Examples Of One-Parameter Pattern Diagrams

Figure 1: Variation in the Economic Life of a Machine with Technical Progress

I have invented graphs for visualizing how the analysis of the choice of technique varies with perturbations of parameters in models of prices of production. This post presents some examples of one type of diagram. One must click on a link with each graph, I guess, to fully understand what is being depicted.

Figure 1 is an extension of an example from Betram Schefold (21 May 2020). This example concerns technological progress and the economic life of a machine in an example of pure fixed capital.

Figure 2 is from an example of two produced commodities with stable relative markups in the two industries (19 September 2020).

Figure 2: The Effects of Variations in Relative Markups

Figure 3 is from another example of fixed capital (3 November 2020). This is a two-commodity model in which machines are used in both sectors

Figure 3: Recurrence of Truncation without Reswitching

Figure 4 is from an example in which the consumption good can be produced with only circulating capital or with a machine with a physical life of two years (1 December 2020).

Figure 4: Triple Switching with Fixed Capital

Figure 5 is from an example in which a machine can last three years (12 December 2020).

Figure 5: An Extension of an Example of Fixed Capital from Salvatore Barone

Figure 6 is from a three-commodity example of non-competitive markets with variations in markups in one industry (11 May 2021).

Figure 6: Variation of Switch Points with the Markup in the Steel Industry

Figure 7 is from the same three-commodity example, but with variations in the markup in another industry (18 May 2021).

Figure 7: Variation of Swith Points with the Markup in the Iron Industry

Figure 8 is an example with extensive rent and technological progress (3 July 2021). This example concerns which type of land is marginal and thus rent-free.

Figure 8: Structural Dynamics with Extensive Rent

Figure 9 is from an illustration of an example to find fluke switch points (28 August 2021).

Figure 9: Technical Progress in An Illustration of an Algorithm to Find Fluke Switch Points

Figure 10 extends an extension of an example from Antonio D'Agata (30 December 2021).

Figure 10: Structural Dynamics in an Example with Intensive Rent

Figure 11 is from an example with extensive rent and markup pricing (29 September 2023).

Figure 11: Variation with Ratio of Markups in Industry to Agriculture

These diagrams were generated out of a research program that I have stumbled upon.

Austrian Economists Rediscovering Sraffa

Some recent papers by economists of the Austrian school rediscover some aspects of post-Sraffian price theory. Others would benefit from more knowledge of post-Sraffian price theory. But the authors do not know this.

Fillieule (2007) is a rediscovery of Sraffa's standard commodity. He sets out a special case of Hayekian triangles in which an infinite series of datad labor inputs are used to produce current net output. "Only circulating capital is taken into account", and "the proportion between capital goods and originary factors is the same in all stages." Fillieule, unlike Sraffa, has wages advanced instead of being paid out of net output. He gestures at Sraffian subsystems. Production at any year can be viewed as decomposed into producing the net output, producing the capital goods needed to produce net output one year hence, producing capital goods needed for the production of the capital goods that go into producing net output two years hence, and so on.

Consider the analysis of the choice of technique. Different techniques have different standard commodities. One must pick one numeraire in the analyis. The numeraire cannot simultaneously be two different standard commodities. I do not know if these observations undermine Fillieule's conclusions.

Mateusz Machaj (2015) responds to the Fillieule (2007) and Hülsmann (2011). He emphasizes intertemporal labor intensity and considers variations in the amount of labor (originary factors more generally) hired at each stage of production. It is unclear to me how such variations can be independent of one another. Those working in the direct production of corn are presumably producing for immediate consumption and seed corn for the production of seed corn for use in production next year. In other words, some ratio of their labor is simultaneously going into production at every stage of production illustrated in a Hayekian triangle. I doubt Machaj's 2017 book resolves this question.

Howden (2016) is a response to Machaj (2015). Howden rejects that one can analyze a change in the rate of profits without considering individual savings and investment decisions. He adopts an outdated supply (savings) and demand (investment) approach to explaining interest rates and fails to see that an open model can be considered. Howden correctly notes that Machaj's description of changes in the amount of labor applied at specified stages is unmotivated. But he sticks to obsolete physical notions of roundaboutness. His article is full of quotations for ideas that some, including Austrian-school economists, would say have been transcended:

"the assertion that artificial reductions to the interest rate cause an unsustainable lengthening in the structure of production is the central tenet of the Austrian theory of the business cycle."

Machaj (2017a) is a reply to Howden (2016).

Manish (2018) is a response to Machaj (2017b) and defends the Pure Time Preference Theory (PTPT) theory of the rate of interest. I am not sure that it makes sense for a general preference for present goods over future goods outside a steady state, when relative quantities are changing. Nor am I sure that the Austrian approach of imputing values to higher order goods can explain interest rates without presuming interest rates.

Granot (2019) is a rediscovery of price Wicksell effects. He finds that for a given technique, the average period of production varies non-monotically with the interest rate. This result was explained by Sraffa in Section 48, pages 44-45, of his book.

Harwick (2022) and Iborra (2021) reference me. A previous version of Milana (2023) did reference me. He still references Osborne. Even though Harwick sticks unknowingly to considering one-way models from originary factors - no consideration of production of commodities by means of commodities for him, I can find something to agree with. He thinks simple models are a good way to approach capital theory. One should not start with the most general model. For me, the most general model would be one of general joint production, multiple types of labor, no simplifications of simple fixed capital, multiple types of land on each of which many types of agricultural commodities can be grown, and so on.

References

• Renaud Fillieule. 2007. A formal model in Hayekian macroeconomics: the proportional goods-in-process structure of production. Quarterly Journal of Austrian Economics. 10: 193-208.
• Er'el Granot. 2019. An overlooked scenario of "reswitching" in the Austrian structure of production. Quarterly Journal of Austrian Economics. 22 (4): 509-532.
• Cameron Harwick. 2022. Unmixing the metaphors of Austrian capital theory. The Review of Austrian Economics 35 (2): 163 - 176.
• David Howden. 2016. The interest rate and the length of production: a comment. Quarterly Journal of Austrian Economics. 19 (4): 345-358
• Jörg Guido Hülsmann. 2011. The structure of production reconsidered. Working paper.
• Rafael Garcia Iborra. 2021. A financial analysis of reswitching. Revista Procesos de Mercado 18 (1): 220 - 244.
• Mateusz Machaj. 2015. The interest rate and the length of production: an attempt at refomulation. Quarterly Journal of Austrian Economics. 18 (3): 272-293.
• Mateusz Machaj. 2017a. Interest and the length of production: a reply. Quarterly Journal of Austrian Economics. 20 (2): 164-170.
• Mateusz Machaj. 2017b. Money, Interest, and the Structure of Production: Resolving Some Puzzles in the Theory of Capital. Lexington.
• G. P. Manish. 2018. A brief defense of Mises's conception of time preference and his pure time preference theory of interest. Quarterly Journal of Austrian Economics. 21 (2): 95-109.
• Carlo Milana. 2023. Refuting Samuelson's capitulation on the re-switching of techniques in the Cambridge capital controversy. The Review of Austrian Economics. Not yet assigned to an issue.

A Parameter Space for an Example of Harrod-Neutral Technical Progress

Figure 1: A Two-Dimensional Parameter Space

The above is for this example. I wish somebody would be inspired by this to write it up with mathematical proofs. What I see here is found by numerical methods.

Figure 1 shows a partition of the parameter space based on fluke switch points. The dashed line shows the temporal path in the previous post. Each of the solid lines are parallel affine functions, with a slope of unity. A proof that these slopes are unity should be able to handle a model with any number of produced commodities.

Milovan Djilas On The Soviet Union As State Capitalism

What to make of the Soviet Union? Apparently, the description of it as state capitalism goes back to Lenin. Djilas description of it as such is central to his best-known book:

"Abstract logic would iпdicate tћat tће Communist reyolution, when it achieves, under different conditions and Ьу state compulsioп, the same things achieved Ьу industrial revolutions and capitalism in the West, is nothing but а form of state-capitalist revolution. The relationships which are created Ьу its victory are state-capitalist. This appears to Ье even шоrе true because the new regime also regulates all political, labor, and other relationships and, what is more important, distributes the national income and benefits and distributes material goods which actually have been transformed iпto state property.

Discussion on whether or not the relationships in tће U.S.S.R. апd in other Communist countries are state-capitalist, socialist, or perhaps something else, is dogmatic to а coпsideraЬle degree. However, such discussion is of fundamental importance.

Even if it is presumed that state capitalism is nothing other than the 'antechamber of socialism,' as Lenin emphasized, or that it is the first phase of socialism, it is still поt опе iota easier for the people who live uпder Communist despotism to endure. lf the character of property апd social relationships brought about Ьу thе Communist revolution is streпgthened and defined, tће prospects for liЬeration of the people from such relationships become more realistic. If the people are поt conscious of the nature of the social relationships iп which they live, or if tћеу do not see а way in which they сан alter them, their struggle cannot ћаvе any prospect of success.

If the Communist revolution, despite its promises апd illusions, is state-capitalist iп its undertakings witћ state-capitalist relationships, tће only lawful and positive actioпs its fuпctionaries сап take are the опеs tћat improve their work апd reduce the pressure апd irrespoпsiЬility of state admiпistratioп. Тће Coшmunists do not admit iп theory tћat they are workiпg in а system оf state capitalism, but their leaders behave tћis way. Тћеу coпtшually boast about improviпg tће work of tће admiпistration апd about leadiпg tће struggle 'agaiпst bureaucratism.'

Moreover, actual relationships are not those of state capitalism; these relationships do поt provide а method of improving the system of state admiпistration basically.

Iп order to establish the пature of relatioпships which arise iп thе course of thе Communist revolution and ultimately become estaЬlished iп the process of industrialization and collectivizatioп, it is пecessary to peer further iпto the role and manner of ореrаtiоп of tће state under Communism. At present, it will be sufficient to point out that in Communisш the state macћineтy is not tће instrument wћiсћ really determines social and property relatioпships; it is only tће instrument Ьу which these relatioпsћips are protected. In truth, everythiпg is accomplished in thе nаше of thе state and througћ its regulations. Тће Communist Party, iпcluding tће professional party bureaucracy, stands above the regulations and behind every siпgle one of thе state's acts.

It is the bureaucracy whiсћ formally uses, adшinisters, and controls Ьоtћ пationalized анd socialized property as well as the entiтe lifе of society. Тће role of tће bureaucracy in society, i.e., monopolistic administration and control of national income and пational goods, consigпs it to а special privileged positioп. Social relatioпs resemЬle state capitalism. Тће more so, because tће carryiпg out of industrialization is effected not with tће ћеlр of capitalists but with the ћеlр of tће state machine. In fact, this pгivileged class perfoтms tћat functioп, using tће state machiпe as а cover апd as ап iпstrurneпt.

Ownership is пothing other tћan tће right of profit and control. If оnе defines class benefits Ьу this right, thе Communist states have seen, in the final analysis, thе origin of а пеw form of ownership or of а new ruling and exploiting class.

In reality, the Communists wете uпаЬlе to act differently from аnу ruling class that preceded them. Believiпg that they were building а new and ideal society, tћеу built it for themselves in tће only way they could. Their revolution and their society do not appear eitћer accidental or unпatural, but appear as а matter of course for а particular country and for pгescriЬed peгiods of its developmeпt. Because of this, no matter ћоw extensive and inhuman Communist tyranny ћаs been, society, in the course of а certain period - as long as industrialization lasts - has to and is аЬlе to endure this tуrаппу. Furthermore, this tyranny no longer appears as something inevitaЬie, but exclusively as ан assurance of the depredations and privileges of а new class.

In contrast to earlier revolutions, the Commuпist revolution, conducted in the nаше of doiпg away with classes, has resulted in the most complete authority of any siпgle пеw class. Everything else is sham and an illusion." -- Djilas (1957)

As I understand it, party functionaries were assigned to state offices. In this way, the party formed a parallel to the official government. Furthermore, these party members became the owners of collectivized property, that is, they controlled it. This is the new class.

Djilas says that communist revolutions differed from previous revolutions in that they were not a matter of an already hegemonic class coming to power. The post-revolution institutions had not already grown up in old society, but had to be created and imposed by force, by the communist party. The leaders believed they were creating a classless society. But, after the revolution, they created a class to bring about a needed industrialization, at great cost.

References

• Milovan Djilas. 1957. The New Class: An Analysis of the Communist System.
• Vladimir Lenin. 1918. The chief task of our day. 'Left-wing' childishness and the petty-bourgeois mentality. Collected WorksVol. 27: 323-354.
• Vladimir Lenin. 21 April 1921. The tax in kind (the significance of the new policy and its conditions). Collected WorksVol. 32: 329-365.

Elsewhere: Data On Capitalism And Other Systems

The first is a distateful counting of the victims of capitalism in the twentieth century. The second concludes that no-longer-actually-existing socialism was about as efficient as western countries. The last argues that general prosperity first declined with the introduction of capitalism.

• Salvatore Engel-DiMauro. 2021. Anti-communism and the hundres of millions of victims of capitalism. Capitalism Nature Socialism 32(1): 1-17.
• Peter Murrell. 1991. Can neoclassical economics underpin the reform of centrally planned economies?. Journal of Economic Perspectives 5(4): 59-76. This issue has a symposium on transition economies, with other interesting articles.
• Dylan Sullivan and Jason Hickel. 2023. Capitalism and extreme poverty: a global analysis of real wages, human height, and mortality since the long 16th century. World Development 161: 1-18.

Here are a couple of other links:

• Louis-Philippe Rochon argues that we should not teach neoclassical ewconomics to undergraduates.
• The P2P Foundation seems like an interesting approach.

Another Example of Harrod-Neutral Technical Progress And The Choice Of Technique

Figure 1: Variation in the Maximum Wage and the Cost-Minimizing Technique with Time

This post presents an example in which some coefficients of production vary from those in example. Reswitching, capital reversing, and the reverse substitution of labor do not arise in this example.

Table 1 shows the coefficients of production for this example. The labor coefficients vary identically with the the labor coefficients in the previous example. a_2,1(a), a_3,1(a), a_2,1(b), a_3,1(b), a_1,2(c), a_3,2(c), and a_1,2(d) are all larger in this example.

Table 1: The Technology

Input	Iron Industry		Steel Industry		Corn Industry
	a	b	c	d	e	f
Labor	(15/2) e-φt	32 e-σt	(13/2) e-φt	60 e-σt	(15/2) e-φt	55 e-σt
Iron	1/6	2/5	1/20	1/10	1	0
Steel	1/20	1/20	1/4	3/10	0	1/4
Corn	1/15	1/15	1/15	0	0	0

Table 2 repeats the definition of the techniques of production. As in the previous example, the Alpha and Theta techniques each undergo Harrod-neutral technical progress.

Table 2: Techniques

Technique	Processes
Alpha	a, c, e
Beta	a, c, f
Gamma	a, d, e
Delta	a, d, f
Epsilon	b, c, e
Zeta	b, c, f
Eta	b, d, e
Theta	b, d, f

As usual, prices of production are defined for each moment in time. Given the wage or the rate of profits, one can find the cost-minimizing technique. Figure 1, at the top of this post, and Figure 2 depict how the dependence of the cost-minimizing technique on distribution varies with time. These graphs are drawn for the specified rate of technical progress. The variation of the cost-minimizing technique with distribution is invariant in each numbered region, although the specific rate of profits, for example, at which a switch point occurs does vary.

Figure 2: Variation in the Maximum Rate of Profits and the Cost-Minimizing Technique with Time

At the maximum rate of profits, the wage is zero. Variations in labor coefficients do not matter. In this case, the Beta technique remains cost-minimizing for all time at a wage of zero. The cost-minimizing technique at the maximum wage varies from Alpha to Theta, as the pure technique with the faster growth in technical progress becomes dominant. Beta and Theta vary in the iron-producing and steel-producing processes. Ultimately, at the extreme right of the graphs, two switch points exist as distribution varies.

I guess these two examples illustrate general properties of Harrod-neutral technical progress in the case where all techniques require the production of the same commodities and all of these commodities are basic in the sense of Sraffa. Fluke cases will arise over time. So-called 'perverse' switch points need not arise, but can.

A Characterization Of Neoliberalism From Wendy Brown

I have been reading Brown (2015). She acknowledges neoliberalism is difficult to define:

"Three decades out, rich accounts by geographers, economists, political theorists, anthropologists, sociologists, philosophers, and historians grappling with these questions have established that neoliberalism is neither singular nor constant in its discursive formulations and material practices. This recognition exceeds the idea that a clumsy or inapt name is draped over a busy multiplicity; rather neoliberalism as economic policy, modality of governance, and order of reason is at once a global phenomenon, yet inconstant, morphing, differentiated, unsystematic, contradictory, and impure, what Stuart Hall calls a 'field of oscillations' or Jamie Peck calls 'unruly historical geographies of an evolving interconnected project.' Neoliberalism is a specific and normative mode of reason, of the production of the subject, 'conduct of conduct,' and scheme of valuation, yet in its differential instantiations and encounters with extant cultures and political traditions, it takes diverse shapes and spawns diverse content and normative details, even different idioms.

Thus the paradox of neoliberalism as a global phenomenon, ubiquitous and omnipresent, yet disunified and nonidentical with itself. This dappled, striated, and flickering complexion is also the face of an order replete with contradiction and disavowal, structuring markers it claims to liberate from structure, intensely governing subjects it claims to free from government, strengthening and retasking states it claims to abjure. In the economic realm, neoliberalism aims simultaneously at deregulation and control. It carries purpose and has its own futurology (and futures markets), while eschewing planning. It seeks to privatize every public enterprise, yet valorizes public-private partnerships that imbue the market with ethical potential and social responsibility and the public realm with market metrics. With its ambition for unregulated and untaxed capital flows, it undermines national sovereignty while intensifying preoccupation with national GNP, GDP, and other growth indicators in national and postnational constellations."

Brown's emphasis is on how neoliberalism remakes the self. Under neoliberalism, people are all regarded as independent entrepreneurs, each trying to increase their human capital. This conception extends to areas that do not necessarily have anything to do with money. How much time should invest in relationships? What best practices should parents adopt in raising their children?

This way of thinking about people contrasts with an older notion of the utility-maximizing consumer. Our preferences form a field that we move around in through exchange. I think John Stuart Mill is important for articulating a pre-marginalist view of economic man. Homo economicus has a history and has varied over the development of political economy.

Brown and Marcuse both share a concept about how capitalism corrupts our non-working time. In One Dimensional Man, Marcuse deplores the prevalence of instrumental reason. For Brown, the neoliberal concept of the self is not a member of a social class. In the neoliberal view, we no longer have workers and capitalists. We are longer examples of homo politicus. I think of Hannah Arendt as an idealized picture of political man, what we could be reasoning together in the public square, in the agora. Brown also mentions homo legalis, the subject of right and an emphasis of Foucault and his concept of governability.

Reference

• Wendy Brown. 2015. Undoing the Demos: Neoliberalism's Stealth Revolution. Zone Books.

Harrod-Neutral Technical Change And The Choice Of Technique

Figure 1: Variation in the Maximum Wage and the Cost-Minimizing Technique with Time

1.0 Introduction

I thought I would revisit the application of my analysis of fluke switch points to an example of Harrod-neutral technical change. Two techniques are assumed to experience Harrod-neutral technical change. The same commodities are produced with both techniques. No capital goods are produced for one technique that are unproduced in the other. Consequently, the techniques have no processes in common. At least two processes must be available in each industry. So more than two techniques must exist.

I think these ideas could be worked up into something. I will probably spend some time toying with the example.

2.0 Technology

This economy produces a single consumption good, called corn. Corn is also a capital good, that is, a produced commodity used in the production of other commodities. In fact, iron, steel, and corn are capital goods in this example. So three industries exist. One produces iron, another produces steel, and the last produces corn. Two processes exist in each industry for producing the output of that industry. Each process exhibits Constant Returns to Scale (CRS) and is characterized by coefficients of production. Coefficients of production (Table 1) specify the physical quantities of inputs required to produce a unit output in the specified industry. All processes require a year to complete, and the inputs of iron, steel, and corn are all consumed over the year in providing their services so as to yield output at the end of the year. The technology is specified for a specific moment in time, and improves over time.

Table 1: The Technology

Input	Iron Industry		Steel Industry		Corn Industry
	a	b	c	d	e	f
Labor	(15/2) e-φt	32 e-σt	(13/2) e-φt	60 e-σt	(15/2) e-φt	55 e-σt
Iron	1/6	2/5	1/200	1/100	1	0
Steel	1/200	1/400	1/4	3/10	0	1/4
Corn	1/300	1/300	1/300	0	0	0

A technique consists of a process in each industry. Table 2 specifies the eight techniques that can be formed from the processes specified by the technology. If you work through this example, you will find that to produce a net output of one bushel corn, inputs of iron, steel, and corn all need to be produced to reproduce the capital goods used up in producing that bushel.

Table 2: Techniques

Technique	Processes
Alpha	a, c, e
Beta	a, c, f
Gamma	a, d, e
Delta	a, d, f
Epsilon	b, c, e
Zeta	b, c, f
Eta	b, d, e
Theta	b, d, f

The Alpha and Theta techniques each undergo Harrod-neutral technical progress. The labor coefficients for the Alpha technique decrease at the the rate φ and those for the Theta technique decrease at the rate σ. The other techniques consist of a mixture of processes from these two techniques.

3.0 Prices of Production

A system of equations can be set out for prices of production, for each technique,at any moment of time. I assume that net output consists of a bushel corn, and that this net output is the numeraire. Wages are paid out of the surplus product after the harvest. Given competitive conditions, the same rate of profits are obtained in each industry.

These assumptions are sufficient to determine the wage and the prices of produced commodities, for each technique, at the given moment in time, as a function of the rate of profits.

4.0 The Choice of Technique

The cost-minimizing technique at a moment of time can be found by constructing the wage frontier as the outer envelope of the wage curves for the eight techniques. Given the rate of profits, the cost-minimizing technique maximizes the wage. Given the wage, it maximizes the rate of profits.

Figure 1, at the top of this post, and Figure 2 depict how the dependence of the cost-minimizing technique on distribution varies with time. These graphs are drawn for the indicated rates of neutral technical progress in the Alpha and Theta techniques. Figure 1 graphs the maximum wage and the wage at each switch point on the frontier. Figure 2 graphs the rate of profits, both the maximum and at each switch point on the frontier. Figure 2 also shows the rate of profits at switch points between -100 percent and zero. The thin vertical lines partition time into numbered regions. Each partition corresponds to a fluke switch point.

Figure 2: Variation in the Maximum Rate of Profits and the Cost-Minimizing Technique with Time

The ranking of techniques by the maximum rate of profits does not vary with time. At the maximum rate of profits, the wage is zero. Variations in labor coefficients do not matter. In this case, the Alpha technique remains cost-minimizing for all time at a wage of zero. It is not necessary, in general, that the cost-minimizing technique at a zero wage, be one of those experiencing Harrod-neutral technical change. For other coefficients of production, the Beta technique, for example, could be cost-minimizing at a zero wage.

In general, the cost-minimizing technique at the maximum wage starts with the technique with the slowest rate of neutral technical progress. Over time, the cost-minimizing technique becomes the technique with the largest rate of technical progress.

In the example, the Alpha technique is cost-minimizing at the start of time, whatever the distribution of income. Region 1 illustrates this lack of dependence of the cost-minimizing technique on distribution. the Alpha technique remains cost-minimizing for all time at a wage of zero. Since the rate of Harrod-neutral technical progress is assumed to be greater for the Theta technique, eventually Theta is cost-minimizing at the maximum wage. One can see the effects of technical progress with the exponential growth of the maximum wage in Figure 2.

Consider Region 7 in the Figures. At a non-fluke switch point, only one process changes in the cost-minimizing technique. As the wage increases, the corn-producing process changes at the switch point between Alpha and Beta. At the second switch-point with increasing wages, the cost-minimizing process in steel production changes. Finally, at the switch point between Delta and Theta, the cost-minimizing process in in iron production changes.

In Region 6, which process changes first, with increasing wages, in iron and steel production varies. The iron process varies at the switch point between Beta and Zeta. At a higher wage, the steel process in the cost-minimizing technique varies at the switch point between Zeta and Theta. The partition between Region 6 and Region 7 has a fluke switch point in which the iron and steel-producing processes change simultaneously.

Region 2 exhibits reswitching between the Alpha and Beta techniques. The switch point at the lower wage is an example of capital-reversing, also known as a positive real Wicksell effect. Around this switch point, a higher wage is associated with the employment of more labor per unit of net output. It also exhibits the reverse substitution of labor. In Regions 2, 3, and 4, the labor coefficient in Process f exceeds the labor coefficient in Process e. A higher wage at this switch point between Alpha and Beta is associated with greater employment per unit of gross corn output.

5.0 Conclusion

The introduction of switch points and the variation in the cost-minimizing technique at the maximum wage is, in some sense, a general property of technology formed out of techniques experiencing Harrod-neutral technical progress. With time, switch points are introduced as fluke cases. These fluke cases need not create examples of reswitching, capital-reversing, reverse labor substitution, or process recurrence. But they do in the example.