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.

A Switch Point Along The Same Wage Curve With Multiple Agricultural Commodities

Figure 1: Wage Curves Around An Anomalous Switch Points

This post presents another anomalous switch point. A switch point is anomalous in that it has properties that cannot hold for a switch point in a model of single production, with inputs of labor and circulating capital alone.

This example is one with multiple agricultural commodities and intensive and extensive rent. The technology and the endowments of land are the same as in this example.

Required net output, that is, final demand, varies. I start by postulating that final demand consists of 28 bushels wheat and 28 bushels rye. Under this assumption, Alpha, Beta, Epsilon, and Lambda are feasible techniques.

The cost-minimizing technique at a given rate of profits must be:

• Feasible.
• Have non-negative prices for all commodities produced under the technique, have a non-negative wage, and have non-negative rents on all scarce lands.
• Such that no process not operated under the technique obtains extra profits.

Epsilon is cost-minimizing up to a rate of profits of approximately 223.6 percent. A reswitching of the order of efficiency occurs over the range at which Epsilon is cost-minimizing. After the switch point, as illustrated in Figure 1, Alpha is cost-minimizing.

Figure 1 also illustrates a fake switch point at a rate of profits of approximately 219.0 percent. The wage curves for Alpha and Delta intersect at the fake switch point. The wage curve for Alpha is also the wage curves for Epsilon and Zeta. Likewise, the wage curve for Delta is also the wage curves for Eta and Theta. Epsilon is the unique cost-minimizing technique at and around this fake switch point. The prices of produced commodities (iron, wheat, and rye) differ, at the switch point, between the techniques for the two intersecting wage curves. In this sense, the fake switch point resembles the one in the example from Bidard and Klimovsky. The rent on type 2 land is positive under Epsilon, which would not be the case is this switch point was non-fake. Nor are the rents on type 1 land zero under Eta and Theta at this fake.

But consider again the switch point between Epsilon and Alpha. Under Alpha, only type 1 land is farmed, but only partially. Epsilon extends Alpha to produce wheat on type 2 land, to the extent of its endoment. The switch point lies along a single wage curve, which is anomalous.

Suppose that final demand was small enough that both Alpha and Gamma were feasible. For example, Alpha, Beta, Gamma, and Delta are the only feasible techniques when required net output consists of 10 bushels wheat and 10 bushels rye. Then Gamma is cost-minimizing from before the switch point, from approximately 176.8 percent. Alpha is cost-minimizing after the switch point. As with Epslion, under Gamma wheat is produced on type 2 land. But, unlike Epsilon, type 2 land is not farmed under Gamma to the extent of its endowment and the process in which wheat is produced on type 1 land is no longer operated. With this final demand, the example is one of reswitching between Gamma and Delta, at a lower rate of profits than shown.

Or suppose final demand consisted of 30 bushels wheat and 30 bushels rye. Then Beta, Epsilon, Iota, Kappa, and Lambda are feasible. Then this is a switch point between Epsilon and Iota. The same processes are operated under Epsilon and Iota, but which land is scarce varies. Iota is a technique in which landlords obtain intensive rent on type 1 land. The rent on type 1 land is negative under Iota before the switch point.

I have now found switch points:

• Along a single wage curve, with no intersecting wage curve; with variation in which processes are operated between the cost-minimizing techniques.
• In which wage curves intersect, but no variation occurs in which processes are operated between the cost-minimizing techniques.

The above switch point between Epsilon and Alpha combines these two phenomena, in some sense. I have also found fake switch points:

• In which wage curves intersect; the cost-minimizing technique does not vary.

These results suggest that concept of a switch point is not tightly tied to intersections of wage curves in models of joint production.

Michael Overton Interviewing Margaret Wright On Operations Research

I do not know what order these should be in or even if this is the entire interview. I did not know of either Margaret Wright or Michael Overton before stumbling on this. Apparently she was once president of the Society of Industrial and Applied Mathematicians, worked with George Dantzig at Stanford, and so on.

• Is linear programming polynomial time?
• Karmaker's algorithm
• Creating algorithms and writing software
• First job at GTE Sylvania
• Early years in California, Arizona and choosing Stanford
• Operations research at Stanford
• Faculty in math and computer science at Stanford
• Committees and SIAM
• Advisory Committees and the NAS
• Unexpected connections
• Accomplishements and progress for women

I think I have not appreciated how much progress has been made in the last few decades:

"... but look back and see the progress we've made. So in optimization at various points people have said well, for nonlinear problems, you can solve problems with hundreds of variables. Of course, that's a very imprecise statement. They never say what kind of problems or whatever. Today we had a talk where the person was talking about hundreds of thousands or millions of variables. That's an amazing change. It's an amazing change in capability. And it's not all due to computer hardware. I think sometimes people think, oh, machines are faster; machines are bigger. But it's smarter and better algorithms, which is the area you and I work in, right? Not making faster machines. We try to take advantage of them, but we don't make them run faster. And to me, that's astonishing. And the great part of it, I think there's still interesting problems that don't have many variables in this non-derivative optimization area." -- Margaret Wright

I do not understand interior point methods or why the Simplex algorithm works so well on average.

Anomalous Switch Points

This post is to remind me that I have discovered some anomalous switch points. I am introducing the concept of an anomalous switch point here.

Consider a switch point in a model of single production, with inputs of labor and circulating capital alone. At a (generic) switch point, one process replaces another in an industry that produces a commodity that exists in both techniques. Other processes can be introduced or removed if some capital goods are used only in one of the two processes for the common industry. The switch point is on the wage frontier formed by the outer envelope of the wage curves for all techniques. Two wage curves intersect at the switch point.

An anomalous switch point differs in some property from a generic switch point in models of circulating capital alone.

The anomalous switch points under consideration here are not flukes. A fluke switch point is one in which any permutation of some parameters destroys the qualitative property under consideration for the switch point. A switch point in which two wage curves are tangent on the frontier is an example of a fluke. A switch point in which two processes are replaced, one in each of two industries that exist in the techniques with intersecting wage curves. In this example with both types of flukes, and more, four wage curves intersect at switch point for the second kind of fluke.

Anomalous switch points include:

• A switch point in which the same processes are operated for both techniques: This example is one of extensive rent. The levels of operation of the processes and the land that is scarce vary around the switch point.
• Another switch point in which the same processes are operated for both techniques: This example is one of intensie and extensive rent with multiple agricultural commodities.
• A switch point along a single wage curve: This example combines fixed capital and extensive rent. Two techniques, Nu and Omicron, have the same 'solving system' and, hence, the same wage curve. The techniques differ in the economic life of machine when operated on scarce land that pays extensive rent.

Other switch points can be considered anomalous. D'Agata (1983) has examples with non-unique and non-exisitng cost-minimizing techniques in a model of intensive rent. Two techniques are cost-minimizing before a switch point. No cost-minimizing technique exists after the switch point. I think D'Agata's examples are more challenging to Sraffa's price theory than mine. Woods (1990) also has an example in joint production, without rent.

A non-fluke switch point in a model of joint production in whcih three wage curves intersect is another anomalous switch point. Bidard and Klimovsky have a genuine switch point like this in the paper in which they introduce the concept of a fake switch point. I think I also have examples in my models that combine intensive and extensive rent.

I do not consider anomalous a switch point on the wage frontier, in which the frontier is not the outer envelope of wage curves. The wage frontier must be the outer envelope in models of single production, but researchers in joint production established last century that this property need not hold in models of joint production, including in models of extensive rent.

Fake switch points can also be anomalous. With joint production, a question arises about which process should be replaced when a new process is introduced. A fake switch point, in a model of joint production, is an intersection of (non-tangent) wage curves in which the cost-minimizing technique does not change. The intersection's location and existence depend on the numeraire. The price of a commodity produced under both techniques whose wage curves intersect varies among techniques.

A fake switch point can be anomalous in that it deviates from properties of Biard and Klimovsky's example:

• Example fixed capital and extensive rent: Prices of commodities produced under both techniques do not vary among techniques at switch points. Price and rent vary between techniques only for non-commodities (that are free) under the non-cost-minimizing technique.

Technical terms: Switch point, Anomalous switch point, Fake switch point, Anomalous fake switch point, Fluke switch point.

References

• D’Agata, A. 1983. The existence and unicity of cost-minimizing systems in intensive rent theory, Metroeconomica 35: 147-158.
• Bidard, Christian and Edith Klimovsky. 2004. Switches and fake switches in methods of production. Cambridge Journal of Economics 28 (1): 88-97.
• Vienneau, Robert L. 2024. Characteristics of labor markets varying with perturbations of relative markups. Review of Political Economy 36(2): 827-843.
• J. E. Woods (1990) The Production of Commodities: An Introduction to Sraffa, Humanities Press International