Other parameters in Region 3 can result in switch points further apart on the wage frontier. The price of an old machine, at prices of production for the Beta technique, can be more noticeably negative when the Alpha technique is cost-minimizing.

5.0 Compare and Contrast Regions 2 and 5

Comparing and contrasting the single switch point in Regions 2 and 5 is interesting. Figures 4 and 5 illustrate the application of the direct method to analyze the choice of technique. When the machine is junked after one year, the price of an old machine is zero. Figure 4 shows extra profits in operating the machine for the second year with prices of production in this case. Around the switch point in Region 2, it pays to run the machine for a second year for higher rates of profits. On the other hand, around the switch point in Region 5, it pays to run the machine for the second year at lower rates of profits. Figure 5 shows the price of the old machine, given prices of production, when the machine is run for two years. A negative price shows that the cost-minimizing firm should truncate the economic life of machine to one year. Both figures yield the same conclusion about the choice of technique in the two regions. (This consistency is guaranteed in a pure fixed capital example with no superimposed joint production.)

Figure 4: Regions 2 and 5 with Price of Old Machine of Zero

Figure 5: Price of Production when Machine Runs for Two Years

Around the switch points in both Regions 2 and 5, a lower wage is associated with cost-minimizing firms wanting to hire more labor, given net output (Table 3). As one might expect, the adoption of a more labor-intensive technique is associated with lower net output per worker. It seems that the economic life of a machine cannot be mapped to the capital-intensity of a technique. Adopting a technique in which a machine is run longer is not necessarily more capital-intensive in that it does not necessarily raise output per worker for the economy as a whole. This counter-intuitive result, at least by traditional neoclassical and Austrian teaching, obtains in Region 2.

Table 3: Selected Characteristics of Switch Point in Regions 2 and 5

	Region 2	Region 5
Economic Life of Machine	Run for two years at higher rate of profits	Run for one year at higher rate of profits
Consumption per Person-Year	Decreased at higher rates of profits	Decreased at higher rate of profits
Employment, given net corn output	Increased at lower wage	Increased at lower wage

6.0 Conclusion

Unambiguous physical measures are available here for examining central claims in Austrian capital theory. Net output in a stationary state in this model consists of a single consumption good, and labor is taken as homogeneous. Around a switch point exhibiting capital-reversing, a lower interest rate is associated with the adoption of a technique that produces less net output per unit of labor time. If a financial measure of capital intensity is adopted such that, around all switch points, lower interest rates are associated with the use of a technique with a longer average period of production, the association between more roundabout methods of production and greater productivity is broken. Austrian capital theory and Austrian business cycle theory fails to be sustained

In a model of fixed capital with only a single machine in use, the number of production cycles for the economic life of the machine is an unambiguous measure of roundaboutness. The numerical example in this chapter reveal that no connection necessarily exists between lower interest rates and the extension of the economic life of a machine. The example in Region 3 is a reswitching example. Necessarily, in a reswitching example in a model of fixed capital, a lower rate of profits is associated, around one of the switch points, with the truncation of the economic life of the machine.

The Austrian theory of capital is also refuted in Region 2 in the example, even with a single switch point. Around the switch point, a lower rate of profits is associated with a truncation of the economic life of a machine, not the extension of how long this machine is used in production cycles. And that truncation is associated with a more capital-intensive technique, as is seen in an increase in net output per worker. These examples demonstrate that the underlying vision behind the Austrian story is simply incorrect. Attempts to evade this proof by adopting a financial definition of capital simply ignore the points at issue.

Financial Economics

This is a list of some of what I think one should know if one wants to talk to investors interested in theory. This post is not about making money and is probably not up-to-date. My references are fairly popular, and mostly old. I include one recent popular book as an example. Most of the references I do not recall very well, and I have not read Ben Graham. But many seem to know that Warren Buffet recommends this book. This post is non-critical. Keen and Quiggin in Debunking Economics and Zombie Economics, each have a chapter of criticism.

• Behavioral finance: The application of behavioral economics to finance.
• Beta: A parameter in the CAPM.
• Black Scholes formula: A formula for pricing options.
• Capital Asset Pricing Model (CAPM): A model that relates the risk of an asset to the market as a whole.
• Efficient Market Hypothesis (EMH): A model in which all information is quickly built into asset prices. The EMH comes in at least three types.
• Equity Premium Puzzle: The observed phenomena for stocks (or shares) to trade at higher prices, as compared to bonds, than can be justified by the EMH.
• Lévy distribution: A family of probability distributions that, except for the limiting case of the Gaussian distribution, have an infinite variance. The Cauchy distribution is also a member. Benoit Mandelbrot recommends this as a model for changes in asset prices.
• Martingale Theory: A branch of mathematics in which a stochastic process exhibits a special case of the Markov property. I recall learning about a drunkards walk and the gambler's ruin problem, but I do not recall this term in any of my formal math courses.
• Modigliani and Miller (M and M): A model that implies, under idealizations, that it does not matter if corporations finance investments with equity or debt.
• Noise trading: Trading on random variations in the price of an asset, instead of fundamentals. I know of this from some late 80s work of DeLong, Shleifer, Summers, and Waldmann.
• Stochastic Calculus, also known as Ito Calculus: A branch of mathematics in which one can talk about the derivatives and integrals of a set of random variables indexed on continuous time. Such a stochastic process is different from a single realization).
• Value-at-risk: A formula that applies to an investment portfolio.
• Volatility skew: An anomaly, inconsistent with the Black-Scholes formula, that emerged in markets for options.

One also needs to know about puts, calls, indices, credit default swaps, types of spreads (e.g. a broken wing butterfly spread) and so on if one wants to be a financial analyst. As usual, this is an aspirational post. I do not claim to know all of this, and maybe I have gotten some of the above incorrect.

References

• Akerlof, George A. and Robert J. J. Shiller. 2010. Animal Spirits: How Human Psychology Drives the Economy, and Why It Matters for Global Capitalism. Princeton University Press.
• Bernstein, Peter L. 2009. Capital Ideas: The Improbable Origins of Modern Wall Street.
• Davies, Daniel. 2018. Lying for Money: How Legendary Frauds Reveal the Workings of our World. Profile Books.
• Derman, Emanuel. 2016. My Life as a Quant: Reflections on Physics and Finance.
• Graham, Benjamin. The Intelligent Investor
• Henwood, Doug. 1997. Wall Street: How It Works and for Whom. Verso.
• MacKenzie, Donald. 2008. An Engine, Not a Camera: How Financial Models Shape Markets. MIT Press.
• McCauley, Joseph L. 2009. Dynamics of Markets: The New Financial Economics, 2nd edition. Cambridge University Press.
• Thorp, Edward O. and Sheen T. Kassouf. 1967. Beat the Market: A Scientific Stock Market System.

Elsewhere

• A podcast interview with Philip Mirowski about how, roughly, neoliberals are exploiting the Corona Virus crisis in America.
• A book, Nine Lives of Neoliberalism, edited by Dieter Plehwe, Quinn Slobodian, and Philip Mirowski. Somewhere this is or was freely downloadable in PDF.
• A podcast interview with Marshall Steinbaum about the Chicago school of economics.
• A podcast episode, by two economics professor, trying to present an overview of Joan Robinson.
• A downloadable book, Labour and Value: Rethinking Marx's Theory of Exploitation, by Ernesto Screpanti.
• Two young friends discuss Steve Keen's book, Debunking Economics.

A Refutation Of Austrian Capital Theory And Austrian Business Cycle Theory

1.0 Introduction

I have not posted about a non-fluke switch point in a while. This is an example from Bertram Schefold. I have examined perturbations and variations of this example before.

Here I present an example with tables exhibiting arithmetic. Is this any more transparent than examples presented with graphs?

I have been listening to some lectures on YouTube, especially Richard Wolff. I now have another hypothesis why mainstream economists have been promoting lies, ignorance, and nonsense for half a century: fear. The history of economics includes purge after purge after purge. Maybe many mainstream economists are cowed by their rulers.

2.0 Technology

Three processes are available for use in production. Each process is specified by coefficients of production (Table 1), when operated at an unit level. The person-years of labor employed, the bushels of corn used up in a process, and the number of new and old machines are specified. Outputs consist of bushels corn and new and old machines. Corn is both a consumer good and functions as circulating capital. Machines function as fixed capital. A machine's productivity varies with its age. An older machine requires less labor to operate, but more circulating capital.

Table 1: Coefficients of Production for The Technology

Input	Process
	(I)	(II)	(III)
Labor	1/10	43/40	1
Corn	1/16	1/16	1/4
New Machines	0	1	0
Old Machines	0	0	1
Outputs
Corn	0	1	1
New Machines	1	0	0
Old Machines	0	1	0

Suppose all three processes are run at unit level in parallel. At suppose at the start of the year, the firm has one new machine, one one-year old machine, and 3/8 bushels corn. The output of the first process is one new machine. The previously existing new machine is consumed in the second process, leaving an output of one one-year old machine. The third process uses up the one one-old year machine. So these processes reproduce the stock of new and old machines. But they also use up inputs of 3/8 bushels corn in producing a gross output of two bushels corn. Summing over all three processes, 2 7/40 person years of labor produce, with the capital stock, a net output of 1 5/8 bushels corn. The labor intensity of this technique is 87/65 person-years per bushel.

Assume free disposal for old machines. Another technique would be operated when the use of the machine is truncated after one year. In this case, one should consider the first and second processes being run in parallel at unit level, with a capital stock of one new machine and 1/8 bushels corn reproduced each year. Under this technique, 1 7/40 person years of labor are employed across the two processes. Net output is 7/8 bushels corn. The labor intensity is 47/35 person-years per bushel.

The more labor-intensive technique is the one with the truncated economic life of the machine. How many production cycles firms choose to run machines is an unambiguous physical measure in this example. And choosing to run the machine longer is a choice to adopt a less labor-intensive technique. Just as Eugen Böhm Bawerk says, a longer period of production, in some sense, is a more capital-intensive method. And that increase in the period of production results in greater output per worker. (I am not claiming that the number of production processes is the Austrian average period of production. I am merely noting how transparent the use of time is in this example.)

3.0 Some Accounting

One can easily see how a single firm would operate the last two processes in parallel, or only the process using the new machine, if the use of the machine is truncated. If such a firm was vertically integrated, they would also produce new machines with the first process. The firm can take the wage and the price of corn from the market, under various idealizations. For simplicity, I take a bushel corn as the numeraire. What prices would the accountants use to evaluate new and old machines?

3.1 At an Initial Wage

Consider a starting wage of 35/71 bushels per person-year and prices of machines shown in Table 2. For each process, the cost of capital inputs are the sum of the inputs of corn and machines of specified vintages, evaluated at the given prices. Wages are found from the labor input, evaluated at the given wage. Revenues are the sum of the outputs of corn and machines of specified vintages, evaluated at given prices. I assume wages are paid at the end of the year. So the rate of profits is the ratio of the difference between revenues and wages to the capital costs. With these prices, the owners are happy to operate all three processes. They make the same rate of processes in each, and prices do not signal that they should make any changes.

Table 2: Initial Prices

w = 35/71 ≈ 0.4930, p0 = 99/568 ≈ 0.1743, p1 = 1/284 ≈ 0.003521
	Capital Costs	Wages	Revenues	Rate of Profits
I	0.0625	0.04930	0.1743	100 percent
II	0.2368	0.5299	1.004	100 percent
III	0.2535	0.4930	1	100 percent

3.2 A Higher Wage

Now suppose the wage is 9,055/14,016 bushels per person-year. Table 3 shows accounting when the prices of new and old machines are unchanged. Notice that the rate of profits has fallen, with the rise in the wage, in all processes. But it has fallen to different levels, given that ratio of wages to the cost of capital originally varied among the processes. David Ricardo discusses this effect in the first chapter of his Principles of Political Economy and Taxation. Obviously, the price at which machines are entered into the firm's books must be changed to reflect the change in wages.

Table 3: Initial Prices with Raised Wage

w = 9,055/14,016 ≈ 0.6460, p0 ≈ 0.1743, p1 ≈ 0.003521
	Capital Costs	Wages	Revenues	Rate of Profits
I	0.0625	0.06460	0.1743	75.5 percent
II	0.2368	0.6945	1.004	30.5 percent
III	0.2535	0.6460	1	39.6 percent

Table 4 shows a set of prices such that the same rate of profits is obtained in all three processes. This is not the end of the story, though, The price of a one-year old machine is slightly negative. (My approach for perturbing reswitching examples can make this price more noticeably negative, but maybe I would end up with even more messy fractions.) Instead of decreasing the revenues for the second process from the output of old machines, the managers of the firm can simply throw the old machine away and enter a price of zero for it on its books.

Table 4: Raised Wage and Updated Prices of New and Old Machines

w = 9,055/14,016 ≈ 0.6460, p0 ≈ 0.1531, p1 ≈ -9.563 x 10-5
	Capital Costs	Wages	Revenues	Rate of Profits
I	0.0625	0.06460	0.08852	41.64 percent
II	0.2156	0.6945	0.3054	41.64 percent
III	0.2499	0.6460	0.3539	41.64 percent

Table 5 shows the result of truncating the use of machines. One must, however, set a new accounting price for new machines, as well. Without this adjustment, different rates of profits are obtained in the first two processes. Notice the rate of profits is indeed lower in the third process, which is not used by cost-minimizing firms.

Table 5: Raised Wage and Truncated Use of Machines

w = 9,055/14,016 ≈ 0.6460, p0 ≈ 0.15313, p1 = 0
	Capital Costs	Wages	Revenues	Rate of Profits
I	0.0625	0.06460	0.15313	41.64 percent
II	0.21563	0.6945	1	41.68 percent
III	0.25	0.6460	1	41.58 percent

Table 6 shows the final results of correct accounting, with increased wages. The rate of profits, r, is 5/12, halfway between 1/3 and 1/2. Those rates of profits are the switch points in this example. I have told this story as a matter of accounting for vertically integrated firms. But these are the only prices on the market consistent with a long period position with the postulated wage. How and whether market prices would converge to these prices of production, in a gravitational process (as in Adam Smith's metaphor) is not clear to me. I like the idea that Sraffa's book is about little more than accounting. This idea is not too far away from what Ajit Sinha has been arguing for a number of years.

Table 6: Raised Wage, Truncation, Updated Price of New Machines

w = 9,055/14,016 ≈ 0.6460, p0 = 1,431/9,344 ≈ 0.15315, p1 = 0
	Capital Costs	Wages	Revenues	Rate of Profits
I	0.0625	0.0646	0.15315	41.67 percent
II	0.21565	0.6945	1	41.67 percent
III	0.25	0.6460	1	41.58 percent

3.3 Summary

Table 7: Summary

Wage	Labor Intensity	Rate of Profits
35/71 ≈ 0.4930 bushels per person-yr.	87/65 ≈ 1.338 person-yrs. per bushel	100 percent
9,055/14,016 ≈ 0.6460 bushels per person-yr.	47/35 ≈ 1.343 person-yrs. per bushel	5/12 ≈ 41.7 percent

At a higher wage, firms want to run machines for one year, not two years. The economic life of machines is shortened from the physical life. And firms want to hire more workers to produce a net output.

Why might the wage rise and the rate of profits fall? In one theory, known to be nonsense, a shock might lead to labor be less abundant, as compared to capital. Perhaps people become more forward-looking and more willing to save, or the population falls for some reason. Wages rise, and firms take this as a signal to substitute capital for labor. But, in the example, a higher wage is associated with the adoption of a less capital-intensive technique and a rise in labor intensity. Somehow, if equilibrium is to be obtained, an increase in the labor force must be accompanied by a rise in wages.

Perhaps one can find a financial measure of capital, such as Hicks' average period of production, where a higher capital-intensity is always associated with a lower rate of profits around a switch point. But then one would have to grapple with the fact that more 'capital' does not always result in more output. Austrian school economists cannot seem to handle that their theory of 'malinvestment' is just incorrect.

Old Findings For New Times

From John Kenneth Galbraith's The Affluent Society (1958), I know that widespread attitude to waged work among some in the United States is outdated. The conventional wisdom is that work is necessary because it is needed to produce the goods that sustain society. That was largely true before productivity increased so much, for example, in the post war golden age. Some jobs are still essential, by any narrow definition, but much wage work goes to creating goods and services that in any previous society would have been considered useless luxuries. (As I get older though, I disagree with Galbraith about medicines to improve peristalsis.) But waged work, in the current system, is essential for providing the income needed to sustain the demand to keep the system going.

From Paul Davidson and Joan Robinson, I know about the distinction between historical and logical time. It as not as if the economy is in an equilibrium that will be approached again, and quickly, after a downward shock is removed. People will recall, and those who are out of work will try to cut back their spending. States and localities that have had to increase their spending to address such a shock will need to retain the ability to spend, and even to increase spending.

From Michal Kalecki's "Political aspects of full employment" (1943), I know that the ruling bourgeois class cannot be counted on to support what is even in their immediate short term financial interest. Unemployment is convenient for keeping the mass majority of the population, the labor force, cringing and hard to press for more of a share in the commodities that they produce. Even so, the backwardness of politics in the United States these days is hard to explain.

From Hannah Arendt's Eichmann in Jerusalem (1963), I know that one strategy in implementing totalitarianism is to declare a marginal group stateless, outside your laws and international laws. Refugees and immigrants are one such group that one could try to apply this strategy to, if you are for evil. From Carl Schmitt's The Concept of the Political (1932), I know that sovereign is he who can declare the state of exception. I resent that these ideas are relevant today.

A Fluke Switch Point On The Wage Frontier

Figure 1: A Switch Point On The Wage Frontier with Wage Curves Tangent

This post extends the example in my article in Structural Change and Economic Dynamics, suitably emended.

Figure 2 shows an enlargement of part of the parameter space. The parameters of the point where the boundaries of Regions 1, 2, and 3 intersect are shown. In Region 1, the Beta technique is uniquely cost-minimizing for all feasible wages; there are no switch points. Region 2 is a reswitching example, with Beta cost-minimizing at low and high wages. One switch point exists in Region 3, with the Beta technique cost-minimizing at low wages.

Figure 2: Part of Parameter Space

The boundary between Regions 1 and 2 is tangent to the boundary between Regions 1 or 2 and Region 3. In what I am calling a reswitching pattern, the scale factor for the rate of profits is found as a double root for a polynomial equation. I have extended the boundary between Regions 1 and 2, with the dotted line, to show where this double root occurs with a negative scale factor for the rate of profits.

Figure 1, at the top of this post, shows wage curves for the example for the parameter values noted in Figure 2. (I used Octave to help with my arithmetic.) The Beta technique is cost-minimizing for all feasible wages. When the wage is at its maximum, the Alpha technique is also cost minimizing. And, at the switch point, the two wage curves are tangent. This is a fluke switch point twice over.

This sort of fluke switch point cannot be expected to be found in empirical data from, say, National Income and Product Accounts. The fluke cases I have been developing are important in that they illustrate partitions in a parameter space for certain models of the choice of technique. They arise as certain characteristics of markets vary with a perturbation of model parameters.

I am not sure what to make of structures within the parts of the parameter space I have been exploring. If you think about, you can see why that must be a point of tangency in Figure 2. Maybe the most striking structure I have found is parallel lines for partitioning a parameter space associated with an example of Harrod-neutral technical change.

I write this stuff as escapism. A lot of economists I build on are in Italy, which is a worrisome place to be these days. I hope you are doing well.

A Fluke Case With Two Fluke Switch Points

Figure 1: Switch Points On The Axis For The Rate Of Profits And At r = -100 Percent

This is an example of a fluke case in the analysis of the choice of technique. The interest in flukes, for me, is that they show how the characteristics of markets can change. They provide insight into structural economic dynamics, as Luigi Pasinetti calls it.

I have previously shown a fluke case, with a switch point on the axis for the rate of profits with a real Wicksell effect of zero. A perturbation of the example can lead to a reswitching example. The switch point at a wage of zero (when the workers live on air) then becomes one at a positive wage. And around that switch point, a higher wage is associated with cost minimizing firms hiring more workers to produce a given net output.

In the example in this post, the switch point on the axis for the rate of profits exhibits neither a forward nor a reverse substitution of labor. The labor coefficient in the corn industry does not vary with the processes in the technique. The Alpha technique has a ghostly presence. It can only be chosen, and not even uniquely so, when the wage is zero. A perturbation of this example can lead to one of the reverse substitution of labor. The switch point on the axis for the rate of zero would also become one at a positive wage. And that switch point might be the only switch point on the frontier at a non-negative rate of profits. Around that switch point, a higher wage is associated with cost-minimizing firms hiring more workers to produce a given gross output of corn. The labor coefficient in the corn-producing process for the technique preferred at a higher wage is larger.

Table 1: Coefficients of Production for The Technology

Input	Iron	Corn Industry
		Alpha	Beta
Labor	1	0.64097922	0.64097922
Iron	9/20	0.00157618	0.01686787
Corn	2	0.48125981	0.0674715

Table 1 specifies the technology in my usual way. I assume labor is advanced, and wages are paid out of the product at the end of a production cycle. I take a unit of corn as numeraire. Prices of production are here defined with a uniform rate of profits between the industry. I found this example with numerical exploration, so there is some round-off error in the figures.

This post is another demonstration that explaining wages and employment by supply and demand, even under ideal competitive conditions, is incoherent nonsense.

A Market Algorithm

Figure 1: Specification of a Market Algorithm

1.0 Introduction

This article is heavily based on Bidard (2004).

An approach to the analysis of the choice of technique, in keeping with construction of the outer envelope of wage curves, is to consider replacing processes, more or less, one at a time. This post presents this approach as following an algorithm.

Assume that a set of techniques exist where all techniques are at least viable, indecomposable, and produce the same set of commodities. From the set of techniques, one can form a set of processes. In each process, workers produce a single commodity at the end of the year from certain inputs. The inputs, by assumption, are totally consumed in the course of the year. I also assume that the numeraire is specified.

Consider the algorithm specified by the flowchart in Figure 1. For this to be an algorithm, Steps 1 and 3 must be fully specified. One might as well assume that a known pseudo random number generator is used with a specified initial seed. Whether or not a candidate process yields extra profits is found in Step 5 with the prices of production calculated in Step 2. A process yields extra profits if and only if:

p a_.,j (1 + r) + w a_0,j > p_j

where a_0,j is the direct labor coefficient, and a_.,j is a column vector for the new process. I am imagining that a_.,j is the j column of the Leontief input-output matrix for a new technique. This new technique is formed by replacing a process in the technique previously selected in Step 2. Since, by assumption, no joint production exists, the process to be replaced is easily found. It is the process in the current technique that produces the same commodity as the candidate process. I have taken the wage as given in this specification of the algorithm. One could just as well take rates of profits as given.

This algorithm converges to a cost-minimizing technique. Consider the sequence of Steps enumerated as ‘2, 3, 4, (5, 7, 9)*, 5, 6, 2’. This expression denotes a single path around the loop on the bottom left of Figure 1, including zero or more paths around the loop on the right. As long as the loop on the right is repeated less times than the number of techniques, this path can be repeated. The question arises whether or not this algorithm contains an infinite loop. In a simple case, a process would be introduced into a technique because it is cost-minimizing for prices corresponding to the first technique, and that first technique would be cost-minimizing at the prices corresponding to the new technique. It can be shown that the existence of an infinite loop is impossible, under the assumption that no joint production exists. The algorithm always terminates.

(The use of metalinguistic symbols of parentheses and an asterisk to denote a repeated sequence of symbols is a convention in defining regular expressions. A sequence of symbols in a language, where the grammar of that language is specified by a regular expression, is accepted by a finite state machine, a type of automata. This is the lowest level of the Chomsky hierarchy. Chomsky (1965) uses transformational grammars to characterize human languages, which he argues are at the highest level of the hierarchy.)

Furthermore, except at switch points, the cost-minimizing technique found by the algorithm is unique. Which technique is initially selected at Step 1 or how processes are ordered at Step 3 does not matter, except for performance. The same cost-minimizing technique is ultimately found. The algorithm terminates with the selection of any one of the techniques that are cost minimizing at a switch point, depending on these details.

The algorithm is specified sequentially in Figure 1. Steps 3, 4, 5, 7, and 9 can be distributed. Inasmuch as this algorithm is executed in a capitalist economy, these steps are, in fact, distributed across firms. One might also modify the algorithm to apply when the set of processes and techniques are not known at that start of algorithm. Innovation and technical progress can be accommodated with an appropriate modification of Step 4 and Step 9. Step 7 should be eliminated, and the algorithm would be defined without a termination step, like daemons in operating systems. When the algorithm is modified for distributed processing, more than one process might be introduced into a technique simultaneously, including in the same industry. For which technique, then, are prices calculated in Step 2? This relates to the question of when labor expended in new processes is ‘socially necessary’, as Marx put it.

References

• Bidard, Christian. 2004. Prices, Reproduction, Scarcity. Cambridge: Cambridge University Press.
• Chomsky, Noam. 1965. Aspects of the Theory of Syntax. Cambridge: M.I.T. Press.

Another Example Of The Factor Price Frontier In The Space Of Rental Prices

Figure 1: Real Factor Price Frontier

1.0 Introduction

I am planning on posting at an even slower rate for a while.

This post continues my exploration of a way of visualizing the choice of technique proposed by Carlo Milana. In this post, I show how to correctly apply his visualization to an example from my 2017 ROPE paper.

2.0 Technology

Two techniques are available for producing corn, the consumption good. Each technique consists of a flow-input, point-output technology, with a finite number of dated labor inputs. The technology can also be represented with intermediate produced commodities explicitly shown. Table 1 sets out the example as a Leontief input-output table, in some sense. Each column lists the inputs in a production process needed to produce a unit output of the commodity named in the column heading. The entries for the row for corn are all zero, indicating it is not an input into any production process. All processes require a year to complete and completely use up their commodity inputs in producing their outputs. Each process requires a year to complete, and inputs must be hired at the start of the year, independently of when payments for inputs are contracted to be paid out. The example includes four factors of production: labor, and three capital goods.

Table 1: Coefficients of Production for The Technology

Input	Industry 1	Industry 2	Industry 3	Corn Industry
				Alpha	Beta
Labor	50	0	115	66	0
Commodity 1	0	1	0	0	0
Commodity 2	0	0	0	1	0
Commodity 3	0	0	0	0	1
Corn	0	0	0	0	0

The Alpha process consists of the processes for producing the first two commodities and the corn-producing process labeled Alpha. The Beta process consists of the process for producing the third commodity and the corn-producing process labeled Beta. The net output of a technique, when all processes comprising that technique are operated at the unit level, is a bushel of corn. The non-labor inputs needed to continue production with that technique are reproduced in the same quantities with this activation of processes.

3.0 Price System

I here formulate systems of equations (and inequalities) in terms of spot prices and rental prices for factors of production. A rental price pays for the services of a factor of production, and is paid at the end of the year. I formulate the example with the following variables:

• w_L: The wage, paid at the end of the year. Also known as the rental price for labor.
• p₁: The spot price for the first produced capital good.
• w₁: The rental price for the services of the first capital good.
• p₂: The spot price for the second produced capital good.
• w₂: The rental price for the services of the second capital good.
• p₃: The spot price for the third produced capital good.
• w₃: The rental price for the services of the third capital good.
• p_c: The spot price for corn.
• r: The interest rate.

In a circulating capital model of long period positions, rental prices and spot prices relate like so:

w_j = p_j(1 + r), j = 1, 2, 3

Since this is not a model of a slave economy, no spot price exists for labor. Corn is never used as a factor of production and does not have a rental price.

The price equations are such that no extra profits can be made in any process. Furthermore, costs do not exceed revenues in any operated process. Corn is assumed to be the numeraire. Figure 1, above, graphs the solution. This is actually a two-dimensional representation of a projection of a four-dimensional structure into three dimensions. The fourth dimension is the rental price for the first produced capital good.

3.1 Prices for the Alpha Technique

Suppose managers of firms have adopted the Alpha technique. The condition that the corn-producing process in the Alpha technique is adopted and pays no extra profits is expressed as:

66 (w_L/p_c) + (w₂/p_c) = 1

The above equation gives rise to the blue plane in the figure. The analogous condition for the process to produce the first capital good is expressed as:

50 (w_L/p_c) = (p₁/p_c)

The same sort of condition for the process for producing the second capital good is:

(w₁/p_c) = (p₂/p_c)

When the Alpha technique is adopted, prices may or may not enable managers of firms to activate the process for producing the third capital good. This condition is express as an inequality:

115 (w_L/p_c) ≥ (p₃/p_c)

In the graphed solution, the above inequality is treated as an equality, giving rise to the factor-price curve for the Alpha technique. An inequality arises for the corn-producing process in the Beta technique.

(w₃/p_c) ≥ 1

The above inequality cannot be combined with the other equations in the Alpha price system except between the switch points. That is, the factor price curve for the Alpha technique is the factor price frontier only between the switch points.

3.1 Prices for the Beta Technique

Now suppose that managers of firms have adopted the Beta technique. The condition that the corn-producing process in the Beta technique is adopted and pays no extra profits is expressed as:

(w₃/p_c) = 1

The above equation gives rise to the red plane in the figure. The analogous condition for the process to produce the third capital good is expressed as:

115 (w_L/p_c) = (p₃/p_c)

Inequalities arise for the processes for producing the first and second capital goods:

50 (w_L/p_c) ≥ (p₁/p_c)

(w₁/p_c) ≥ (p₂/p_c)

Likewise, an inequality arises for the corn-producing process in the Beta technique:

66 (w_L/p_c) + (w₂/p_c) ≥ 1

3.3 Solution of Price Equations

Table 2 displays the solution for the two systems of equations and inequalities. The equations impose a relationship between the wage and the interest rate, either of which could be given from outside the period of production. Spot prices for the three capital goods can be found by discounting rental prices to the start of the year.

Table 2: Factor Prices in the Example

Price	Alpha	Beta
(wL/pc)	1/(2 (33 + 25 (1 + r)2))	1/(115 (1 + r))
(w1/pc)	25 (1 + r)/(33 + 25 (1 + r)2)	10/23
(w2/pc)	25 (1 + r)2/(33 + 25 (1 + r)2)	10 (1 + r)/23
(w3/pc)	115 (1 + r)/(2 (33 + 25 (1 + r)2))	1

In both systems of equations, the rental prices of factors of production are expressed as functions of the interest rate. That is, factor price curves in Figure 1 are specified parametrically. Both factor price curves lie in their respective planes. Switch points lie on the intersection of the two planes in Figure 1. Outside the switch points, the factor price curve for the Beta technique is the factor price frontier. Between the switch points, the factor price curve for the Alpha technique is the factor price frontier.

4.0 Conclusion

Milana is correct in asserting that the interest rate is not a factor price, that is, a rental price for the services of a factor of production. The label "factor price frontier" should properly be reserved for a locus in the space of rental prices. This post has illustrated these claims by showing how to draw such a factor price frontier for a reswitching example with a specific structure.

On "Democratic Socialism"

1.0 Introduction

This post is about some usages of the phrase "democratic socialism".

2.0 Democratic Socialists of America (DSA)

In the context of current American politics, I think the most salient usage today of this phrase is associated with Bernie Sanders' campaign and with the Democratic Socialists of America.

DSA was founded in 1982 when the Democratic Socialist Organizing Committee (DSOC) merged with the New American Movement (NAM). The DSOC was established with Michael Harrington leading others out of the Socialist Party (SP) (Gorman 1995: p. 144-145). Apparently, 500 people attended the DSOC founding convention in 1973 (Harrington 1988: 17).

Michael Harrington will forever be known for The Other America. In this book, he deliberately did not use the word "socialism". And this book had some influence on the policies of Kennedy and Johnson and the latter's war on poverty. He also was something of a theorist. The Twilight of Capitalist is an attempt to apply a tradition of an "underground" Marxism to the conjuncture of 1970s "late capitalism". Harrington mentions Rosa Luxemburg, George Lukacs, Karl Korsch, the Frankfurt school, and Antonio Gramsci, for example, as well as more current thinkers. Hegel and dialectics are important to how Harrington understood Marx.

Some of the left want to establish a political party for the working class and saw that the Democratic party is not such a party. So they think they should have their own party. DSA is and DSOC was the opposite of that. DSA can be said to be openly pursuing a strategy of entryism. The goal is to influence the Democrats from within.

3.0 An Older Usage

But the term goes back much further than these movements in the United States in the 1970s and 1980s. "Democratic socialism" was used in English, in the United States, in the 1950s and early 1960s, by scholars discussing the "revisionism" of Eduard Bernstein.

I turn to the Second International shortly before 1900. As I understand it, a literal translation of the leading socialist party was something like the "Social Democratic Party of Germany" (SPD). I do not want to read much into the phrase "social democratic" here. At the time, Georgi Plekhanov and Vladimir Lenin were in the Russian Social Democratic Party.

In 1899, Engel's literary heir, Eduard Bernstein published a book. The Preconditions of Socialism and the Task of Social Democracy is a literal translation of its title, I guess. The book built on articles he published earlier in Die Neue Zeit. "The final goal is nothing to me, the movement is everything" is a well-known pithy statement from Berstein. He argued for pursuing reforms, supporting trade unions, and a parliamentary party on the foundation of universal suffrage.

Rosa Luxemburg saw a chance here to raise her profile in the socialist movement. Her response, Reform or Revolution, is another classic.

I have always thought of Karl Kautsky as a politician trying to keep advocates of all these tendencies within a single party. His grandson (Kautsky 1994) argues he was consistent, from the time that Lenin hailed him as the leader of the orthodoxy to the time Lenin called him a renegade. Here is a quote from the later time:

"For us... Socialism without democracy is unthinkable. We understand by modern Socialism not merely social organisation of production, but democratic organisation of society as well. Accordingly, Socialism is for us inseparably connected with democracy. No Socialism without democracy." -- Karl Kautsky, The Dictatorship of the Proletariat (1918), as quoted in Kautsky (1994).

By the way, John Kautsky tells of running into college students who were surprised that his granddad's first name was Karl; they thought somehow or other it was "Renegade"

Around 1900, splits and disagreements between more and less radical factions in socialist parties were an international phenomenon. In France, the syndicalist Georges Sorel was a radical and Jean Jaurès was more reformist. The Russians split in 1903, between the Mensheviks and the Bolsheviks. I gather a large part of the Menshevik faction walked out of the party congress, leaving the Bolsheviks the ability to call themselves the "majority", even though they were a minority of the party.

I skip forward any number of years. Maybe half of Sidney Hook's 1955 book is short selections from others. His reading number 54 is excerpted from a statement "adopted by the Socialist International at Frankfurt-on-Main, Germany, 1951." And it is entitled, "The aims and tasks of democratic socialism".

I think of Sidney Hook as an exemplar of an advocate of social democracy. I guess this section argues that the distinction between social democracy and democratic socialism was, at one time, not clear.

References

• Eduard Bernstein. 1961. Evolutionary Socialism: The Classic Statement of Democratic Socialism (trans. by Edith C. Harvey). Schocken.
• Peter Gay. 1952. The Dilemma of Democratic Socialism. Columbia University Press.
• Robert A. Gorman. 1995. Michael Harrington: Speaking American. Routledge.
• Michael Harrington. 1962. The Other America: Poverty in the United States.
• Michael Harrington. 1976. The Twilight of Capitalism. Simon and Schuster.
• Michael Harrington. 1988. The Long-Distance Runner: An Autobiography. Henry Holt.
• Sidney Hook. 1955. Marx and the Marxists. D. Van Nostrand.
• Maurice Isserman. 2001. The Other American: The Life of Michael Harrington.
• John H. Kautsky. 1994. Karl Kautsky: Marxism, Revolution & Democracy. Transaction Publishers.

Two Propositions: Neoclassical Economics Is Incoherent; A Classical Theory Of Value Exists

Some Mathematics Useful In Understanding Classical Political Economy

I consider the following to have been well established about half a century ago:

1. Marginalism or so-called neoclassical economics is impossible to formulate consistently and with practical applications.
2. A mathematically rigorous approach to the classical theory of value, from William Petty through David Ricardo, including Karl Marx, exists.

Mainstream economists ignore the truth of both propositions. Until they stop spouting lies and nonsense, these propositions should be re-iterated again and again. (On the other hand, I appreciate the work involved in compiling National Income and Products Accounts.)

I find a difficulty in publishing re-iterations of these propositions. I expect editors and reviewers of, say, the American Economic Review, the Journal of Political Economy, or the Quarterly Journal of Economics would simply not publish papers stating either proposition. You can publish articles in, say, the Review of Political Economy which re-state these propositions, but any such article must contain something novel. For my purposes, I seem to stumbled upon a research program that includes:

• Exploring what still holds when prices of production are defined with persisting non-uniform rates of profits.
• Exploring and visualizing the effects of perturbing parameters in models of prices of production.
• Refuting those who claim to have some other analysis of the choice of technique in which, say, reswitching examples are supposedly mistaken.

Others have other focii for their research. For example, historians of political economy might be interested in the publication of critical editions of Marx-Engels Collected Works (MEGA) or of Piero Sraffa's archives. Over the last couple of decades, some have worked on exploring problems in joint production and some limitations of the long period method, such as non-reproducible, exhaustible natural resources (as seen, for example, in the corn-guano model). Many other issues have been explored.