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.

Problems With The Economic Calculation Problem

Hakim on the Economic Calculation Problem

Reactionaries often bring up the Economic Calculation Problem (ECP) as a fatal objection to socialism, considered as entailing central planning. Ludwig Von Mises put this forth in 1920 as an argument in principle that central planning is guaranteed to be highly inefficient. He postulates that the planning authority knows the prices of consumer goods and all technical possibilities, including the endowments of originary factors of production. But without prices of intermediate goods, the planning authority cannot make rational decisions about how to produce commodities. Like Enrico Barone, Von Mises insists the planning authority must re-introduce prices for intermediate goods and a market for 'capital'.

Friedrich Hayek changed the question. He argued that efficient central planning was impractical, not impossible in principle. For Hayek, prices bring about a coordination among entrepreneurs of their plans and expectations. Hayek raised the question on how the planning authority could gather the data they need for their equations. He emphasized dispersed tacit knowledge of time and space.

I emphasize that what the ECP is is disputable. Also, it is inapplicable to the ideas of anarcho-syndicalism, council communists, and so on. Anyways, this post poses some problems with using the ECP as an objection to socialist central planning.

Magnitude of costs of failures of coordination. Neither Von Mises nor Hayek attempt to estimate the costs of a failure of coordination. Since they say a capitalist economy will always be in a disequilibrium state, capitalism will also suffer costs of discoordination at any point of time. How much more are the costs in a centrally planned society, as opposed to a capitalist society? What is the empirical evidence that the ECP was a major problem for the U.S.S.R?

Externalities. For economists of the Austrian school, the extent of the coordination of plans and expectations of diverse agents is a criterion for welfare economics. This approach contrasts with the maintream marginalist criteria of Pareto and Hicks-Kaldor efficiency. The approach of the Austrian school does not seem to me to adequately account for externalities, such as global warming. To Von Mises' credit, he does bring up the destruction of the unpriced natural beauty of a waterfall in discussing its use for power generation.

How do prices bring about coordination? To me, when Hayek describes economic coordination, he is describing something like Hicks' model of temporary equibrium, as in Value and Capital, or the Arrow-Debreu model of intertemporal equilibria, as in Debreu's Theory of Value. Much research suggests such a coordinated state cannt be expected to be brought about by disequilibrium market processes. (Issues exist in how my favorite model can describe trends in capitalist economies, particularly in accounting for if joint production.)

Mises is mathematically mistaken. Suppose prices of commodities provided as components of final demand, technical possibilies, and endowments of originary factors of production are given to the Ministry of Planning. The level at which to operate each production process is found as the result of the solution to an optimization problem. One does not need prices of factors of production to solve the primal problem. Such prices emerge as the solution of the dual problem. Von Mises' mistakes and dogmatism may have been useful in that they encouraged others to explore one approach to price theory.

Mises and Hayek misunderstand capitalism. Anyways, most prices in a capitalist economy do not communicate knowledge like Hayek describes. They do not continuously fluctuate under the influence of supply and demand. Rather, prices of manufactured commodities are usually full cost prices or administrated prices, set by firms. Variations in the level of output, inventories, and queues of orders are of some importance.

Above, I have not said anything about improvements in computer networks or computer speed. I do not see how IBM'a North Pole computer (Modha's blog) would be helpful in linear programming. Hakim recomments Cottrell and Cockshott (1993) for those who want to know more about the ECP. I have not read The People's Republic of Walmart, which some recommend.

Toni Negri, Bob Solow, Tony Thirwall

I feel each of these three needs more than I am able to say. I find intriguing radicals attacking communist parties from the left, as Negri and others (Autonomia) did in Italy in the 1960s and 1970s. I draw on those who have all sorts of arguments with Solow. I find him witty. Thirwall I associate with Nicholas Kaldor and development economics.

• Antonio Negri (1933 - 2023). Repost of 2015 interview from Democracy Now. Libcom page of works related to Negri.
• Robert Solow (1924 - 2023): MIT obituary. Russell Sage Foundation obituary. 1987 Nobel announcement.
• Tony Thirwall (1941 - 2023). Repost of an obituary from John McCombie.

Misrepresentations Of Keynes' Work

I claim that what mainstream economists teach about what Keynes wrote is often false and nonsenical. Unfortunately, this is quite impressionistic in that I do not give examples of these misrepresentations. I am writing here only about the General Theory. I suppose some mainstream economists might respond that they do not teach about Keynes at all.

Some say Keynes work was about policy, not theory. Keynes specifically says otherwise in the first sentences of the preface to his major work:

"This book is chiefly addressed to my fellow economists. I hope that it will be intelligible to others. But its main purpose is to deal with difficult questions of theory, and only in the second place with the applications of this theory to practice. For if orthodox economics is at fault, the error is to be found not in the superstructure, which has been erected with great care for logical consistency, but in a lack of clearness and of generality in the premises."

Some say Keynes claimed that persistent unemployment was caused by sticky wages or prices. Franco Modigliani (1944) is the locus classicus for this view. But Keynes starts Chapter 19 by stating exactly the opposite:

"...the classical theory has been accustomed to rest the supposedly self-adjusting character of the economic system on an assumed fluidity of money-wages; and, when there is rigidity, to lay on this rigidity the blame of maladjustment.

It was not possible, however, to discuss this matter fully until our own theory had been developed. For the consequences of a change in money-wages are complicated. A reduction in money-wages is quite capable in certain circumstances of affording a stimulus to output, as the classical theory supposes. My difference from this theory is primarily a difference of analysis; so that it could not be set forth clearly until the reader was acquainted with my own method."

Keynes thinks institutions that make money wages sticky downward are stabilizing, not an explanation of persistent unemployment. He notes that workers and employers may have no means of negotiating over real wages, instead of money wages. And he argues that it is rational for workers to be concerned with relative wages.

Some say Keynes confined his theory to the short run. At least one model in the General Theory is set in Marshall's short run. Investment is ongoing, but the stock of capital equipment is taken as given. This short run equilibrium is suppose to point of attraction in a very short run dynamics. Keynes, however, introduces a notion of long run equilibrium in chapter 5:

"If we suppose a state of expectation to continue for a sufficient length of time for the effect on employment to have worked itself out so completely that there is, broadly speaking, no piece of employment going on which would not have taken place if the new state of expectation had always existed, the steady level of employment thus attained may be called the long-period employment corresponding to that state of expectation. It follows that, although expectation may change so frequently that the actual level of employment has never had time to reach the long-period employment corresponding to the existing state of expectation, nevertheless every state of expectation has its definite corresponding level of long-period employment."

Some say that Keynes' major policy position was to recommended counter-cyclical fical and monetary policy. It is surprisingly hard to find any such argument in the General Theory. I think, as far as policy goes, Keynes recommended institutional changes, especially in Chapter 24, the final chapter of the General Theory. Keynes wants a less unequal distribution of income. He thinks there is some justification for some inequality:

"For my own part, I believe that there is social and psychological justification for significant inequalities of incomes and wealth, but not for such large disparities as exist to-day. There are valuable human activities which require the motive of money-making and the environment of private wealth-ownership for their full fruition. Moreover, dangerous human proclivities can be canalised into comparatively harmless channels by the existence of opportunities for money-making and private wealth, which, if they cannot be satisfied in this way, may find their outlet in cruelty, the reckless pursuit of personal power and authority, and other forms of self-aggrandisement. It is better that a man should tyrannise over his bank balance than over his fellow-citizens; and whilst the former is sometimes denounced as being but a means to the latter, sometimes at least it is an alternative. But it is not necessary for the stimulation of these activities and the satisfaction of these proclivities that the game should be played for such high stakes as at present."

Keynes looks forward to permanently low interest rates, "the euthanasia of the rentier", progressive taxes, and "communal saving through the agency of the State". These changes will lead to the disappearance of rentier aspect of capitalism, which is a transitional stage. The goal is to deprive "capital of its scarcity-value within one or two generations". Keynes thinks these changes are consistent with entrepreneurship:

"Thus we might aim in practice (there being nothing in this which is unattainable) at an increase in the volume of capital until it ceases to be scarce, so that the functionless investor will no longer receive a bonus; and at a scheme of direct taxation which allows the intelligence and determination and executive skill of the financier, the entrepreneur et hoc genus omne (who are certainly so fond of their craft that their labour could be obtained much cheaper than at present), to be harnessed to the service of the community on reasonable terms of reward."

Probably the most famous policy pronouncement in the General Theory is a phrase in the following:

"I conceive, therefore, that a somewhat comprehensive socialisation of investment will prove the only means of securing an approximation to full employment; though this need not exclude all manner of compromises and of devices by which public authority will co-operate with private initiative."

It might be helpful to think of the General Theory as containing several models, not all worked out, in a broader setting. The IS-LM model is only one of these models. Keynes theory is set in historical time, with business cycles occurring. A major point is to abolish a seperation between a microeconomic analyis in terms of real values and a monetary theory of nominal values.

I suppose one motivation for this post is Matias Vernengo's recent response to James Crotty. It seems every decade or so some Post Keynesian writes a book putting forth something like the unoriginal claims in this blog post.

References

• A. Asimakopulos. 1991. Keynes's General Theory and Accumulation. Cambridge University Press.
• Victoria Chick. 1983. Macroeconomics after Keynes: A Reconsieration of the General Theory. MIT Press.
• James Crotty. 2019. Keynes Against Capitalism: His Economic Case for Liberal Socialism. Routledge.
• Paul Davidson. 2007. John Maynard Keynes. Palgrave Macmillan.
• Stephen A. Marglin. 2021. Raising Keynes: A Twenty-First-Century General Theory. Harvard University Press
• Hyman Minsky. 1975. John Maynard Keynes. McGraw-Hill.
• Robert Skidelsky. 1983 - 2001. John Maynard Keynes (Three volumes). Viking.

Aims And Tasks Of Democratic Socialism

Socialist and coomunist parties have formed various internationals over the course of centuries. I consider a declaration of the Socialist International, adopted at its First Congress held in Frankfort-on-Main on 30 June-3 July 1951 an authoritative statement of "The Aims and Tasks of Democratic Socialism". This declaration was re-affirmed in 1962. The declaration starts as follows:

1. From the nineteenth century onwards, capitalism has developed immense productive forces. It has done so at the cost of excluding the great majority of citizens from influence over production. It put the rights of ownership before the rights of man. It created a new class of wage-earners without property or social rights. It sharpened the struggle between the classes.

Although the world contains resources which could be made to provide a decent life for everyone, capitalism has been incapable of satisfying the elementary needs of the world’s population. It proved unable to function without devastating crises and mass unemployment. It produced social insecurity and glaring contrasts between rich and poor. It resorted to imperialist expansion and colonial exploitation, thus making conflicts between nations and races more bitter. In some countries powerful capitalist groups helped the barbarism of the past to raise its head again in the form of Fascism and Nazism.

2. Socialism was born in Europe as a movement of protest against the diseases inherent in capitalist society. Because the wage-earners suffered most from capitalism, Socialism first developed as a movement of the wage-earners. Since then more and more citizens — professional and clerical workers, farmers and fishermen, craftsmen and retailers, artists and scientists — are coming to understand that Socialism appeals to all men who believe that the exploitation of man by man must be abolished.

3. Socialism aims to liberate the peoples from dependence on a minority which owns or controls the means of production. It aims to put economic power in the hands of the people as a whole, and to create a community in which free men work together as equals.

4. Socialism has become a major force in world affairs. It has passed from propaganda into practice. In some countries the foundations of a Socialist society have already been laid. Here the evils of capitalism are disappearing and the community has developed new vigour. The principles of Socialism are proving their worth in action.

5. In many countries uncontrolled capitalism is giving place to an economy in which state intervention and collective ownership limit the scope of private capitalists. More people are coming to recognise the need for planning. Social security, free trade unionism and industrial democracy are winning ground. This development is largely a result of long years of struggle by Socialists and trade unionists. Wherever Socialism is strong, important steps have been taken towards the creation of a new social order.

6. In recent years the peoples in the underdeveloped areas of the world have been finding Socialism a valuable aid in the struggle for national freedom and higher standards of life. Here different forms of democratic Socialism are evolving under the pressure of different circumstances. The main enemies of Socialism in these areas are parasitical exploitation by indigenous financial oligarchies and colonial exploitation by foreign capitalists. The Socialists fight for political and economic democracy, they seek to raise the standard of living for the masses through land reform and industrialisation, the extension of public ownership and the development of producers' and consumers' cooperatives.

7. Meanwhile, as Socialism advances throughout the world, new forces have arisen to threaten the movement towards freedom and social justice. Since the Bolshevik Revolution in Russia, Communism has split the International Labour Movement and has set back the realisation of Socialism in many countries for decades.

8. Communism falsely claims a share in the Socialist tradition. In fact it has distorted that tradition beyond recognition. It has built up a rigid theology which is incompatible with the critical spirit of Marxism.

9. Where Socialists aim to achieve freedom and justice by removing the exploitation which divides men under capitalism, Communists seek to sharpen those class divisions only in order to establish the dictatorship of a single party.

10. International Communism is the instrument of a new imperialism. Wherever it has achieved power it has destroyed freedom or the chance of gaining freedom. It is based on a militarist bureaucracy and a terrorist police. By producing glaring contrasts of wealth and privilege it has created a new class society. Forced labour plays an important part in its economic organisation.

11. Socialism is an international movement which does not demand a rigid uniformity of approach. Whether Socialists build their faith on Marxist or other methods of analysing society, whether they are inspired by religious or humanitarian principles, they all strive for the same goal — a system of social justice, better living, freedom and world peace.

12. The progress of science and technical skill has given man increased power either to improve his lot or to destroy himself. For this reason production cannot be left to the play of economic liberalism but must be planned systematically for human needs. Such planning must respect the rights of the individual personality. Socialism stands for freedom and planning in both national and international affairs.

13. The achievement of Socialism is not inevitable. It demands a personal contribution from all its followers. Unlike the totalitarian way it does not impose on the people a passive role. On the contrary, it cannot succeed without thorough-going and active participation by the people. It is democracy in its highest form.

Further sections of the declaration discuss the goals of political democracy, economic democracy, social democracy and cultural progress, and international democracy. I find non-dogmatic the section on economic democracy:

1. Socialism seeks to replace capitalism by a system in which the public interest takes precedence over the interest of private profit. The immediate economic aims of Socialist policy are full employment, higher production, a rising standard of life, social security and a fair distribution of incomes and property.

2. In order to achieve these ends production must be planned in the interest of the people as a whole.

Such planning is incompatible with the concentration of economic power in the hands of a few. It requires effective democratic control of the economy.

Democratic Socialism therefore stands in sharp contradiction both to capitalist planning and to every form of totalitarian planning; these exclude public control of production and a fair distribution of its results.

3. Socialist planning can be achieved by various means. The structure of the country concerned must decide the extent of public ownership and the forms of planning to apply.

4. Public ownership can take the form of the nationalisation of existing private concerns, municipal or regional enterprise, consumers' or producers' cooperatives.

These various forms of public ownership should be regarded not as ends in themselves but as means of controlling basic industrie and services on which the economic life and welfare of the community depend, of rationalising inefficient industries or of preventing private monopolies and cartels from exploiting the public.

5. Socialist planning does not presuppose public ownership of all the means of production. It is compatible with the existence of private ownership in important fields, for instance in agriculture, handicraft, retail trade and small and middle-sized industries. The state must prevent private owners from abusing their powers. It can and should assist them to contribute towards increased production and well-being within the framework of a planned economy.

6. Trade unions and organisations of producers and consumers are necessary elements in a democratic society; they should never be allowed to degenerate into the tools of a central bureaucracy or into a rigid corporative system. Such economic organisations should participate in shaping general economic policy without usurping the constitutional prerogatives of parliament.

7. Socialist planning does not mean that all economic decisions are placed in the hands of the Government or central authorities. Economic power should be decentralised wherever this is compatible with the aims of planning.

8. All citizens should prevent the development of bureaucracy in public and private industry by taking part in the process of production through their organisations or by individual initiative. The workers must be associated democratically with the direction of their industry.

9. Democratic Socialism aims at extending individual freedom on the basis of economic and social security and an increasing prosperity.

A lot of work is still required to fulfill these aims. I do not know how compatible detailed proposals some have put forth are with these aims.

Labor And Land Are No Commodities

I read Karl Polanyi's The Great Transformation: The Political and Economic Origins of our Time years ago. I find its thesis on the first passage of the first chapter:

"Nineteenth-century civilization rested on four institutions. The first was the balance-of-power system which for a century prevented the occurrence of any long and devastating war between the Great Powers. The second was the international gold standard which symbolized a unique organization of world economy. The third was the self-regulating market which produced an unheard-of material welfare. The fourth was the liberal state. Classified in one way, two of these institutions were economic, two political. Classified in another way, two of them were national, two international. Between them they determined the characteristic outlines of the history of our civilization.

Of these institutions the gold standard proved crucial; its fall was the proximate cause of the catastrophe. By the time it failed, most of the other institutions had been sacrificed in a vain effort to save it.

But the fount and matrix of the system was the self-regulating market. It was this innovation which gave rise to a specific civilization. The gold standard was merely an attempt to extend the domestic market system to the international field; the balance-of-power system was a superstructure erected upon and, partly, worked through the gold standard; the liberal state was itself a creation of the self-regulating market. The key to the institutional system of the nineteenth century lay in the laws governing market economy.

Our thesis is that the idea of a self-adjusting market implied a stark Utopia. Such an institution could not exist for any length of time without annihilating the human and natural substance of society; it would have physically destroyed man and transformed his surroundings into a wilderness. Inevitably, society took measures to protect itself, but whatever measures it took impaired the self-regulation of the market, disorganized industrial life, and thus endangered society in yet another way It was this dilemma which forced the development of the market system into a definite groove and finally disrupted the social organization based upon it. " -- Karl Polanyi

By the way Charles Peters has died.

In many ways, this blog is my commonplace book.

Anti-Communist Literature

We live, dead to the land beneath us,
Ten steps away no one hears our speeches.

But where there’s so much as half a conversation
The Kremlin's mountaineer will get his mention.

His fingers are fat as grubs,
And the words, final as lead weights, fall from his mouth.

His cockroache whiskers leer
And his boot tops gleam.

Around him a rabble of ring-necked leaders -
Fawning half men for him to play with.

They whinny, purr or whine.
As he prates and points a finger.

One by one forging his laws, to be flung
Like horeseshoes at the head, the eye or the groin.

And every killing is a treat
For the broad-chested Ossete.

-- Oslip Mandelshtam

This is just a bibliography. I have posted bibliographies before. I want people that are sympathetic to socialism of some sort or another. As usual, I am limited to works in or translated to English. Some of these examples are not clearly anti-communist. These are a mixture of novels and non-fiction. Some of these I have not read. I am sure this selection can be expanded.

• Richard Crossman (ed.). 1949. The God that Failed
• Milovan Djilas. 1957. The New Class: An Analysis of the Communist System. London: Thames and Hudson.
• Stefan Heym. 2022. Radek: A Novel. Monthly Review Press.
• Arthur Koestler. 1941. Darkness at Noon. Macmillan
• Janos Kornai. 1992. The Socialist System: The Political Economy of Communism. Princeton University Press.
• Nadezhda Mandelshtam. 1999. Hope Against Hope: A Memoir. Random House.
• George Orwell. 1945. Animal Farm.
• Boris Pasternak. 1957. Doctor Zhivago. New York: Pantheon Books.
• Francis Spufford. 2012. Red Plenty. Graywolf Press.
• Eugene Zamiatin. 1924. We

Elsewhere

• Girardi, Mamunuru, Halliday, and Bowles investigate, does studying economics make you selfish? In contrast to earlier research, they conclude no.
• Angus Deaton, in his book Economics in America: An Immigrant Economist Explores the Land of Inequality apparently says, "A reader might be forgiven for thinking we are scoundrels concerned only with our own financial gain."
• Apparently, the Rochdale Principles were set out in 1844 in Rochdale, England, as principles for running cooperatives.
• Intentional communities are another example of a non-capitalist institution. I have stumbled upon a web site for the Foundation for Intentional Communities.
• 'Keynesian Spaceman', in comments, informs me I was once brought up in a dispute on a discord server associated with some Austrian economists.
• Some arguments about the CCC have emerged on subreddits over the years.
• Shattering 'Market Theory', an old post on Daily Kos, reporting a discussion on a private email list of one of my numeric examples. (I have mentioned this before.)

Reswitching in a Model of Extensive Rent

My article with the post title is now available at the Bulletin of Political Economy (Volume 16, issue 2, pp. 133-146). The abstract follows:

Abstract: This article presents an example of the reswitching of the order of fertility and of the order of rentability. Whether or not these orders differ from one another varies with distribution for certain parameter ranges in the example. This analysis emphasizes that more rent per acre is not necessarily associated with more fertile land and that the ranking of lands by fertility cannot, in general, be determined from only data on physical inputs and outputs for the available processes.

Variations in the Economic Life of Machines

These posts demonstrate, in a model of fixed capital, that the cost-minimizing choice of the economic life of a machine need not conform to traditional Austrian and marginalist theory. The cost-minimizing choice of technique around a switch point might associate a shorter economic life of a machine with an increased capital intensity. This counter-intuitive variation of the economic life of a machine is independent of capital reversing and the re-switching of techniques, both of which are also illustrated in these posts.

These posts build on the Cambridge capital controversy (CCC). A lower rate of profits may be associated with a decreased value of capital per worker, a decreased ratio of the value of capital to output, and a decreased sustainable steady state of consumption per worker (Harcourt 1972). Capital is not a factor of production, and an equilibrium rate of profits, assuming competitive conditions, is generally not equal to the marginal product of capital (Harris 1973). The unfounded idea in the background is that, in a supply-and-demand explanation of prices and distribution, an increased relative supply of a factor of production supposedly drives its price down and incentivizes entrepreneurs to adopt techniques, out of a given technology, that use that factor more intensively. All sides to the CCC accepted that this theory lacks rigorous foundation:

"Such an unconventional behavior of the capital/output ratio is seen to be definitely possible. ... Moreover, this phenomenon can be called 'perverse' only in the sense that the conventional parables did not prepare us for it" (Samuelson 1996).

Han and Schefold (2006) and Zambelli (2018) have recently found some examples of such 'perverse' switch points, albeit not many, in empirical data obtained from national income and product accounts. Kurz (2021) raises some challenges to this empirical work.

Much of the discussion in the CCC focused on models with only circulating capital. Bidard (2004), Pasinetti (1980), and Schefold (1989) are canonical references in post Sraffian price theory to fixed capital. The economic life of a machine, in the general case of non-constant efficiency, varies with distribution. Steedman (2020) considers a model with an infinite number of alternative types of machines, each being the only basic commodity in the technique in which it used. Machines operate with constant physical efficiency, for possibly a different number of years in industry and agriculture. He finds that a machine with a shorter life can be adopted at a lower interest rate, independently of capital-reversing. In contrast, this article considers variation in the economic life of a single machine. The results established here and by Steedman can be seen as complementary.

The method of analysis is based on comparing stationary states, where prices of production prevail. These models are open, with distribution taken as exogenous. The numeric example is simple enough such that net output consists of a single consumption good, called 'corn'. Corn also functions as circulating capital, while a machine with a physical life of three years represents fixed capital. Both corn and new machines are basic commodities, in the sense of Sraffa. Although no attempt is made to represent production by a series of dated labor inputs, the economic life of the machine seems to be of interest for claims among economists developing capital theory along the lines of the Austrian school. Economists of this school have argued that a greater willingness to defer consumption leads to a greater supply of capital, a lower interest rate, and a greater period of production. In these posts, a greater period of production is identified with a longer economic life of a machine.

The application of perturbation analysis to the analysis of the choice of technique, to identify fluke cases, and to explore how switch points vary with technological change is relatively novel. A fluke case is such that almost any perturbation of model parameters disturbs its qualitative properties. Kurz and Salvadori (1995) is a classic textbook for the analysis of the choice of technique. Vienneau (2018, 2019, 2021, 2024a, and 2024b) extends this analysis to consider the effects of perturbing selected model parameters. In these posts, applying this approach to a single numeric example uncovers surprising variation in the economic life of a machine, including its non-monotonic variation with the rate of profits with neither capital-reversing nor the re-switching of techniques.

Harwick (2022) has noted that some followers of the Austrian school have recently tried to consider Austrian capital theory separately from business-cycle theory. Lewin and Cachanosky (2019) consider a financial measure of capital-intensity, namely the average duration of an investment project. Around any switch point, an increased Duration is associated with a lower interest rate. As emphasized by Fratini (2019), an increased capital intensity, in this sense, is associated with reduced net output per worker around a so-called 'perverse' switch point. Even so, any measure of capital intensity that always increases with a lower rate of profits around a switch point can be associated with a reduction in the economic life of a machine.

Capital-intensity is assessed in these posts by evaluating the price of inputs, either for a given net output or per worker. A reduction in the economic life of a machine is consistent with an increase in capital-intensity. This association between a shorter economic life and greater capital-intensity can arise around a switch point in which a smaller rate of profits results in the adoption of a more capital-intensive technique, with a consequent greater net output per worker. It can also arise around a 'perverse' switch point in which a less capital-intensive technique is adopted at a lower rate of profits. Neither type of switch point is a fluke case, as can be seen by contrasting such switch points with genuine fluke cases.

On The Uselessness Of Economists

If you believed something different, you wouldn't be sitting where you are sitting

Suppose one wants to discuss capitalism versus socialism or some smaller matter. One might think the discipline of political economy, now known as economics would be helpful. But it is not.

What is taught in most universities in the United States was shown to be nonsense more than half a century ago. I find it hard to account for this except on the grounds of political ideology. I realize that most academic economists and their students that persist do not experience themselves as propagandists. And it does take some study to master the mathematical models, even if they are incoherent.

Obviously, exceptions exist. I am most aware of the economics departments at the University of Massachusetts at Amherst, the New School, the University of Missouri at Kansas City, and the University of Utah. And I think the situation might be different in some other countries. At least, they can list some prominent universities like the above. Furthermore, in taking courses in academic economics, one should learn something useful about how national products and income accounts are kept. Many economists might think they are doing measurement without theory, that these theoretical incoherences that I go on about do not matter to them. And there are many partial models that might be useful in a narrow context.

These sort of questions should have clear answers: For some model, what are the parameters and and what are the variables found in the solution? For each parameter or variable, what are the units of measure? Lately, I have been recommending a John Eatwell lecture on the bomb that Piero Sraffa placed at the foundations of economic theory. Working through Kurz and Salvadori's 1995 textbook is also a good way to understand my favorite devasting criticism of marginalist economics.

Smith's natural prices, Ricardo's prices of production, and Marshall's normal prices all characterize a long-period position or equilibrium, depending on the theory. Marginalist economics is about the allocation of given resources. The quantity and initial distribution of capital goods are among the givens, at least in Walras' formulation. Supply and demand are supposed to clear in all markets in equilibrium, and the capitalists obtain the same rate of profits in all markets. This model is ovedetermined and inconsistent. Walras was mistaken.

Taking the numeraire quantity of capital and its initial distribution as given was another incorrect marginalist approach. The physical composition of capital is supposed to be endogeneous. But prices of capital goods are found as solutions of the model. The quantity of capital is simultaneously inside and outside the model. Knut Wicksell realized this approach does not work. And waiting or abstinence cannot explain profits either.

So from about 1930 to the 1970s, marginalists abandoned long period theory in their most general models. The Arrow-Debreu-McKenzie model of intertemporal equilibrium is the cumulation of this trend. In the model, commodities are distinguished by physical properties, when they are available, and the state of the world. Prices are established in forward markets, found at the start of time.

This is a model of supply and demand in some sense. Households maximize utility subject to constraints. Plans are precoordinated, and all markets clear for all time. On the other hand, one can not draw well-behaved supply and demand schedules at the level of the market, as is shown by the Sonnenschein-Debreu-Mantel theorem.

Economists cannot explain how any economy would get in or approach such an equlibrium. Franklin Fisher investigated this question. Fabio Petri notes that the givens of initial quantities of capital equipment would change if production goes on while the economy is in disequilibrium. The equilibria consistent with the givens are not the equilibria that would be approached. The model does not depict tendencies in any possible capitalist economy.

Given an equilibrium, however, the forward prices embody predictions of what spot prices would be. Mainstream economics, when talking about dynamics, often mean the time paths of these spot prices. A conceptual problem arises here. If markets can open and close later, the model is not the Arrow-Debreu-McKenzie model. Anyways, the rate of profits is not the same among industries at any time period, since prices are typically not stationary.

Mainstream economists have basically given up, as I understand it, on trying to develop any general approach to explaining prices and distribution in a capitalist economy. I think the textbooks are not clear on this point. I like some of the bits of mathematics, such as game theory, in some of these textbooks.

Why study this stuff? Even though academic economists are mostly trapped in an intellectual ghetto, they still have a connection to what ideas are hegemonic. And the disciple of economics provides a puzzle for the sociology of 'knowledge' and the philosophy of science. If academic economists were merely useless, the world would be improved.

How To Find Fluke Switch Points

Figure 1: Convergence of Newton Method

This post steps through an algorithm for finding a fluke switch point. I used a different example when I tried to explain this before. Today, I use an example building on my draft ROPE Article.

Consider Figure 3 in this post, repeated below as Figure 2. Let s₁ = s₂ = 1. I want to find s₃, the markup in the corn industry, such that the wage curves for Gamma, Delta, Eta, and Theta intersect at a single switch point. One wants to find a function one of whose zeros is the desired markup.

Figure 2: Variation of Switch Points with the Markup in the Corn Industry

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.

Table 1: The Technology

Input	Iron Industry		Steel Industry		Corn Industry
	a	b	c	d	e	f
Labor	1/3	1/10	5/2	7/20	1	3/2
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

Given the markups s₁, s₂, and s₃, the wage and prices under Gamma are rational functions of the scale factor for the rate of profits:

w_γ(r) = (f₃ r³ + f₂ r² + f₁ r + f₀)/(g₂ r² + g₁ r + g₀)

p_γ,1(r) = (u₂ r² + u₁ r + u₀)/(g₂ r² + g₁ r + g₀)

p_γ,2(r) = (v₂ r² + v₁ r + v₀)/(g₂ r² + g₁ r + g₀)

Since corn is the numeraire, its price is unity. The coefficients of the polynomials are functions of the coefficients of production for the first, second, and first processes in the iron, steel, and corn industries, respectively, and of the markups.

The Delta technique differs from Gamma in the process for producing corn. The extra profits obtained in operating the second corn-producing process at Gamma prices are:

h₁(r)/(g₂ r² + g₁ r + g₀) = 1

- [(a_f,1,3 p_γ,1(r) + a_f,2,3 p_γ,2(r) + a_f,3,3)(1 + s₃r)

+ a_f,0,3 w_γ(r)]

A switch point between Gamma and Delta is found as an appropriate zero of h₁(r), which is a cubic polynomial. Denote r₁(s₃) as the zero sought for the fluke case.

The extra profits obtained in operating the second iron-producing process at Gamma prices are:

h₂(r)/(g₂ r² + g₁ r + g₀) = p_γ,1(r)

- [(a_b,1,1 p_γ,1(r) + a_b,2,1 p_γ,2(r) + a_b,3,1)(1 + s₁r)

+ a_b,0,1 w_γ(r)]

An appropriate zero of h₂(r) is a switch point between Gamma and Eta. Denote r₂(s₃) as the zero sought for the fluke case.

Consider the following function:

h(s₃) = r₂(s₃) - r₁(s₃)

A zero of h(s₃) is such that the wage curves for Gamma, Delta, Eta, and Theta intersect at a single switch point. At a switch point for Gamma, Delta, and Eta, neither extra profits nor extra costs will be obtained in operating either iron-producing and corn-producing processes. Since the same steel-producing process is operated in all four techniques, Theta is also cost-minimizing at this switch point.

One can find such a zero by applying Newton’s method to two initial guesses, as illustrated in Figure 1 at the top of the post. Some experimentation allows one to determine two initial guesses, s⁰₃ and s¹₃, for the markup in the corn industry and for which roots of the cubics are wanted. The slope of a linear approximation to the function whose zero is sought is:

m_{i + 2} = [h(sⁱ₃) - h(s^{i + 1}₃)]/(sⁱ₃ - s^{i + 1}₃), i = 0, 1, 2, ...

The intercept with the ordinate is:

b_{i + 2} = h(s^{i + 1}₃ - m_{i + 2} s^{i + 1}₃, i = 0, 1, 2, ...

The next iteration is:

s^{i + 2}₃ = - b_{i + 2}/m_{i + 2}, i = 0, 1, 2, ...

In my experience, Newton's method converges fairly rapidly in this application of finding fluke switch points.

"Deserves got nothing to do with it"

This post echos another quotation from somebody who understands something about how rewards are distributed under capitalism.

"In every other country capitalism, competitive and monopolistic, displays the same defects and applies similar political and economic remedies in order to save its life from the new revolutionary attacks of socialism and communism. Regarded more narrowly from my own standpoint of criticism, what has occurred is a display and condemnation of the unequal and unfair character of all markets. For nowhere are the bargaining powers of supply and demand on an equal footing, and everywhere the individual buyers and sellers, whether of goods or services, are so unequal in their 'need' to sell and buy that the advantage accruing from sales at any given price give widely different advantages to those who participate. In other words, whether under monopoly or so-called competitive conditions, markets are intrinsically unfair modes of distribution.

This is my most destructive heresy, and therefore the one for which I have least succeeded in gaining attention, even in the form of hostile criticism, from the orthodox economists. The defence of capitalism consists mainly in ignoring positive attacks and in concentrating upon the errors, follies, and divided counsels of its assailants. Among the business and professional classes and their economic supporters the conviction holds that any property or income legally acquired represents the productive services rendered by its recipient, either in the way of skilled brain or hand work, thrift, risks, or enterprise, or as inheritance from one who has thus earned it. The notion that any such property or income can contain any payment which is excessive, or the product of superior bargaining power, never enters their minds. Writers to The Times, protesting against a rise in the Income Tax, always speak of their 'right' to the income they have 'made,' and regard any tax as a grudging concession to the needs of an outsider, the State.

So long as this belief prevails all serious attempts by a democracy to set the production and distribution of income upon an equitable footing will continue to be met by the organized resistance of the owning classes, which, if they lose control of the political machinery, will not hesitate to turn to other methods of protecting their 'rights.'" -- J. A. Hobson, Confessions of an Economic Heretic

Variation With Markups Of The Analysis Of The Choice Of Technique With Intensive Rent

Figure 1: Variation of the Technique with Markup in Agriculture

This post is a continuation a of a previous example.

I suppose this is the first example in post Sraffian price theory which combines intensive rent and markup pricing. I do not plan on trying to publish it, in a stand-alone article. D'Agata (1983) sets some coefficients to zero to simplify it for his purposes. I would like a range of parameters where I get reswitching or capital-reversing. I have found a case where, given the wage, the cost-minimizing technique is not unique away from switch points. I would like an example where some of the locii in Figure 2 below intersect.

I might as well repeat the data. Table 1 shows the coefficients of production. Only one type of land exists, and three processes are known for producing corn on it. Following D'Agata, assume that one hundred acres of land are available and that net output consists of 90 tons iron, 60 tons steel, and 19 bushels corn. The net output is also the numeraire.

Table 1: The Coefficients of Production

Input	Industry
	Iron	Steel	Corn
	I	II	III	IV	V
Labor	1	1	1	11/5	1
Land	0	0	1	1	1
Iron	0	0	1/10	1/10	1/10
Steel	0	0	2/5	1/10	1/10
Corn	1/10	3/5	1/10	3/10	2/5

All three commodities must be produced for any composition of net output. Table 2 lists the available techniques. Only Alpha, Delta, and Epsilon are feasible for these requirements for use. Not all land is farmed and only one corn-producing process is operated under Alpha. Two corn-producing processes are operated together under Delta and Epsilon.

Table 2: Techniques

Technique	Processes
Alpha	I, II, III
Beta	I, II, IV
Gamma	I, II, V
Delta	I, II, III, IV
Epsilon	I, II, III, V
Zeta	I, II, IV, V

In the non-competitive case, the relative markups in different industries are taken as given. Let the rates of profits be in proportions of s₁, s₂, and s₃, respectively.

Figure 1, at the top of the post, shows the variation in the analysis of the cost-minimizing technique with perturbations of the markup up in agriculture. In drawing this figure, markups in iron and corn production, s₁ and s₂, are assumed unity. At the intersection between the Alpha and Delta wage curves, the rent for Delta is zero. The scale factor at this switch point is the maximum for the Delta technique. At a switch point between Alpha and Epsilon in regions 1, 2, 3, and 4, the rent for epsilon is zero. The scale factor at such a switch point is the maximum scale factor for Epsilon. In regions 5 and 6, the maximum scale factor for Epsilon is the scale factor for which the wage turns negative.

A fluke case exists off to the right where the wage curves for Alpha at Delta intersect at the maximum scale factor for the rate of profits for Alpha. At that switch point, Delta has a scale factor for the rate of profits of zero percent and a rent of zero. The fluke case partitioning regions 2 and 3 is one where the wage curves for Alpha and Epsilon intersect at the scale factor where the wage for Delta first turns positive. The fluke case partitioning regions 3 and 4 is one in which the wage curves for Alpha, Delta, and Epsilon all intersect at a single switch point.

The fluke cases partition regions 4 & 5 and 5 & 6 change some characteristics of the range of the scale factor of the rate of profits in which no cost-minimizing technique exists. At the fluke case partitioning regions 4 and 5, the wage curves for Alpha and Epsilon intersect at the maximum scale factor for Alpha. I have previously provided an analysis of the fluke case dividing regions 5 and 6. Maybe I should not consider these two fluke cases since they arise, in some sense, for switch points off the frontier.

Anyways, Table 2 shows how the analysis of the choice of technique varies among the numbered regions. If wants to look at these results in some detail, one can relate the variation in the analysis of the choice of technique to the fluke cases.

Table 2: The Cost-Minimizing Technique in Selected Regions in Parameter Space

Region	Range for Scale Factor	Cost-Minimizing Techniques
1	0 ≤ r ≤ R*,ε	Epsilon
	R*,ε ≤ r ≤ Rα	Alpha
2	0 ≤ r ≤ R*,ε	Epsilon
	R*,ε ≤ r ≤ Rδ	Alpha
	Rδ ≤ r ≤ R*,δ	Alpha and Delta
	R*,δ ≤ r < Rα	None. Wage for Alpha positive.
3	0 ≤ r ≤ Rδ	Epsilon
	Rδ ≤ r ≤ R*,ε	Delta and Epsilon
	R*,ε ≤ r ≤ R*,δ	Alpha and Delta
	R*,δ ≤ r < Rα	None. Wage for Alpha positive.
4	0 ≤ r ≤ Rδ	Epsilon
	Rδ ≤ r ≤ r*	Delta and Epsilon
	r* ≤ r ≤ R*,δ	None. Wage for Alpha, Delta, Epsilon positive. Rent for Delta and Epsilon positive.
	R*,δ ≤ r < R*,ε	None. Wage for Alpha and Epsilon positive. Rent for Epsilon positive.
	R*,ε ≤ r < Rα	None. Wage for Alpha positive.
5	0 ≤ r ≤ Rδ	Epsilon
	Rδ ≤ r ≤ r*	Delta and Epsilon
	r* ≤ r ≤ R*,δ	None. Wage for Alpha, Delta, Epsilon positive. Rent for Delta and Epsilon positive.
	R*,δ ≤ r ≤ Rε	None. Wage for Alpha, Epsilon positive. Rent for Epsilon positive.
	Rε ≤ r < Rα	None. Wage for Alpha positive.
6	0 ≤ r ≤ Rδ	Epsilon
	Rδ ≤ r ≤ r*	Delta and Epsilon
	r* ≤ r ≤ Rε	None. Wage for Alpha, Delta, Epsilon positive. Rent for Delta and Epsilon positive.
	Rε ≤ r ≤ R*,δ	None. Wage for Alpha, Delta, positive. Rent for Delta positive.
	R*,δ ≤ r < Rα	None. Wage for Alpha positive.

Figure 2, for completeness, illustrates the partition of the parameter space of markups, where the ratios of markups in iron and steel need not be the same. Figure 1 illustrates what happens along a vertical line in Figure 2 at s₂/s₁ is unity. I realize it is hard to see region 4 and to distinguish its boundaries in Figure 2.

Figure 2: Partition Of Parameter Space

I do not draw any great conclusions. This example demonstrates my visualization techniques and perturbation analysis can be applied to an example where the cost-mninimizing technique is not found from a frontier of wage curves. The non-uniqueness and non-existence of a cost-minimizing technique arises in D'Agata's original example.

An Alpha Vs. Delta Pattern For The r-Order Of Fertility With Intensive Rent And Markup Pricing

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

This post is a continuation of a previous example.

This is a fluke case insofar as the Alpha and Delta wage curves intersect at the scale factor for the rate of profits that is the maximum possible for the Epsilon technique. This fluke case is associated with a qualitative change in the range of the scale factor for the rate of profits in which no cost-minimizing technique exists.

The technology, endowments, requirements for use, and techniques are as previously defined. Requirements for use can only be satisfied by the Alpha, Delta, and Epsilon techniques.

I continue to consider markup pricing. The rate of profits is (s₁ r), (s₂ r), and (s₃ r) in the iron, steel, and corn industries. In determining which technique is cost-minimizing, r, the scale factor for the rate of profits is taken as given.

Figure 1, at the top of this post, depicts the wage and rent curves for the different techniques. The wage curves for the cost-minimizing techniques lie on the wage frontier. The wage frontier consists of the wage curves for the Delta and Epsilon techniques up to the switch point between them. The wage frontier ends there. No technique is cost-minimizing between this switch point and the maximum scale factor for the rate of profits for Alpha.

Table 1 goes into more detail on the wage curves than aqnybody probably cares about. I introduce some notation that I will find useful in later posts. R_δ is the scale factor for the rate of profits at which the wage is zero for Delta. R_*,δ is the scale factor for the rate of profits at which the rent is zero for Delta. This is a fluke case because R_*,δ is equal to R_ε. Anyways, in the first range for the scale factor, only the Alpha and Epsilon techniques have wage curves that are eligible to lie on the wage frontier; the wage curve for the Delta technique lies below the axis for the scale factor for the rate of profits. In the next two ranges, all three wage curves are eligible. In the last range of the scale factor, only the wage curve for Alpha is eligible. The rent curve for Delta and the wage curve for Epsilon lie below the axis for the scale factor.

Table 1: Cost-Minimizing Techniques

Lower Bound on r	Upper Bound on r	Techniques
0 percent	Rδ	Alpha has a positive wage
		Delta has a negative wage
		Epsilon has a positive wage and positive rent
		Epsilon is uniquely cost-minimizing
Rδ	r*	Alpha has a positive wage
		Delta has a positive wage and positive rent
		Epsilon has a positive wage and positive rent
		Delta is non-uniquely cost-minimizing
		Epsilon is non-uniquely cost-minimizing
r*	R*,δ	Alpha has a positive wage
		Delta has a positive wage and positive rent
		Epsilon has a positive wage and positive rent
		No cost-minimizing technique exists
R*,δ	Rα	Alpha has a positive wage
		Delta has a positive wage and negative rent
		Epsilon has a negative wage and positive rent
		No cost-minimizing technique exists

I plot extra profits for each process for each technique to demonstrate my claims about which technique is cost-minimizing. Figure 2 shows extra profits for each process at Alpha prices. Extra profits are zero for the three processes comprising the technique. The last corn-producing process can always pay extra profits for any scale factor, while the penultimate process can pay extra profits for any scale factor greater than that at the intersection of the Alpha and Delta wage curves and not exceeding the maximum scale factor for the Alpha technique. The Alpha technique is never cost-minimizing.

Figure 2: Extra Profits with Alpha Prices

Figure 3 plots extra profits for each process for the Delta and Epsilon techniques. Since four of the five processes in the technology are operated for each technique, four of the five processes obtain extra profits of zero for all scale factors between the limits for each technique. If the Delta technique were in operation at a scale factor greater than at the switch point between Delta and Epsilon, farmers would start to operate the fifth process, moving away from the Delta technique. If the Epsilon technique were in operation in this range, farmers would start to operate the fourth technique. A market algorithm would not coverge to any technique for a scale factor for the rate of profits greater than that at the switch point between Delta and Epsilon and not exceeding the maximum scale factor for the Alpha technique.

Figure 3: Extra Profits with Delta or Epsilon Prices

For a smaller markup in agriculture than in this fluke case, three interesting ranges of the scale factor exist where no technique is cost-minimizing. In the first, the Alpha, Delta, and Epsilon techniques can all pay positive wages and non-negative rents, with positive prices. In the second, only the Alpha and Delta techniques can pay positive wages and a non-negative rent. In the third, the Alpha technique can pay a positive wage, while the Delta technique cannot pay a positive rent.

For a larger markup than in the fluke case, the second interesting range of the scale factor has changed. The Delta technique can no longer pay a positive rent. Instead, the Alpha and Epsilon techniques can pay positive wages and non-negative rents, with positive prices.