Old Papers On Rent And One New One

This post annotates some papers that I want to remind myself of.

Montani (1975) references Quadrio Curzio (in Italian), defines the order of fertility and rentability, notes that they are different, and has something like the reswitching of the order of fertility. He does not have the reswitching of the order of rentability. He treats both extensive and intensive rent, but does not combine them. He notes the wage frontier can slope up under intensive rent. I have to read more closely to see if he already has multiple cost-minimizing techniques. I am under the impression that D'Agata first notice this possibility.

Montet (1979) criticizes Metcalfe and Steedman in that their perversities are more general than they know. Land provides another degree of freedom. They have a wage, rent, rate of profits frontier. I generally do not set equations for natural resources out this way. I once set out an example with heterogeneous labor, relabeling 'land' as 'skilled labor'.

Gibson & McLeod (1983) look at extensive, intensive, and external intensive rent. They go into difficulties of defining basics in joint production. One definition is about the decomposability of matrices and the other is about the rank of some sort of block matrix. They define quasi-basics for the latter. D’Agata has some sort of objection to this. They have interchanges in both the CJE and the RRPE.

Erreygers (1995) considers joint production. Toward the end of his paper, he shows how extensive rent fits into this framework. He wants to avoid setting out another equation in the quantity system to constrain levels of operations of processes from requiring more land to be farmed than exist. And rents should be part of the price vector in the price system, not seperate variables. Kurz & Salvadori (1995) show how to define certain block structured matrices to achieve this end. I think Erreygers may have created this approach.

Ianni (2026) is about international trade, not rent. The theory of intensive and extensive rent can show why most lands are specialized, so the theory may have implications for the theory of international trade. Also, my way of analyzing the choice of technique with long-lasting and given ratios of the rate of profits among industries may have implications for trade. Different countries may be modeled as having different rates of profits.

References

• Erreygers, Guido. 1995. On the uniqueness of cost-minimizing techniques. The Manchester School 63: 145-166
• Gibson, Bill and Darryl McLeod. 1983. Non-produced means of production in Sraffa's system: basics, non-basics and quasi-basics. Cambridge Journal of Economics 7: 141-150.
• Ianni, Guido. 2026. Class struggle and the international division of surplus: The distributive surface in the open economy. Metroeconomica
• Montani, Guido. 1975. Scarce natural resources and income distribution. Metroeconomica 27(1): 68=101.
• Montet, C. 1979. Reswitching and primary input use: a comment. Economic Journal 89 (355): 642-647.

Factor Demand Curves For An Example With Fixed Capital And Rent

Figure 1: Demand Curve for Labor

I have created and worked through an example in which a machine with a physical life of three years can be used in producing an agricultural commodity on one of two types of land.

My example is one of capital-reversing. It occurs to me that I have not plotted the demand for so-called factors of production in this example. Accordingly, Figure 1 plots the wage against the employment firms want to offer, given final demand. Switch points are horizontal line segments in this graph. Around the 'perverse' switch point, a higher wage is associated with firms wanting to employ more workers.

Given final demand and the rate of profits, a price system is defined for each technique. I can add up the value of the capital goods that must exist at the start of the year to produce the given final demand. Prices of production are used to aggregate heterogeneous goods. Figure 2 shows the demand for capital, in some sense. Here, too, the 'perverse' switch point is indicated for a step function approximation for an increasing demand curve. The value of capital varies between switch points because of price Wicksell effects.

Figure 2: Demand Curve for Capital

A model with both fixed capital and the rent of natural resources is a step towards realism if you want. It is also a step beyond what can be found from empirical Leontief matrices, as I understand it. Still, wages and employment, for example, cannot be explained in the long run by the interactions of well-behaved supply and demand functions in the labor market.

Some Phenomena In Price Theory

I occasionally list theoretical possibilities that I think interesting. Outside of a working paper at Centro Sraffa, I have not managed to publish papers detailing the possibilities listed in this post. Some I have not even written up outside of blog posts. I now know that:

• The recurrence of truncation can occur without the reswitching of techniques. This possibility arises in an example of pure fixed capital, with long-lived machines used in both industries that exist in the example.
• A switch point can lie along a single wage curve, with no other wage curve intersecting at the switch point. This possibility occurs in an example with both fixed capital and rent.
• The order of rentability can be completely opposite the order of efficiency. This possibility can arise in a model that combines extensive and intensive rent.
• The partitioning of parameter spaces by fluke switch points is useful in the analysis of structural economic dynamics with a choice of technique.
• Capital-theoretic paradoxes are transient, in many instances, in secular time (also known as the very long run).

I have some difficulties in writing these up. First, my status as an independent researcher creating examples as a hobby should make reviewers be a bit skeptical. Second, many may not be interested in these refinements. Does not Kurz and Salvadori (1995) provide a definitive statement of post Sraffian price theory? You need to have mastered quite a bit of that to understand the point of any of these. Third, I try to put each in a somewhat more general framework I cast the first, the recurrence of truncation, as an example of the last. I suggest that the second, a switch point along a single wage curve, is an anomalous switch point, a concept I am introducing. I want to say that the third is an example of a special case of a model of intensive and extensive rent in which 'nice' properties of models of extensive rent obtain; wage curves slope down and no issues of the non-existence or multiplicity of cost-minimiing techniques away from switch points arise. Last, when I make such generalizations, I have trouble casting my results into the abstract theorem-proof form needed to be precise.

Is the analysis of structural economic dynamics with a choice of technique an interesting problem? Maybe a book of bookprints never exists at a point of time. Capitalists do not have option of costlessly choosing another page. When a new technique is introduced, it typically dominates the existing technique. On the other hand, I have trouble with part II of Sraffa's book preceding part III. Part II treats joint production, including rent and fixed capital. Part III treats the choice of technique. Which lands to cultivate and what economic lives of machines to adopt are part of the choice of technique. So maybe I should limit my program to aspects of joint production. But I also have some consideration of Harrod-neutral technical progress.

It seems I still have years of work.

Murray Rothbard Muddled And Confused

1.0 Introduction

I try to read Rothbard's 'Toward a reconstruction of utility and welfare economics' (in On Freedom and Free Enterprise: The Economics of Free Enterprise (ed. Mary Sennholz), 1956). It does not go far toward its declared goal.

Some Austrian fanboys point to this paper to show Rothbard with a good understanding of the technical details of economics. And it fails.

2.0 Demonstrated Preference and Indifference

Rothbard proposes a concept, 'demonstrated preference', but never explains it clearly. He cites Ludwig Von Mises, among others, as a forerunner. He says that "Actual choice reveals, or demonstrates, a man’s preferences."

Rothbard asserts, like Von Mises, that marginal utilities can be ranked. You will find it difficult to identify anybody outside the Austrian school who agree today. I do not see that confining oneself to discrete increments of a single good helps Rothbard make his case.

I find strange Rothbard's rejection of an indifference relation. He writes:

"Indifference can never be demonstrated by action. Quite the contrary. Every action necessarily signifies a choice, and every choice signifies a definite preference. Action specifically implies the contrary of indifference."

And his arguments are quite curious. I do not find this persuasive:

"It is immaterial to economics whether a man chooses alternative A to alternative B because he strongly prefers A or because he tossed a coin. The fact of ranking is what matters for economics, not the reasons for the individuals arriving at that rank."

I would think that if I use a coin flip to decide, I am demonstrating that I do not care which way the decision comes out.

"The other attempt to demonstrate indifference classes rests on the consistency - constancy fallacy, which we have analyzed above. Thus, Kennedy and Walsh claim that a man can reveal indifference if when asked to repeat his choices between A and B over time, he chooses each alternative 50 percent of the time.

The above is silly. Would you say that the agent is indifferent if his preferences were constant over the observed time? Refusing to accept the hypothesis does not answer the question.

Does getting rid of the indifference relation hinder the use of 'demonstrated preference' to derive individual demand functions, whether defined on a discrete space or not? Maybe a primitive relation of 'not preferred to' is all that is needed. But Rothbard does not say.

3.0 Praxeology and Logic

I understand logic to be about the form of an argument or deduction. The content or meaning of propositions that appear in an argument are not supposed to matter for its validity.

Rothbard attempts to clarify a different conception:

"...a fundamental epistemological error ... pervades modern thought: the inability of modern methodologists to understand how economic science can yield substantive truths by means of logical deduction (that is, the method of 'praxeology')."

Rothbard asserts that his starting axioms must be true:

"...economics, or praxeology, has full and complete knowledge of its original and basic axioms. These are the axioms implicit in the very existence of human action, and they are absolutely valid so long as human beings exist. But if the axioms of praxeology are absolutely valid for human exisence, then so are the consequents which can logically be deduced from them. Hence, economics, in contrast to physics, can derive absolutely valid substantive truths about the real world by deductive logic."

We now know that Rothbard is incorrect on the his axioms. But never mind that.

"...mathematical logic is uniquely appropriate to physics, where the various logical steps along the way are not in themselves meaningful; for the axioms and therefore the deductions of physics are in themselves meaningless, and only take on meaning 'operationally,' insofar as they can explain and predict given facts. In praxeology, on the contrary, the axioms themselves are known as true and are therefore meaningful. As a result, each step-by-step deduction is meaningful and true. Meanings are far better expressed verbally than in meaningless formal symbols."

I have no idea what formal logic has to do with physics. As far as I know, the conception that logic is about the form of an argument goes back to Plato and Aristotle. Hegel may have had a different idea. Frege was writing about the foundations of arithmetic, not about physics.

4.0 Von Neumann-Morgenstern Cardinal Utility

Rothbard has a few remarks on the Von Neumann-Morgenstern definition of utility. Their exposition goes along with the development of a theory of measurement. A measurement scale is such that statements about things measured along that scale are only meaningful up to a set of transformations.

But according to Rothbard, "Measurement, on any sensible definition, implies the possibility of a unique assignment of numbers which can be meaningfully subjected to all the operations of arithmetic." "No arithmetical operations whatever can be performed on ordinal numbers." But non-parametric statistics was already being developed then. I think of the Mann-Whitney-Wilcoxon statistic, for example. In fact, the first edition of Sidney Siegel's textbook, Non-Parametric Statistics for the Behavioral Sciences, dates from 1956.

Rothbard tells us that those who follow Von Neumann and Morgenstern only apply probability to repeatable events: "... unique events are not repeatable. Therefore, there is no sense in applying numerical probability theory to such events. It is no coincidence that, invariably, the application of the neo-cardinalists has always been to lotteries and gambling. It is precisely and only in lotteries that probability theory can be applied." And Rothbard also asserts that "The leading adherents of the Neumann-Morgenstern approach are Marschak, Friedman, Savage, and Samuelson". But Leonard Savage, in his 1954 book, starts the development of his personalistic approach to probability with unique events. His application of personalistic probability to small worlds is supposed to apply numeric probabilities to unique events there. So, again, Rothbard is mistaken. (I take no position on whether unique events can meaningfully be assigned probabilities, either in a small world or not.)

5.0 Conclusion

Rothbard makes a lot of other dubious or incorrect statements. I concede that his references are wide ranging.

Rothbard's undergraduate degree was in mathematics. I pity the fool.

Socialism Worked In Bologna, Italy, For Decades

Socialists and communists have been elected in many places, for significant periods of time. Often they introduced policies that improved the lives of most citizens and increased their freedoms. If I were a member of some of those polities, I would almost certainly have disagreements with details of some policy or other. This post is about a place that I do not know much about.

After the end of World War II, Europeans who had resisted fascism in the underground had a certain prestige. That included the Italian Communist Party (PCI). The PCI became the governing party in Bologna and Florence in much of the time after WW II. You can also look to the government of Emilia-Romagna, a region of Italy that includes Bologna.

The PCI did not enter the national government partly as a consequence of Italian foreign policy. They needed to be in alliance with the USA. Perhaps the CIA was involved in interventions to Italian domestic politics.

The PCI introduced a host of reforms including free busing, better health care, better education, housing cooperatives, and generally good government. I have never been to Bologna. Did the PCI have something to do with the maintenance of the Renaissance character of downtown Florence? The Reggio Emilia Approach approach to childcare is still used elsewhere.

I gather that the PCI never was officially part of a national governing coalition, even after Enrico Berlinguer's historic compromise and championing of Eurocommunism. During the years of lead, the PCI found themselves to the right of those, many young, inspired by Operaismo (workerism). This part of my fragments of a story is uninspiring for those who want to pursue an electoral path.

Misinformation From Economists

I have found another source of economists confidently spouting mistakes, Economics Stack Exchange. This has been around for more than a decade.

If I went back in time, I think I would have trouble convincing my 20 year old self that standard introductory textbooks are incoherent nonsense, never corrected.

I quickly found questions on the Cambridge Capital Controversy. What technology do we need to have reswitching to occur? Why is reswitching and reverse capital-deepening a problem exactly? Why did the Cambridge Capital Controversy have no impact on economic modelling? The participants do not seem to have much to say on the topic.

Ten years, ten moths ago, a question was posed: Can capital still be paid its marginal product in the absence of a homogeneous capital stock? This question was inspired by a Krugman answer to critics of Piketty. One answer was offered:

Different sorts of capital used as separate production technologies prevent clean aggregation to a representative form of capital but does not prevent capital from being paid its marginal product...

On the margin the two sorts of capital don't have the same product and so aggregation doesn't make sense here. But in this setting, it is likely that the rental rate on capital would be equated (r₁ = r₁) because why would you buy one sort of capital when the other sort paid more?

The answer is foolish. The variables are supposed to be "rental prices". They might be in units of numeraire units per year per services of ton iron and numeraire units per year per services of square meters of the services of steel sheets, where the latter are of a specified thickness. You could change their values by a change in units. For example, the latter could be in square yards, not square meters. So it makes no sense to equate these values.

I suspect I can find more confusion.

Eurocommunism and Communist Parties In Coalition Governments In Europe

Eurocommunism was a tendency in communist parties in Europe during the 1970s. The Soviet suppression of the Prague Spring cast communist parties in Western Europe in a bad light. How could they follow Moscow's ead after that? So they started articulating their own path and asserted their independence from the Soviet Union.

This tendency was a moderating tendency. Ernest Mandel, a follower of Trotsky and therefore a critic of Stalin, decried this tendency. He called Eurocommunism "the bitter fruits of socialism in one country."

Anyways, two instances of these "bitter fruits" stand out to me. One is the historic compromise, led by Enrico Berlinguer, the leader of the Italian Communist Party (PCI). This involved support for the Christian Democrats (DC). I guess that the PCI did not enter the government in the elections of 1976, but refused to vote against the DC on no-confidence votes in parliament. In some sense, the communists were to the right of the socialists, let alone the workerists outside of the parties.

Another case is Francois Mitterand, a socialist, who was elected president of France in 1981. He took the French Communist Party (PCF) into his governing coalition. The communists did not do well, being sort of domesticated.

That was a while ago. But take a look at Portugal. Antonio Costa, a socialist, was elected Prime Minister in 2015 and served to 2024. This was a coalition government, called the Left Bloc. The Portuguese Communist Party and the Greens were also coalition members. Costa is now President of the European Council. Since 2024, Portugal's Prime Minister is Luís Montenegro, head of a more right-leaning coalition. To confuse me, his party is the Social Democratic Party. I think the names of the parties suggests, to an American, that they are more left-wing than they are now. As of February, the Portuguese president is Jose Seguro, a socialist. I gather that his election was a matter of staving off the far right, in some sense.

So the history of socialism and communism includes typical parliamentary machinations, compromises, coalitions, and so on. To understand Portugal, I should know more about Salazar and the Carnation Revolution.