Jeffrey Miron And Propertarian Advocacy Taught At Harvard

Jeffrey Miron teaches EC1017 at Harvard. "A Libertarian Perspective on Economic and Social Policy" is the course title, and PDFs for the lectures are available for download.

Based on the notes for the three lectures I looked at, Miron supposedly derives propertarian policy from intermediate principles (e.g., "efficiency"), with little to no data on relative magnitudes. I don't care for this approach myself, never mind the policy conclusions. He seems to mention no names. The reading list (from Spring 2009) does not include his book (which I haven't read). Perhaps Miron's experience is that Harvard students can be counted on to bring up Rawls, Karl Popper's piecemeal social engineering, Alan Haworth, and even Nozick.

"When Adam Delved And Eve Span, Who Was Then The Gentleman?"

I had associated the title of this post with the 17th century and the period of the English Civil War. I think it occurs somewhere in Christoper Hill's The World Turned Upside Down: Radical Ideas During the English Revolution. Hill's book is an account of Anabaptists, Diggers, Levellers, Muggletonians, the New Model Army, Ranters, and Quakers - a very heady and confusing mix.

So I was startled yesterday to read the phrase in Crispin: The Cross of Lead. This is a Newberry-prize winning children's book, by Avi. It is set in England in the 14th century. I think it conveys a good idea of the drudgery and isolation of village life at the time; the seemingly unchangable hierarchy; and the bustle, confusion, and filth of a city before modern plumbing. I also like that Christianity is presented as a form of life, a language that all we see cannot but help using.

So is Avi's use of the phrase an anachronism? Hill may reference it, but, if so, the people of his time were harking back to a previous one. Apparently, the phrase is associated with John Ball, the leader of the 1381 Peasants’ Revolt. I know nothing about the Peasants’ Revolt, although Hill does refer to it in one line. But John Ball does appear in Avi’s book. Crispin, our thirteen-year old hero, overhears him conspiring. John Ball says:

"...that no man, or woman either, shall be enslaved, but stand free and equal to one another. That all fees, obligations, and manorial rights be abolished immediately. That land must be given freely to all with a rent of no more than four pennies per acre per year. Unfair taxes must be abolished. Instead of petty tyrants, all laws shall be made by consent of a general commons of all true and righteous men.

Above all persons, our lawful king shall truly reign, but no privileged or corrupt parliaments or councilors.

The church, as it exists, should be allowed to wither. Corrupt priests and bishops must be expelled from our churches.. In their place will stand true and holy priests who shall have no wealth or rights above the common man..."

Update: I've learned a new vocabulary word: A Jacquerie is a peasants' revolt, named after the French peasants' revolt of 1358.

Infinities Of Infinities

1.0 Introduction

This is mathematics, not economics. It is meant to be an introduction to how abstract mathematicians can be.

2.0 Some Definitions for Set Theory

Two sets are the same size if and only if they can be put into a one-to-one correspondence with each other.

A set S₁ is bigger than the set S₂ if and only if:

• A subset of S₁ can be put into one-to-one correspondence with S₂, and
• S₂ cannot be put into one-to-one correspondence with S₁.

A set is countably infinite if and only if it can be put into one-to-one correspondence with the set of natural numbers N = {0, 1, 2, ...}. (The integers and the rational numbers are both countably infinite.)

The power set P(S) formed from the set S is the set of all subsets of S. For example, the power set for the set {a, b} contains four elements:

P( {a,b} ) = {S | S ⊂ {a, b}.} = { ∅, {a}, {b}, {a, b} }

3.0 A Theorem

Theorem For all sets S, the power set P(S) is bigger than the set S.

Proof: First, show that a subset of P(S) can be put into one-to-one correspondence with S. Consider the set of singletons:

{ {a} | a is an element of S }.

Since each singleton {a} is a subset of S, the set of all singletons is a subset of P(S). And the set of all singletons maps one-to-one to S.

Next, show, by a proof by contradiction, that P(S) cannot be put into one-to-one correspondence with S. Suppose that there exists a one-to-one function f that maps S into P(S).

Notice that, for all a ∈ S, f(a) is a subset of S. For any given a in S, either

a ∈ f(a)

or

a ∉ f(a).

Define the set T to be the set of all elements in S that map under f to a set not containing themselves:

T = { a | a ∈ S and a ∉ f(a)}

Since f is one-to-one and T is a (possibly empty) subset of S, there exists, by hypothesis, an element b in S such that

f(b) = T.

Now consider whether or not

b ∈ T.

Suppose true. But, by the definition of T as the set of elements of S that are not elements of the subset of S that they map to, b cannot be in f(b), that is, T. But, if b is not in f(b), by the definition of T, b must be in T. So either way yields a contradiction. Thus, no such b can exist.

So I have shown that there does not exist an element b in S that maps under f to T. Yet T is in P(S). Thus, f cannot be one-to-one. Which was to be demonstrated.

4.0 Applying the Theorem to the Set of Natural Numbers

An interesting property of the above proof is that it applies to both finite sets and infinite sets. So start with N, the set of natural numbers. N contains an infinite number of elements. But, by the theorem, P(N), the set of all subsets of the natural numbers, is a set containing a bigger infinity. One can go on to form a set of infinite sets, each with a bigger size infinity:

U₀ = { N, P(N), P(P(N)), ..., Pⁿ(N), ...}

(Under the Zermelo Frankel axioms for set theory, the elements of a set do not need to all be of the same "type".) One can repeat the process of forming a sequence of power sets:

U₁ = { U₀, P(U₀), P(P(U₀)), ..., Pⁿ(U₀), ...}.

One can even imagine constructing a power set of all these difference size infinite sets in this sequence of sequences of sets:

P( { U₀, U₁, U₂), ...} )

The definitions of infinite sets need not stop here.

4.0 Conclusion
I don't find the above hard to follow if I think of it as merely a matter of syntactic manipulation of symbols. Do I have a clear idea of these infinities of different size infinities after every point in this sequence of definitions? Does anybody? This is not so clear to me.

Reference

• Paul R. Halmos (1960) Naive Set Theory, Springer Verlag

Onieda-Like Community Near Stroud, In Gloucestershire?

Martin Gardner once received a letter referring to "an Oneida-like community near Stroud, in Gloucestershire". The topic of the letter was something else, on visualizing four-dimensional space. Can anybody provide me with more information on this community?

Full Unemployment

I find amusing the political slogan with which I title this post. We want the engineers to do their job in applying control theory to stepping motors, in creating Artificial Intelligences, in developing techniques of information management, etc. such that nobody need work out of necessity. Maybe in some future day, machinery will produce all we need, including more machinery. When the economic problem is solved:

"Man will be faced with his real, his permanent problem - how to use his freedom from pressing economic cares, how to occupy the leisure, which science and compound interest will have won for him, to live wisely and agreeably and well." -- John Myanard Keynes (1930)

Marx and Engels envision a post-capitalist society:

"Where nobody has one exclusive sphere of activity, but each can become accomplished in any branch he wishes, society regulates the general production and thus makes it possible for me to do one thing today and another tomorrow, to hunt in the morning, fish in the afternoon, rear cattle in the evening, criticize after dinner, just as I have a mind, without ever becoming hunter, fisherman, shepherd or critic. -- Karl Marx (1947, p. 22)

Bruce Sterling (1989) imagines that, in such a world, one will cultivate ones taste for "The Beautiful and the Sublime". At any rate, in this pleasant world of tomorrow, all will be able to devote themselves to great cooking, fostering social relationships, art, or whatever one may choose.

Curiously enough, the classical tradition in economics, as exemplified, for example, in Sraffa or Von Neumann, provides tools for analyzing how prices might be formed in a post-scarcity world. For example, Joan Robinson, in her first essay in (Robinson 1962) has a section titled "A model for the future" with a subsection on "The Robots". This is a model of a (maybe impossible) capitalist economy. In my version, all production is carried out in automated factories, and these factories are owned by firms traded on a stock exchange. Everybody owns shares, and the trading of these shares sets up a tendency torwards a uniform rate of profits.

I have described before some formulation of a price system consistent with this institutional set up. For now, I want to describe prices when the managers of each firm in an industry have chosen a process for producing the firm's output. As usual, I assume, for simplicity that all processes require the same time to operate, say, a year. Inputs must be purchased at the beginning of the year, and outputs become available at the end of the year. A reference set of prices satisfies the following system of equations:

p A β = p B

where

• A is a square matrix; a_i,j is the quantity of the ith commodity used as input when the jth process is operated at a unit level.
• B is a square matrix; b_i,j is the quantity of the ith commodity produced as output when the jth process is operated at a unit level.
• p is a row vector of prices; p_i is the price of the ith commodity.
• (β - 1) is the rate of profits.

This formulation allows for robots to last for more than one year. The quantity of a dated robot enters as an input, and the output includes a robot one year older, as well as whatever other outputs are produced by that process. The use of such robots is a special case of the more general model of joint production encapsulated in the above system of equations.

Various conditions must be imposed on the coefficients of production A and B to ensure a solution simultaneously exists for prices and the dual problem of the choice of technique. Von Neumann, in fact, assumes that each commodity is either used as an input or produced as an output in a poisitive amount in each process. Joan Robinson assumes the existence of "some standard physical elements (say, nuts and bolts) that enter into the production both of robots and of salable goods." But I do not want to discuss more of the mathematics in this post.

References

• D. G. Champernowne (1945-1946) "A Note on J. v. Neumann's Article on 'A Model of Economic Equilibrium'", Review of Economic Studies, V. 13, N. 1: pp. 10-18.
• John Maynard Keynes (1930) "Economic Possibilities for our Grandchildren", in Essays in Persuasion, W. W. Norton & Company
• Karl Marx and Frederick Engels (1947) The German Ideology: Parts I & III, International Publishers
• Joan Robinson (1962) Essays in the Theory of Economic Growth, Macmillan.
• Piero Sraffa (1960) , Cambridge University Press.
• J. v. Neumann (1945-1946) "A Model of General Economic Equilibrium", Review of Economic Studies, V. 13, N. 1: pp. 1-9.
• Bruce Sterling (1989) Crystal Express, Ace Books

Nortz's Johnny Cake

Ingredients

1/4 cup sugar
1/3 cup shortening
1 beated egg
1 cup sour milk
1 teaspoon baking soda
1 teaspoon baking powder
1 cup flour
1 1/2 cup cornmeal
1/2 teaspoon salt

1) Mix in above order, stirring thoroughly after adding each ingredient. Bake about 1/2 hour at 400 F.

2) Serve sliced with applesauce or maple syrup.

Makes approximately 10 servings. I usually make a double recipe when making my great-grandmother's Johnny cake.

Phenomenology

"One of the embarrassing dirty little secrets of economics is that there is no such thing as economic theory properly so-called. There is simply no set of foundational bedrock principles on which one can base calculations that illuminate situations in the real world." -- Brad DeLong

My title does not refer to an approach in continental philosophy associated with Husserl and Heidegger. Rather, I refer to a term used in physics and engineering by practitioners who know they are not trying to develop models derived from fundamental laws, but only modeling the phenomena.

I find it of interest that Brad DeLong has recently described economics as phenomenology. A noted "rocket scientist" on Wall Street came to the same conclusion:

"The techniques of physics hardly ever produce more than the most approximate truth in finance because 'true' financial value is itself a suspect notion. In physics, a model is right when it correctly predicts the future trajectories of planets or the existence and properties of new particles, such as Gell-Mann's Omega Minus. In finance, you cannot easily prove a model right by such observation. Data are scarce and, more importantly, markets are arenas of action and reaction, dialectics of thesis, antithesis, and synthesis. People learn from past mistakes and go on to make new ones. What's right in one regime is wrong in the next.

As a result, physicists turned quants don't expect too much from their theories, though many economists naively do. Perhaps this is because physicists, raised on theories capable of superb divination, know the difference between a fundamental theory and a phenomenological toy, useful though the latter may be. Trained economists have never seen a really first-class model. It's not that physics is 'better', but rather that finance is harder. In physics you're playing against God, and He doesn't change his laws very often. When you've checkmated Him, He'll concede. In finance, you're playing against God's creatures, agents who value assets based on their ephemeral opinions. They don't know when they've lost, so they keep trying." -- Emanuel Derman (2004) My Life as a Quant: Reflections on Physics and Finance, John Wiley & Sons.

I think one can read intimations of Soros' reflexitivity or Joan Robinson's historical time in the above quote. Derman is even more direct about a Post Keynesian concept elsewhere:

"Slowly it began to dawn on me that what we faced was not so much risk as uncertainty. Risk is what you bear when you own, for example, 100 shares of Microsoft - you know exactly what those shares are worth because you can sell them in a second at something very close to the last traded price. There is no uncertainty about their current value, only the risk that their value will change in the next instant. But when you own an exotic illiquid option, uncertainty precedes its risk - you don't even know exactly what the option is currently worth because you don't know whether the model you are using is right or wrong. Or, more accurately, you know that the model you are using is both naive and wrong - the only question is how naive and how wrong." -- Emanuel Derman (2004)