Howard Fast Leaves The Communist Party Of The USA After Khrushchev's Secret Speech

This post is another instance of me stumbling over anti-communist literature, in a sense.

I read Howard Fast's novel, Citizen Tom Paine, many years ago. I have never read Spartacus or seen the movie. I think I read April Morning in high school. I think I read Freedom Road at some point. At any rate, I have the impression that reconstruction was actually a moment when it seemed America was coming closer to living up to its promise to provide liberty for all. I also read The Last Frontier at some point.

I believe I knew he was blacklisted. I hadn't known that he actually was a member of the CPUSA. Nor had I known about Peekskill or his time in prison.

Nikita Khrushchev gave his secret speech in February 1956. In it, he denounces the cult of personality around Stalin. I believe this is where the phrase comes from. It looked like that the Soviet Union might fulfill its promise. But by the end of that year, the Soviet Union invaded Hungary to put down their revolution.

The secret speech caused Fast all sorts of struggle. When he left the communist party, he wrote a book explaining his reasons.

"I had a god who walked naked, but nobody among those I loved said so; for even as the innocent wisdom of Hans Christian Andersen held that those who could not see the king's clothes were persons of small intellect and unfit for the positions they held, so in my world, it was the conviction of millions of good and wise folk that only those who had lost all honor, dignity, decency and courage would dare to point out that this god whom we worshiped for his noble raiment was indeed naked and ugly in his nakedness.

Who would be without honor, dignity, decency and courage?

In the little town where I live, there is a little store, unimportant and of no consequence, and out of this store an old man ekes a living. This is an old man who mourns a hurt which will not heal, the kind of hurt many who read this will know intimately, for twenty years ago the young son of this man fell in Spain, fighting in the Lincoln Battalion for the Spanish Republic and the freedom of men. His son lies buried in the distant Spanish soil, and for twenty years the hurt in this old man was as if it had happened yesterday.

He had a little salve to rub on the terrible sore. This was the salve, that his son had died in the best of causes, the fight for the liberation of mankind. But in 1956, a man called Khrushchev delivered a certain 'secret report' - telling a story of Russia and the Communist movement that I and my friends had heard before but had never believed before. Now Khrushchev made proof of twenty'five years of 'slander,' and we believed. And among those who believed because they had to believe was this old man whose son had laid down his life in Spain.

I came into his store one day in that month of June and he was weeping. He asked me,

'Why did my son die?'

For had I not held, all of my thinking life and in all that I wrote, that one son of man was all the sons of man? He then said to me, but not in words - for a broken heart does not make a gentle person cruel or vindictive - not in words but with the look in his eyes -

'That I, a plain man did not comprehend this is no wonder; but you, Howard Fast, spoke and wrote and pleaded this cause - and why? Can you tell me why?'" -- Howard Fast, The Naked God: The Writer and the Communist Party, 1957.

None of this means Fast did not keep the same values:

"I am neither disillusioned nor depressed, and I have lived through grim times, but times when mankind made gigantic strides forward. Though the Communist Party is disciplined and often splendid in military action, I do not think it can claim credit for the events we have seen. Socialism, justice and the brotherhood of man are mighty and irresistible forces; they will grow to fruition in spite of the Communist Party - and Soviet socialism will not forever lie supine under the heel of the commissar."-- Howard Fast, chapter 15.

Capital-Reversing In A Pertubation Of An Example Of The Recurrence Of Truncation

Figure 1: The Wage Frontier for an Example of Capital-Reversing

I am continuing to explore perturbations of coefficients of production for inputs of circulating capital in this example. The example is of the recurrence of truncation without either the reswitching of techniques or capital reversing. This post presents a perturbation in which the recurrence of truncation no longer occurs, but capital-reversing now arises.

Tables 1 and 2 present the coefficients of production for the example. The technology has the minimum structure, in a model in which multiple commodities are produced, and inputs of labor, circulating capital, and fixed capital are needed in each industry. Also, managers of firms in both industries have a choice of the economic life of a machine. In this perturbation, a_{1, 1} is higher than in the example I started with. a_{1, 3} is the same. I varied a_{1, 2} and a_{1, 4} to find this example of capital-reversing.

Table 1: Inputs for The Technology

Input	Industry
	Machine		Corn
	I	II	III	IV
Labor	1/10	8	43/40	1
Corn	32/50	2/5	1/8	0.38944767
New Machines	1	0	1	0
One-Year Old Machines (1st type)	0	1	0	0
One-Year Old Machines (2nd type)	0	0	0	1

Table 2: Outputs for The Technology

Output	Industry
	Machine		Corn
	I	II	III	IV
Corn	0	0	1	14/25
New Machines	2	5/2	0	0
One-Year Old Machines (1st type)	1	0	0	0
One-Year Old Machines (2nd type)	0	0	1	0

Table 3 repeats the definition of the available techniques. I will observe that a switch point between Beta and Gamma cannot exist without that switch point being simultaneously a point at which all wage curves intersect.

Table 3: Specification of Techniques

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

Figure 1, at the top of this post, depicts the wage curves for the four techniques. It is not visually striking. In particular, the wage curves for Beta and Delta are hard to distinguish by eye. Figure 2, below, is an enlargement of part of the wage curves so that you can see that Beta and Delta have different wage curves. The sequence of wage curves on the frontier, in order of an increasing rate of profits, is Alpha, Beta, Delta. Gamma is never on the frontier.

Figure 2: The Wage Frontier for an Example of Capital-Reversing (Enlargement)

This example is one of my usual illustrations that the Austrian and marginalist theories of capital are muddled and confused. Around the switch point between Beta and Delta, a lower interest rate is associated with the truncation of the machine in the corn industry and a less-capital intensive technique. Net output per worker has decreased for the economy as a whole. Around the switch point between Alpha and Beta, a lower interest rate is associated with the truncation of the machine in the machine industry and a more capital-intensive technique. Net output per worker is increased for the economy as a whole.

A lower interest rate need not encourage capitalists to adopt more capital-intensive techniques. No necessary association exists with extending the economic life of a machine and adopting a more capital-intensive technique.

Socialism Worked In A Village In China In 1979

By socialism, I mean 'socialism with Chinese characteristics'. An emphasis on developing and liberating the forces of production is one aspect of socialism. Trying to seek truth from facts is one way that you might phrase one of those Chinese characteristics. Another characteristic is a matter of seeking democratic initiatives from below, especially from rural areas. The principle of household responsibility is in tension with the principle of collectively 'eating from one big pot'. But Mao's 'On contradiction' shows that such tensions will continue in socialism. Household responsibility is not in tension with a community collectively owning the land.

This inadequate preamble suggests why socialists could embrace these events:

"On the 24th of November, 1978, representatives from the 18 families of Xiaogang Village, of Fengyang County in Anhui Province, met and signed what was then a secret document. In 79 characters, the document stated that each family would subdivide their collective land, work their allocated plots to meet government quotas, and then sell any surplus for their own benefit. The reason: back in 1958 the village population was 120, but 67 died from hunger during 1958–1960 (in the midst of the 'Great Leap Forward'). Starvation had haunted them once again in 1978 and they feared for the future. The result of the secret agreement: in the following year, the farmers of Xiaogang village produced six times the amount of grain compared to the previous year, and the per capita income of the farmers increased from 22 to 400 RMB. Why was the document a secret? With the fully collectivised system in force, any form of buying and selling was regarded as a 'capitalist' exercise and thus punishable. The farmers knew they were taking a risk, but they were fortunate that the local and provincial CPC officials were sympathetic to their endeavour. So also was the new leadership of the country, with Deng Xiaoping at the head. By the next spring, the word of Xiaogang's move was out. While some accused them of undermining socialism, the country's leadership saw it very differently: this would be the beginning of the household responsibility system and thus of the rural reform that drove the first period of the Reform and Opening-Up. By 1984, the household responsibility system had been implemented across the country." – Roland Boer. 2021. Socialism with Chinese Charateristics: A Guide for Foreigners. Springer. p. 85

I certainly do not think of socialism as a blueprint to be fashioned beforehand and imposed from above. Any feasible development of socialism will include the development and modification of institutions and policies at different times and places. The Reform and Opening-Up initiative seems to have been a good idea at the time, although maybe, like the French Revolution, it is too soon to tell. Later developments showed the need for a tack more towards port.

Boer's book is in definite contrast with David Harvey's 2005 A Brief History of Neoliberalism. Harvey is one of those foreigners who Boer says do not understand China. I think of the events recounted above as not too far from how I understand the German mark community or Russian mir village assembly worked. After these events, the land remained collectively owned. Neither absentee owners nor wage laborers existed. The existence of markets is not sufficient for capitalism, as can be seen by millennia of pre-capitalist experience with simple commodity production.

Boer depicts the cultural revolution, starting in 1966, and the gang of four, as deviations from Mao Zedong Thought. He depicts the inequality growing in the 'wild 90s' as a deviation, as well. Boer ties some ideas in the Confucian tradition to some Marxist ideas. The time of xiaokang (moderate or acceptable time of well-being) precedes datong (great unity). Likewise socialism precedes Communism. Boer writes about the four moderizations, in agriculture, industry, national defence, and science and technology, which China has been bringing about in the last few decades. According to Boer on Mao, contradictions will still exist in socialism, but they will not necessarily be antangonistic. Boer has a schematic approach to contradiction analysis. You should identify the principal contradiction and pay attention to the particularity of the contradiction.

When Boer writes about two systems in one one country, he writes about the Hong Kong Special Administration Region (SAR), the Macau SAR, and Taiwan, as if Taiwan was not a different country. He says nothing about 1989 events in Tienanmen Square. In writing about human rights, he emphasizes that China is an example of anti-colonialism, while claims that human rights are individual and innate is a claim that came from the western peninsula of Europe. I had not thought of China in this context. I am more likely to think of Stephen Biko and Frantz Fanon like this. I know very little about China.

Boer, in his discussion of Xi Jiping thought, emphasizes this 2018 speech on Marx. It is confusing to think how a country can be run by communists who introduce institutions that are widely perceived as capitalist, and yet the ruling party still perceives themselves as building communism.

A Two-Commodity Example Of Harrod-Neutral Technical Change And The Choice Of Technique

Figure 1: Wage Curves for a Fluke Case

1.0 Introduction

This post revisits Harrod-neutral technical change, in the context of the choice of technique. I used Matlab code to obtain the results in this post.

2.0 Technology

The technology (Table 1) in this example is a modification and extension of a reswitching example from Bruno, Burmeister, & Sheshinski (1966). Each column specifies the physical inputs (labor-hours, tons, bushels) needed to produce a specified output at a specified point in time. Each process uses up its inputs and exhibits constant returns to scale (CRS). Technical change results in the reduction of labor coefficients. The labor coefficients for the first processes in the two industries decrease at the same rate, while the labor coefficients in the other two processes also decrease at the same rate, but possibly differing from the rate of decrease in the first processes.

Table 1: A Technology

	Iron Industry		Corn Industry
	Process a	Process b	Process c	Process d
Labor	e1 - θt	(2/5) e1 - φt	(33/50) e1 - θt	(1/100) e1 - φt
Iron	a1,1,a = 0	a1,1,b = 1/3	a1,2,c = 1/50	a1,2,d = 71/100
Corn	a2,1,a = 1/10	a2,1,b = 1/20	a2,2,c = 3/10	a2,2,d = 0
OUTPUTS	1 ton iron	1 ton iron	1 bushel corn	1 bushel corn

A technique consists of a process for producing corn and a process for producing iron. Four techniques (Table 2) exist in this economy. Iron and corn are basic commodities, in the sense of Sraffa, in all techniques. Alpha and Delta experience Harrod-neutral technical change, possibly at different rates. Beta and Gamma combine processes from the two techniques with neutral technical change. How does the analysis of the choice of technique, with prices of production, vary as technical change occurs in secular time?

Table 3: Specification of Techniques

Technique	Iron Industry	Corn Inudstry
Alpha	Process a	Process c
Beta	Process a	Process d
Gamma	Process b	Process c
Delta	Process b	Process d

3.0 Prices of Production and the Choice of Technique

Prices of production must be such that managers of capitalist firms are willing to continue producing iron and corn. In calculating prices of production, I abstract from secular change in labor coefficients.

A price system is associated with each technique. I assume labor is advanced, and wages are paid out of the surplus at the end of the year. A bushel corn is the numeraire. For each technique, the wage and the price of iron can each be expressed as a function of the rate of profits.

Figure 1 plots the wage curves for the four techniques, at a given time and with given rates of technical change. The technique with the highest wage is cost-minimizing at a given rate of profits. The outer envelope is the wage frontier. It is composed out of the wage curves for the Delta, Alpha, and Beta techniques. The wage curve for Gamma is on the frontier only at the first switch point, at approximately 45.8 percent. This is a fluke switch point. Around this switch point, a higher wage or lower rate of profits results in processes in both industries changing in the cost-minimizing case. Only one industry has two processes in cost-minimizing techniques in a non-fluke switch point.

The other switch point, at approximately 167.1 percent, is not a fluke and illustrates capital- reversing. The Beta technique requires less labor, through the economy as a whole, to produce a net output of a bushel corn than the Alpha technique does. Around the switch point, a higher wage is associated with firms wanting to employ more labor per bushel corn produced net in the economy.

4.0 Partitions of the Parameter Space by Fluke Switch Points

A switch point at which four wage curves intersect is only one of four fluke switch points that arise in the example, depending on the rates of technical progress and the time. Figure 2 shows a partitioning of the parameter space, based on these fluke switch points. Each of the partitions is an affine function with a slope of unity. This property of the partitioning of the parameter space, that all partitions are straight parallel lines with unit slope, is a consequence of considering techniques with processes drawn from two techniques undergoing Harrod-neutral technical change.

Figure 2: A Partition of the Parameter Space

The analysis of the choice of technique is qualitatively invariant in each numbered region. Table 3 lists the cost-minimizing techniques, in order of an increasing rate of profits, in each region. Only techniques on the frontier are listed. Capital-theoretic ‘paradoxes’ that arise in each region are noted. Only the switch point in region 5 corresponds to obsolete marginalist intuition. A lower wage or higher rate of profits, around the switch point, is associated with a more labor- intensive and less capital-intensive technique.

Table 3: Specification of Techniques

Region	Techniques	Properties
1	Delta, Gamma, Alpha, Beta	Capital-reversing, reverse substitution of labor for Alpha vs. Beta switch point.
2	Delta, Beta, Alpha, Beta	Reswitching, capital-reversing, and the reverse substitution of labor.
3	Beta, Alpha, Beta	Reswitching, capital-reversing, and the reverse substitution of labor.
4	Alpha, Beta	The reverse substitution of labor.
5	Alpha, Beta	'Non-perverse' switch point.

5.0 A Trajectory through the Parameter Space

The dashed line in Figure 2 represents a possible trajectory through the parameter space, with fixed rates of technical progress for the production processes. Figures 3 and 4 graph the maximum wage and the wage at switch points, as functions of time, along this trajectory. At the intersection of the trajectory with the partition for the fluke switch at which at which four wage curves intersect the wage curve for the Beta technique replaces the wage curve for the Gamma technique on the frontier. The wage curve for the Delta technique no longer appears on the frontier at a nonnegative rate of profits after the trajectory passes the partition for the switch point between Beta and Delta on the wage axis. Similarly, when the trajectory crosses the next partition, the first switch point between Alpha and Beta is no longer on the frontier at a nonnegative rate of profits.

Figure 3: A Trajectory Through the Parameter Space

Figure 4: A Trajectory Through the Parameter Space (Cont'd)

When this switch point between Alpha and Beta exists at a rate of profits of -100 percent, a_c,0,2 = a_c,0,2. In other words, around the other switch point, at a positive, feasible rate of profits, a higher wage leaves unchanged how much labor is hired per unit of gross output in the corn industry. Before the trajectory crosses the partition for this fluke switch point, the labor coefficient in the last process is less than the labor coefficient in the penultimate process. A higher wage around the illustrated switch point is associated with more employment in the corn industry per unit of gross output. This is the reverse substitution of labor.

Harrod-neutral technical progress cannot change the ranking of techniques by the maximum rate of profits. In this example, one of the mixed techniques, Beta, is cost-minimizing at the maximum rate of profits. At the start, Delta is cost-minimizing at a rate of profits of zero, and the example exhibits capital-theoretic ‘paradoxes’. If the rate of neutral technical progress in Alpha exceeds the rate of neutral technical progress in Delta, Alpha must eventually be cost-minimizing at a rate of profits of zero. The trajectory in the example illustrates how capital-theoretical ‘paradoxes’ can disappear.

6. Conclusions

Harrod-neutral technical progress yields particularly simple structures in the parameter space. All partitions corresponding to fluke switch points are parallel affine functions with slopes of unity, and the rates of profits at which fluke switch points occur do not vary with neutral technical progress. The fluke at which four wage curves intersect illustrates this property. No double fluke cases, at the intersections of partitions can arise here. Likewise, no fluke switch points can appear on the axis for the rate of profits.

I previously claimed that technology that supports multiple switch points between two techniques can only be a temporary phenomenon, as one technique supplants another with technical progress. The results of the numerical experimentation in this post are in tension with that claim. In some trajectories, neutral technical change eliminates the capital-theoretic ‘paradoxes’ of reswitching and capital-reversing. In other trajectories, it does not.

I created the example to start with reswitching. If neutral technical progress in Delta exceeds that in Alpha, the reswitching example persists through secular time.

In practice, technical change will vary in its rate and have biases. For example, Marx-biased technical change is a mix of capital-using and labor-saving technical change (Foley, Michl, & Tavani 2019). Technical change will often involve more than processes from two existing techniques. It frequently includes the creation of new industries and new commodities. The analysis of Harrod-neutral technical change, entangled with the choice of technique, provides a baseline to contrast with structures in parameter spaces found in other analyses.

Review of Boettke, Candela, and Truitt: The Socialist Calculation Debate

Boettke, Candela, and Truitt (2024) is in the 'Cambridge elements: Austrian economics' series. It is 85 pages

The first chapter is an overview. Von Neumann, Kantorvich, and Leontief are mentioned. The authors acknowledge that current scholarship rejects the revisionism of Don Lavoie, which seemed to have won around the time of the fall of the Soviet Union. Chapter 2 is a recap of the original debate. Chapter 3 presents the views of Hayek, including in rebuttal of Lange and Lerner. Hayek's The Road to Serfdom is emphasized, including some negative reviews. Chapter 4 goes into Lavoie's revisionism and some socialist responses. Chapter 5 is mostly the authors' response to cybersocialist proposals. They say contemporary scholars miss the point. Tacit knowledge of time and space does not even exist without a price system. Chapter 6 is about economists you might not realize were inspired by the calculation argument. This includes Buchanan and public choice, Coase and transaction costs, and Alchian and evolutionary arguments. Kirzner is also mentioned, but you would expect him. Chapter 7 is a two-page conclusion.

I do not understand this book series. Entries in it are short and cannot be comprehensive. This book does not mention Barone's paper, before Von Mises. It does not mention any literature or arguments distinguishing Hayek's and Von Mises' arguments. Instead, Hayek is treated as if his argument is continuous with Von Mises. It is, I think, unclear on welfare comparisons. I know that Von Mises or Hayek were supposedly clear that they were not making claims about maximizing a social welfare function or about Pareto optimality. I do not know why David Ramsay Steele is not referenced.

I appreciate the references, but I do not think one can get a clear understanding of the arguments against Von Mises or Hayek. Some of the references were new to me. Trying to explain general equilibrium theory (GET) shortly is a challenge. The importance of the socialist calculation argument can be seen in motivating developments in GET. I also do not see how you can understand more current arguments about computational complexity from this book

I am not sure one can fully understand Von Mises or Hayek's arguments, either. The authors accurately notes that Von Mises grants the planners knowledge of the prices of consumer goods, as coming from a market just for them (pp. 17-18). And, on p. 24, Von Mises grants the planner 'complete information about the technological possibilities of their era'. As far as I am concerned, Von Mises' argument is invalid.

But, on p. 24-25, the authors take it back. They say, Mises had his argument 'under constant refinement in articulation of the details.' Supposedly, Hayek's emphasis on disequilibrium is also in Von Mises, specifically, in his argument about socialist calculation.

Strangely enough, this book has Hitler as a socialist, along with Stalin and Mao. The book echoes Hayek's assertion that socialists created the intellectual climate for Nazis. The historical dubiousness of this claim is not noted. Following Hirschman, I think The Road to Serfdom is a jeopardy argument. I agree with the authors that it is not an argument about a slippery slope, a kind of perversity argument.

I think this book must be directed to those who already have quite a background. It does not have the space to back up its assertions with a scholarly apparatus. Maybe it is for those who already have quite a background, but want to find out more about 21st-century arguments, particularly the reactions of some economists of the Austrian school to them. The book has no index.

References

• Barone, Enrico. 1908, 1935. The ministry of production in the collectivist state. (Tr. in Collectivist Economic Planning (ed. by F. A. Hayek).
• Bockman, Johanna. 2011. Markets in the Name of Socialism: The Left-Wing Origins of Neoliberalism. Stanford University Press.
• Boettke, Peter, Rosolino A. Candela, and Tegan L. Truitt. 2024. The Socialist Calculation Debate. Cambridge University Press.
• Steele, David Ramsay. 1999. From Marx to Mises: Post Capitalist Society and the Challenge of Economic Calculation. Open Court.

More On Truncation Without Reswitching

Figure 1: Partitions For A Parameter Space

This post extends this and this. I am considering perturbations of coefficients of production in a numerical example of the recurrence of truncation without the reswitching of techniques.

The example consists of two industries that produce new machines and corn, respectively. The physical life of a machine is two years in each industry. Corn acts as circulating capital, as well as the consumption good.

As the result of technical change, coefficients of production vary. No variation in labor coefficients or of the output matrix are considered here so as to retain forward substitution of labor in the corn industry at the switch point between Alpha and Gamma and reverse labor substitution at the switch point between Beta and Delta. Accordingly, I consider permutations of the coefficients of production in the first row of the input matrix. These coefficients of production specify inputs of circulating capital for each process, when operated at unit level.

Previously, I considered perturbations of the pair of coefficients that specify the inputs of corn needed for each machine when the machine is run in the second year of its life. Today, I consider perturbations in a_1,1 and a_1,3, the coefficients that specify the inputs of corn needed for each machine when the machine is run in the first year of its life.

Figure 1, at the top of this post, partitions a part of the parameter space. In drawing this figure, a_1,2 = 0.635 and a_1,4 = 0.319. Each partition corresponds to a fluke switch point. For the values of a_1,2 and a_1,4 in Table 1 in this post, the parameters corresponding to the fluke switch point in which the four wages curves intersect on the axis for the rate of profits is an economically meaningless point in the second quadrant.

A switch point is a fluke if it is a knife edge case in which almost all perturbations of model parameters destroy its defining properties. Four of the five partitions correspond to a switch point on the axis for the rate of profits. With four techniques, switch points between six pairs are possible. A switch point between Alpha and Delta can only occur as an intersection of all four curves. The same goes for a switch point between Beta and Gamma. These two pairs of techniques correspond to the partition for the switch point at which all four wage curves intersect.

The sequence of techniques along the wage frontier is invariant in each numbered region in the slice of the parameter space in Figure 1. Table 1 lists the cost-minimizing techniques in each region, in order of an increasing rate of profits. Other partitions, depicted in Figure 2, exist up and to the right. One is for a switch point between Alpha and Gamma on the wage axis, and another is for the switch point between Gamma and Delta on the wage axis. Three new regions are associated with these partitions. Gamma is cost-minimizing, whatever the distribution of income, for a high enough value of a_1,3, not exceeding unity, in the upper left. Delta is cost-minimizing alone in a region to the northeast. Gamma and Delta are cost-minimizing, in that order for an increasing rate of profits, in a region bounded below by region 3 and also by these two additional regions.

Table 1: Overview of Regions

Region	Techniques	Notes
1	Alpha	No switch point.
2	Alpha, Gamma	Lower rate of profits associated with truncation in corn industry, greater output per worker.
3	Alpha, Gamma, Delta	Lower rate of profits associated with truncation, greater output per worker.
4	Alpha, Gamma, Delta, Beta	Recurrence of truncation in corn industry.
5	Alpha, Beta	Lower rate of profits associated with truncation in machine industry, greater output per worker.
6	Gamma	No switch point.
7	Gamma, Delta	Lower rate of profits associated with truncation in corn industry, greater output per worker.
8	Delta	No switch point.

Figure 2: An Expanded View of Partitions For A Parameter Space

Suppose technical change lowers corn inputs for the first year a machine is operated, in either industry, while leaving all other coefficients of production unchanged. Some trajectories going roughly from the northeast to the southwest in Figures 1 and 2 cross through region 4. Under this specific form of technical progress, the recurrence of truncation can arise and then disappear in secular time. But it need not.

Alternative Textbooks Have Been Available For Teaching Introductory Economics For Decades

"It is true that we cannot, in the time available, teach every- thing that we would like. But why do we pick out for treatment just that selection of topics that is least likely to raise any questions of fundamental importance?" -- Joan Robinson

Over the years, many have proposed textbooks for introductory economics. Some of these are supplementary readings. I include introductions to both micro and macroeconomics:

• Richard Goodwin. 1970. Elementary Economics from the Higher Standpoint. Cambridge University Press.
• Joan Robinson and John Eatwell. 1973. An Introduction to Modern Economics. McGraw-Hill.
• Marc Linder. 1977. Anti-Samuelson (2 volumes). Urizen Books.
• Walsh, Vivian and Harvey Gram. 1980. Classical and Neoclassical Theories of General Equilibrium: Historical Origins and Mathematical Structure. Oxford University Press.
• Morishima, Michio. 1985. The Economics of Industrial Society. Cambridge University Press.
• Yanis Varoufakis. 1998. Foundations of Economics: A Beginner's Companion. Routledge
• Hugh Stretton. 2000. Economics: A New Introduction. Pluto Press.
• Steve Keen. 2002, 2011. Debunking Economics. Zed Books.
.
• Tony Myatt and Rod Hill. 2010. The Economics Anti-Textbook: A Critical Thinker's Guide to Microeconomics. Zed Books.
• Thomas, Alex M. 2021. Macroeconomics: An Introduction. Cambridge University Press.
• Goodwin, Neva et. al. 2024. Essentials of Economics in Context, 2nd edition. Routledge.
• CORE Econ. 2024. The Economy 2.0: Economics for a Changing World.

I have not read a few of those myself. This list is confined to textbooks. Maybe a few are too advanced for introductions. Some are now of historical interest. Thomas' textbook, I guess, is focused on India. I do not include more popular writing. Most I've only dipped into.

Alternative approaches have been available for half a century.

Elsewhere

• Hasan Piker gets endorsed, by Customs and Border Protection (CBP), as being successful at promoting his ideas.
• David Harvey on Sraffa in the New Left Review.
• The most recent episode of Matt Sitman and Sam Adler-Bell's podcast, Know Your Enemy, is on the effects of podcasts on last year's U.S. presidental election.

Perturbation Of A Model Of The Recurrence Of Truncation

Figure 1: A Partition of Part of the Parameter Space

1.0 Introduction

This post is a continuation of the example in a previous post. That example is of the recurrence of truncation without reswitching. I here consider perturbations of selected coefficients of production and of relative markups in the two industries.

2.0 Perturbation of Efficiency of Circulating Capital for Old Machines

The first industry in the example produces machines, and the second produces corn. Machines constitute fixed capital, and corn functions as circulating capital, as well as a consumption good.

Two processes are available in each industry. The second process uses an old machine to produce the output of that industry, whether a new machine or corn. Old machines are specific to the industry in which they were (jointly) produced. The choice of technique, in this model of pure fixed capital, is equivalent to choosing to truncate the economic life of a machine in either industry. The four possible techniques are defined, along with the technology, in the previous post.

Consider perturbations of a_1,2 and a_1,4. The first coefficient of production is the amount of corn input, as circulating capital, needed to operate an old machine in the machine industry. The second coefficient of production is the input of corn needed to operate an old machine in the corn industry.

Figure 1, at the top of this post depicts a partition of the resulting parameter space. The variation of the choice of technique with distribution is invariant in each numbered region. Table 1 lists the cost-minimizing techniques, in order of an increasing rate of profits in each region.

Table 1: Overview of Regions

Region	Techniques	Notes
1	Alpha	No switch point.
2	Alpha, Gamma	Lower rate of profits associated with truncation in corn industry, greater output per worker.
3	Alpha, Gamma, Delta	Lower rate of profits associated with truncation, greater output per worker.
4	Alpha, Gamma, Delta, Beta	Recurrence of truncation in corn industry.
5	Alpha, Beta	Lower rate of profits associated with truncation in machine industry, greater output per worker.

The diagram yields the following results:

• Region 1: If old machines are inefficient enough, then the economic life of machine is one year.
• Region 5: With improvement in the efficiency of old machines in the machine industry, machines are operated for two years in the machine industry at large rates of profits.
• Region 2: With improvement in the efficiency of old machines in the corn industry, machines are operated for two years in the corn industry at large rates of profits
• Region 4: Recurrence of the truncation of machines in the corn industry occurs at a specific range of these coefficient of production.
• Region 3: With sufficient improvement in the efficiency of old machines, no possibility arises of the economic life of machine being operated for two years only in the machine industry, whatever the distribution of income.

All these regions are around a quintuple fluke switch point. The partition between regions 1 and 5 occurs for parameters for which managers of firms are indifferent, when the wage is zero, about the economic life of a machine in producing new machines. The partition between regions 1 and 2 occurs when managers of firms are indifferent, also at a wage of zero, about the economic life of a machine in producing corn. The intersection of these two partitions must also be an intersection of the other three partitions.

3.0 Perturbation of Relative Markups

Now suppose the technology is fixed, as in the post. Let s₁ r be the rate of profits in the machine industry, and s₂ r the rate of profits in the corn industry. As a normalization condition, I assume the sum of the relative markups is unity:

s₁ + s₂ = 1

Figure 2 displays the effects on the choice of technique of perturbations of persistent relative markups.

Figure 2: Effects on The Choice of Technique of Perturbations of Relative Markups

High enough market power for the corn industry, as compared to market power in the machine industry, can eliminate the possibility of extending the economic life of the the machine in the corn industry. This is seen in region 5, to the left on the graph. Persistent high enough market power for the machine industry, can also eliminate the recurrence of the truncation of machines in the corn industry. This is seen in region 3 to the right on the above graph.

4.0 Conclusion

The choice of technique varies with variations in distribution between wages and profits. Both technical progress and changes in market power can have similar effects, in the large. In this example, both can bring about or eliminate the recurrence of the truncation of the economic life of the machine in one industry. Technical progress, however, has the benefit of increasing productivity.

Steve Keen On His Breakaway From Nonsense In Marginalist Economics

Steve Keen appeared on the 30 April epsiode of 1Dime Radio, a podcast. Towards the start, he tells a story:

"My change actually came from a very technical piece of economics because my first-year lecturer is a still a good friend these days, Professor Frank Stillwell - back in those days, he was Doctor Frank Stillwell – explained what's called the theory of the second-best in the first-year lectures. And this is something you normally learn in a third or fourth-year honors course or master's or PhD qualifying. And by the time you’ve got to that level, most people were being so saturated with neoclassical thinking that they would have just regarded it as, 'Oh, that’s a nice little curiosity', and they forget about it. What it showed was that = I think it got the originators the Nobel prize at one point – they show that if you were two steps away from what's regarded as perfection by neoclassical economics, then moving one towards it, and not the whole two, would actually make social welfare worse. And the example that Frank used was if you have wage negotiations, the ideal according to neoclassical theory is that you have workers who bargain on their own personnel right and firms who, again, bargain for employees on an individual basis – no collusion within labour or capital.

But the real world is you’ve got trade unions on one side and employer associations on the other. So in the neoclassical view, you get equilibrium where the worker gets paid their marginal product. That's the ideal. When you allow that there's both trade unions and monopolies (employer associations), you move to another point where it's indeterminate what the wage will be and it’s a bargaining point which might make the firms better off or the workers better off compared to the ideal. But if you abolish one or the other, either get rid of the trade union or get rid of the employer association, the outcome is necessarily lower social welfare than the previous case where had both the trade union and the employer association.

And I fell for the conventional argument. I accepted all the idea of supply and demand and equilibrium and so on. And then to have if pointed out that if you take into account the reality there’s plenty of distortions from what's called the perfectly competitive ideal, then getting rid of them sequentially will make things worse. I thought, there's got to be something wrong with the theory if you can simply demolish it so easily. So I checked my textbook. There was no mention of the theory of the second-best there

I then went down to the economics department library, which is in the same building as where the lectures were, the Merewether Building at Sydney University. And I went looking for the journal papers. I found the original. And then I was horrified that this is not covered in the textbooks.

So I went to the journals again looking for the most recent journal papers. And I found one by Paul Samuelson which was called – first of all I found a journal paper by a Marxist and that surprised me. That was in the Cambridge Journal of Economics by Bhaduri. And I was amazed that a Marxist got into a journal. That surprised me. But then I read Samuelson, a paper called 'A summing up'. And he basically conceded defeat in a debate over the definition of capital which I did even know was happening. But it was actually taking place between 1960, when Piero Sraffa published A Production of Commodities by Means of Commodities, through to the – probably petered out in the late sixties. No mention of it, Samuelson conceded defeat in that paper, but you read his textbook which I had at the time – no recognition of the dispute there either. So I thought I'm being lied to by my textbooks.

And I stopped reading the textbooks. I read them anyway for reference, obviously. But I go and take a look at the journal papers and seeing what's being said in the journals. And the gap between what I was being taught versus the journals wasn't a case that I was getting the simplified version in the textbooks and the sophisticated stuff is in the journals. I was seeing completely contrary results for absolutely fundamental arguments in the textbooks. And I just thought these textbooks are mendacious. Whether they know it or not, they're lying about the nature of economics.

So that was my breakaway point and I’ve never looked back. So that's why I regard economics as unscientific in the extreme, because there have been so many anomalies and so many logical disproofs, and so many empirical failings, this theory should not even be around anymore. It should be like phlogiston in chemistry. But it still dominates economics today. And they are so bloody arrogant about it. That's the other terrifying thing. They are so sure that they’ve got the right answers to everything when history and logical analysis shows that they've got the wrong answers to everything." -- Steve Keen (My transcription)

Richard Lipsey and Kelvin Lancaster published 'The general thory of second best' in 1956-1957, in the Review of Economic Studies. Neither won the Nobel prize. Lancaster won the John Bates Clark medal, which is very prestigious.

Keen does not go into this, but I think a distinction exists between the theory of the second best and the results of the Cambridge capital controversy (CCC). John Eatwell is good on this disticntion. The theory of the second best is one of a number of imperfections and frictions, like transaction costs, information asymmetries, principal agent problems, externalities, search costs, and incomplete contracts. Underlying these imperfections and frictions is an ideal theory. But the CCC shows that this ideal theory is incoherent. Maybe I am too firm on this distinction. If you are clear on all these imperfections and frictions, you know that the ideal is unattainable anyways, whatever policy the government adopts. Talk of government non-intervention in the economy is incoherent.

I think Keen is conflating Amrit Bhaduri's 1969 Economic Journal article, 'On the significance of recent controversies on capital theory: a Marxian view' with later articles.

Paul Samuelson did modify the tenth edition of his textbook. But later editions are befuddling.

I might as well say something about how I developed my views, keeping in mind that I have never been an academic economist. Sometime in the 1980s, I came across a reference to Robinson as the 'British Galbraith'. I had always like Galbraith, who I thought of as a popular writer and advocate of liberalism. So I looked up Joan Robinson's writing. I came across much about Sraffa and the Cambridge capital controversy. I ended up reading some of the same journal articles as Keen. I do not know that you should trust my self-depiction, but perhaps I continued looking for some, any response that defends what is in the textbooks for intermediate microeconomics. I could see that the question was not merely whether aggregate production functions, in macroeconomics, are a useful simplification.

Those defending marginalist economics in the CCC do not end up supporting the view in the textbooks. Capital is not a factor of production. If follows that interest is not a payment for the services of a factor of production. The aggregate production function is theoretically unfounded. Marginal productivity is not a theory of distribution. Equations relating payments to marginal products are merely part of the formulation of a system of general equilibrium. No theoretical foundation exists for well-behaved supply and demand functions in, say, labor markets. Maybe I am wrong, but I see it as very difficult to defend mainstream academic teaching as well-informed and honest.

Recurrence Of Truncation Without Reswitching

Figure 1: Wage Curves In The Example

1.0 Introduction

I have presented this example before. This example is another case of exploring or demonstrating code written for Matlab or Octave.

The structure of the example is the minimum multi-industry example with circulating and fixed capital in all industries and in which the choice of technique is to select the economic life of a machine.

The recurrence of truncation is like the recurrence of a process in single production. As far as I know, no numeric example exists in the literature of the recurrence of truncation without reswitching. This example might have been surprising if I were writing half a century ago. Its possibility is obvious in the work of Bertram Shefold, Heinz Kurz & Neri Salvadori, Ian Steedman, and others. Although reswitching and capital-reversing do not arise in the example, the reverse substitution of labor does.

2.0 Technology and Techniques

Two industries exist in the example. One industry produces machines, and the other industry produces corn. Corn is a consumption good, the good for circulating capital, and the numeraire. Machines are fixed capital. Each machine has a physical life of two years. Old machines cannot be transferred between industries. I assume constant returns to scale (CRS) and the free disposal of old machines. Labor is advanced and paid out of the surplus of corn.

Tables 1 and 2 show the inputs and outputs for each process known to the managers of firms. For example, the inputs, at a unit level of operation, consist of 1/10 person-years, 1/16 bushels corn, and one new machine. The outputs, available after a year, are two new machines and one machine a year older.

Table 1: Inputs for The Technology

Input	Industry
	Machine		Corn
	I	II	III	IV
Labor	1/10	8	43/40	1
Corn	1/16	3/20	1/8	53/200
New Machines	1	0	1	0
One-Year Old Machines (1st type)	0	1	0	0
One-Year Old Machines (2nd type)	0	0	0	1

Table 2: Outputs for The Technology

Output	Industry
	Machine		Corn
	I	II	III	IV
Corn	0	0	1	14/25
New Machines	2	5/2	0	0
One-Year Old Machines (1st type)	1	0	0	0
One-Year Old Machines (2nd type)	0	0	1	0

The machines operate an non-constant efficiency in both industries. An old machine, in the machine industry, is used to produce more new machines than a new machine. The inputs of labor services and corn increase with the age of the machine. In the corn industry, an ole machine is used to produce less corn than a new machine. The input of labor services decrease and the corn input increases with the age of the machine.

With this specification of the technology, the economic life of the machine must be chosen in each industry. Table 3 lists the available techniques. The machine is truncated in both industries in the Alpha technique. The machine is operated for its full physical life in both industries in the Delta technique. In Beta and Gamma, the machine is truncated in one industry and operated for its full physical life in the other.

Table 3: Specification of Techniques

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

3.0 Price Systems and the Cost-Minizing Technique

The economic life of a machine is chosen to minimize cost. A system of equations for prices is associated with each technique. This system can be solved. In the solution, the wage is a function of the rate of profit. Each price of a produced commodity is also a function of the rate of profits.

Figure 1 shows the wage curves, for the four techniques in the example. The cost-minimizing technique at each wage or rate of profits is the technique with its wage curve on the outer frontier. The cost-minimizing techniques are indicated on the figure. Maybe I should experiment with perturbing parameters to see if I can get a more visually obvious graph. Figure 2 shows an enlargement, emphasizing rates of profits around the switch point between Gamma and Delta.

Figure 2: Wage Curves In The Example (Enlarged)

At any rate, the cost-minimizing techniques, in order of an increasing rate of profits, are Alpha, Gamma, Delta, and Beta. Each pair of techniques at a switch point on the frontier differs in one process. A switch point in which the economic life of a machine differs in both industries would be a fluke case. No fluke switch points exist in this example, without perturbing some coefficients of production.

4.0 Prices of Old Machines

Identifying when prices of old machines are negative provides another method of analyzing the choice of technique in models of pure fixed capital. A negative price indicates that the economic life of a machine should be shortened. The machine should be truncated and discarded.

Figure 3 plots the price of old machines in the machine industry, for the two techniques in which old machines are operated in this industry. The switch points, at which the price of an old machine is zero, are indicated. As can be seen in Figure 2, the switch point between Alpha and Beta is not on the outer frontier.

For rates of profits less than that at the switch point between Gamma and Delta, the price of an old machine in the machine industry is negative for the Delta price system. If the Delta technique were in operation, prices would signal that machines in the Delta industry should be truncated. This trunction results in the Gamma tecnique being adopted.

Figure 3: The Price of an Old Machine in Machine Production

Figure 4 plots the price of old machines in the corn industry. Old machines are operated in this industry only for Beta and Delta. Since the price of these old machines are negative, in the Gamma price system, for rates of profits less than the rate at which the price is zero, the machine is truncated at these rates and the Alpha technique is adopted. Likewise, at rates of profits greater than the rate at which the price of this machine is zero, in the Delta system, the machine is truncated and the Beta technique is cost-minimizing at these rates.

Figure 4: The Price of an Old Machine in Corn Production

This analysis of prices of old machines has re-justified the analysis of the choice of technique in Section 4.

5.0 Extra Profits in Extending the Economic Life of Machines

A third method of examining the choice of technique is available.

Under Alpha and Gamma, the machine is truncated in the machine industry. The price of an old machine in the machine industry is zero under those price systems. Figure 5 shows extra profits, for each technique, available in operating the machine for a second year. if the life of this type of machine is extended under Gamma, the Delta technique is adopted. Extra profits are available in so extending the life of the machine at any rate of profits greater than at the switch point between Gamma and Delta. Gamma cannot be cost-minimizing in this range.

Figure 5: Extra Profits in the Machine Industry

The machine is truncated in the corn industry for Alpha and Beta. Figure 6 shows extra profits in the corn-industry, for all techniques, in operating the machine for a second year. Extra profits cannot be obtained for Alpha up to the switch point between Alpha and Gamma. Likewise, extra profits are not available for Beta, in extending the life of the machine in corn-production, for rates of profits greater than at the switch point between Beta and Delta. This method of analyzing the choice of technique, not surprisingly, yields the same result as the other two.

Figure 6: Extra Profits in the Machine Industry

6.0 Recap

The above has illustrated three equivalent methods of analyzing the choice of technique for a pure fixed capital model. Table 4 summarizes the results for this numerical example. The bounds on the ranges of the rates of profits are approximate. Matlab has a funtion, roots(), that returns the (possibly complex) zeros for a polynomial of any degree. I use this function in finding the intersections of wage curves in this example.

Table 4: Cost-Minimizing Techniques

Range	Technique	Truncation
0 ≤ r ≤ 70.21%	Alpha	Machines truncated in both industries.
70.21% ≤ r ≤ 71.19%	Gamma	Machines truncated in machine-production.
71.19% ≤ r ≤ 87.5%	Delta	Machines operated at full physical life in both industries.
87.5% ≤ r ≤ 122.8%	Beta	Machines truncated in corn-production.

At any rate, the machine is truncated in corn-production when both the Alpha and the Beta technique are cost-minimizing. The truncation of the machine in corn-production recurs, being part of the cost-minimizing technique at extremes of low and high rates of profits. This is not, however, an example of the reswitching of techniques.

Negative real Wicksell effects occur at all four switch points. Around each switch point, a lower rate of profits and higher wage is associated with a greater net output of corn per person-year. At the switch point between Alpha and Gamma, truncation in the corn industry is a switch to a more capital-intensive technique. Likewise, at the switch point Gamma and Delta, truncation in the machine industry is a switch to a more capital-intensive technique. As usual, these results disagree with Austrian capital theory and the ideas of economists of this school about roundaboutness.

Around the switch point between Alpha and Gamma, a lower rate of profits or higher wage is associated with truncation in the corn industry and a greater gross output of corn per person-year hired in the corn industry. Around the switch point between Delta and Beta, contrawise, a lower rate of profits or higher wage is associated with the extension of the economic life of the machine in the corn industry and a decrease in the gross output of corn per person-year hired in the corn industry. This second switch point is a manifestation of the reverse substitution of labor, one of those 'perverse' phenomena found in the Cambridge capital controversy.

Menger's Principles Is Obsolete

Carl Menger has a theory of consumer demand, in his Principles of Economics. This theory, one expression of utility theory, is ejected or ignored by other marginalist economists. Bohm-Bawerk is an exception. He also puts forth this theory. For those who want to read something shorter, I recommend William Smart's 1891 An Introduction to the Theory of Value. Heinz Kurz has recently written about Menger.

I take current theory to be revealed preference theory, which was developed by Paul A. Samuelson. Gerard Debreu's 1959 Theory of Value: An Axiomatic Analysis of Economic Equilibrium is canonical. in the theory, each consumer has a preference relation over a space of goods. Suppose all goods can be enumerated. Debreu has No. 2 Red Winter Wheat as an example of one good. Suppose a consumer is presented with vectors of n goods, where n is the number of goods available. Each vector specifies the quantity of each good available. The consumer is assumed to be able to tell, for each pair of vectors, whether they prefer the first to the second, they prefer the second to the first, or they are indifferent between them. Given certain assumptions on preferences, a utility can be assigned to each vector. This utility has some of the properties of numbers. You may not have the mathematics to understand some expositions of this theory, and other expositions exist, for example, in terms of choice functions.

Menger, by contrast, looks at one good at a time. He has a couple of chapters on the theory of the good. In his chapter on value, he classifies wants or needs into different classes. For example, food might be a class. A good, say, water, might go into several classes. You can drink water, use it to water your lawn, or use it to fill a swimming pool. These might be three different classes. The consumer has ranks, in each class, of satisfactions or utilities. The first gallon of water, in the drinking class, might have a rank of 10, while each successive gallon has a lower rank. When the consumer obtains a new gallon of water, they must look at the next satisfaction to be obtained, with the given distribution of existing goods among the classes. The consumer will then allocate this next gallon among these uses accordingly.

None of the structure in Menger's theory survives in modern economics. I think even Kelvin Lancaster's1966 New approach to consumer theory is something different.

Other aspects of Menger’s book are also obsolete. But I want to only focus on one aspect at a time.

An Example Of Fixed Capital From Salvatore Baldone

Figure 1: Wage Curves For A Technique In The Example

1.0 Introduction

I have explored this example from Baldone before, including perturbations of coefficients of production. My purpose here is to demonstrate that my Matlab code for Sraffian analysis can yield the correct results. (I have an off-by-one error that I hard-coded around in obtaining these graphs.)

My favorite method of analyzing the choice of technique applies to models of pure fixed capital. In such models, machines that last over multiple production periods are the only element of joint production. If a machine does not have constant efficiency over its physical life, the analysis of the choice of technique includes a decision on the economic life of the machine. The choice of technique can still be analyzed by the construction of the wage frontier as the outer envelope of wage curves. Unlike in single production, a wage curve can slope up off the frontier.

Baldone's numerical example illustrates an equivalent method for analyzing the economic life of a machine. It focuses attention on negative prices of old machines. The cost-minimizing technique is such that old machines are discarded, not operated. And it is an example of the reswitching of techniques.

2.0 Technology, Techniques, and Quantity Flows

Each column in Tables 1 and 2 defines a production process. Managers of firms know about each process. The first produces new machines, and the remaining three produce corn with machines of various vintages. For instance, a bushel corn and a one-year old machine are produced, in the second process, from inputs of 1/5 person-years of labor, 2/5 bushels corn, and one new machine.

Table 1: Inputs for The Technology

Input	Process
	(I)	(II)	(III)	(IV)
Labor	2/5	1/5	3/5	2/5
Corn	1/10	2/5	289/500	3/5
New Machines	0	1	0	0
One-Year Old Machines	0	0	1	0
Two-Year Old Machines	0	0	0	1

Table 2: Outputs for The Technology

Output	Process
	(I)	(II)	(III)	(IV)
Corn	0	1	1	1
New Machines	1	0	0	0
One-Year Old Machines	0	1	0	0
Two-Year Old Machines	0	0	1	0

I call Alpha the technique in which the machine is disposed of after one year and Beta the technique in which the machine is discarded after two years. In Gamma, the machine is run for its full three physical years

Suppose Alpha is adopted, and the first two processes are operated at a unit level. A new machine is simultaneously produced by the first process and operated to its economic life in the second. One bushel corn is produced. One half bushel is used to replace the corn input, leaving a net output of 1/2 bushel corn. This net output is produced by 3/5 person-years labor. Thus, Alpha requires 1.2 person-years per net bushel output ( = (3/5)/(1/2) = 6/5). I leave it for the reader that Gamma requires approximately 1.2103 person-years per net bushel corn, and that Beta requires approximately 1.3015 person-years per net-bushel produced.

3.0 Prices

In a vertically integrated firm, new and old machines are not sold on markets. Nevertheless, the accountants must enter prices on the books. The accounting I outline here can be used to derive the formula for an annuity if the efficiency of the machine were constant. However, since that is not the case, a general approach to depreciation is illustrated.

Let r be the interest rate, as given from the market, w the wage, p₀ the price of a new machine, p₁ the price of a one-year old machine, and p₂ the price of a two-year old machine. The interest rate is also known as the rate of profits. When the Gamma technique is operated, prices must satisfy the following system of four equations:

(1/10)(1 + r) + (2/5) w = p₀

((2/5) + p₀)(1 + r) + (1/5) w = 1 + p₁

((289/500) + p₁)(1 + r) + (3/5) w = 1 + p₂

((3/5) + p₂)(1 + r) + (2/5) w = 1

I take the wage as paid at the end of the year, and all prices are expressed in terms of the net product.

If the interest rate is given, the above system consists of four linear equations in four variables. It can be solved.

The price systems for the other two techniques are a subset of those. The price system for Beta, for instance, consists of the first three equations, with the price of a two-year old machine set to zero.

4.0 Non-Negative Prices and the Choice of Technique

"With decreasing or changing efficiency ... a problem of the choice of technique, that is, of the optimal truncation date, arises. Premature truncation is advantageous as soon as the price (book value) of a partly worn out instrument of production becomes negative. Since the price of a machine (either new or 'aged') is equal to the capital value one gets by discounting all future net recipts that may be obtained by further use of it, where the going rate of profit is taken as the discount rate, negative prices would indicte 'losses' and would thus contradict the assumption of a fully settled competitive position of the economy." -- Kurz and Salvadori (1995: 212).

I can find when the price of each machine is positive. For new machines (Figure 2), their prices are positive:

• For Alpha, when 0 < r < 74.2 percent
• For Beta, when 0 < r < 73.8 percent
• For Gamma, when 0 < r < 72.7 percent.

The upper limits are approximate. The wage curves in Figure 1, at the top of this post, intersect the axis for the rate of profits at these upper limits.

Figure 2: Prices of New Machines

One-year old machines have positive prices (Figure 3):

• For Beta, when 43.6 percent < r < 62.7 percent
• For Gamma, when 4.1 percent < r < 56.9 percent

Under Alpha, the machine is discarded after one year, and the prices of old machines are identically zero. Beta is not operated outside the limits in which the price curve for Beta intersects the abscissa in Figure 3. If the machine were being truncated after two years, it would pay to discard it after one year. The same applies to Gamma. The analysis, so far, shows that Alpha would be adopted at the extremes of low and high rates of profits,

Figure 3: Prices of One-Year Old Machines

Two-year old machines have positive prices (Figure 4):

• For Gamma, when 0 < r < 55.7 percent

Since the price of a two year old machine is negative for rates of profits greater than at the switch point, Gamma will not be operated at those rates of profits.

Figure 4: Prices of Two-Year Old Machines

I can now summarize the analysis of the choice of technique for this example. Managers of firms will not adopt a technique when the outputs of a process in the technique has a negative price. Thus, each technique will be adopted in the following intervals:

• Alpha, for 0 < r < 4.1 percent and 62.7 percent < r < 74.2 percent
• Beta, for 55.7 percent < r < 62.7 percent
• Gamma, for 4.1 percent < r < 55.7 percent

Now, I can look at what happens around the three switch points:

• Around r = 62.7 percent, a lower interest rate is associated with a switch from Alpha to Beta, a more roundabout technique. But net output per worker falls. A more roundabout technique is less capital-intensive.
• Around r = 55.7 percent, a lower interest rate is associated with a switch from Beta to Gamma, a more roundabout technique. And net output per worker rises.
• Around r = 4.1 percent, a lower interest rate is associated with a switch from Gamma to Alpha, a less roundabout technique. And net output per worker rises. A less roundabout technique is more capital-intensive.

Only the middle switch point validates Austrian capital theory. Clearly, economists of the Austrian school have made mistakes in logic.

I like to note that the above argument is not about aggregation.

5.0 Conclusion

The above constitutes a proof that Austrian capital theory is mistaken. It relies on an identification, in the example, of more roundaboutness with a longer economic life of a machine. Austrian economists have tried to express their central insight that a greater use of capital is equivalent to a greater use of time in several disparate ways.

Perhaps greater roundaboutness should be identified with the use of different, better machines. By putting aside some time each day, Crusoe can make a net, instead of relying on whatever lies about at hand when catching fish. Or perhaps roundaboutness should be measured by a average period of production. Or by a financial measure of duration. What about those Hayekian triangles?

Since the central insight happens to be wrong, each of these formulations can be demonstrated to be, at best, ad hoc. But for each formulation, to be shown wrong in detail, requires a separate argument. Such can be provided and has been provided for most. Both Austrians and more mainstream marginalists have been in the position, for decades, that every economist is their own capital-theorist.

References

• Baldone, Salvatore (1974), Il capitale fisso nello schema teorico di Piero Sraffa, Studi Economici, XXIV(1): 45-106. Trans. in Pasinetti (1980).
• Kurz, Heinz D. and Neri Salvadori. 1995. Theory of Production: A Long-Period Analysis. Cambridge: Cambridge University Press.
• Pasinetti, Luigi L., (1980) (ed.), Essays on the Theory of Joint Production, New York: Columbia University Press