Graphs in Economic Theory: Good and Bad
I have known about the following problem for about 45 years. This is the first time that I have gone into print with it. There's a first time for everything.
I am in the process of rethinking economic theory. I have been working on this for over 50 years. I have got the basic reconstruction in mind, but the hard part will come when I write the third pillar of my series, Christian Economics: Scholar's Edition. I hope to begin this project no later than May. Let's make it May 1. "Mayday! Mayday!"
What I'm about to tell you is extremely easy to understand. If you have read anything in Austrian school economics, you already understand it. And yet even the greatest of the disciples of Ludwig von Mises made a fundamental compromise in his presentation of Austrian school economics. It undermines the entire Austrian school methodology. Worse, he knew he was doing it. I'm speaking of Murray Rothbard.
I am probably the first person ever to read Rothbard's Man, Economy, and State who is still alive. I was sent a copy as soon as it was published: the fall of 1962. It was sent to me by a man who was recruiting me into the movement: F. A. Harper, who had published the book through the William Volker Fund. Within a couple of months, he was fired. He then set up the Institute for Humane Studies.
I did not read the book until the following summer, when I was hired by the Volker Fund as a summer intern. Harper had by then departed.
I recognized immediately how important the book was. It made Ludwig von Mises' magnum opus, Human Action (1949), more understandable. It had lots of footnotes. Also, it had lots of graphs. At the time, that seemed to me to be an advantage. I no longer think so.
Let me start with one of these graphs. In the edition published by the Ludwig von Mises Institute (2001), this graph appears on page 88.
This is the most important graph in the book. I will go beyond this: this is the most important graph that I have ever come across in the history of economic theory. Why is this? Because the intersecting curves are not curves. They are a series of X's and O's.
The heart, mind, and soul of Austrian school economics is this: individual action is individual. People make decisions. These decisions are discrete. (They may not be discreet, but that is another matter.) An individual chooses between two options: his highest-ranked option and the second-highest-ranked option. All human action is specific. A person chooses one option rather than another.
The graph describes this in what I cannot resist calling a graphic way. The decisions are discrete. This is how every supply and demand graph should look. There should never, ever be a graph with a curve. There should also never be a graph with a straight line.
Why is this? Because, going back to Euclid, we have been told that a line is a series of infinitesimal points. The line is solid, despite the fact that it is supposedly made up of points. It is not made up of points. Points are infinitesimal. There is no such thing as infinitesimal. I knew that had to be fake when I took geometry at age 13. I went along with it anyway. I wanted to pass the course. The concept is wholly illegitimate when we are talking about human action. There are no infinitesimal decisions. There are only discrete decisions. Thus, the very existence of a straight line or a curve denies the fundamental presupposition of Austrian school economics. There is no way to reconcile Austrian school economics and curves in a graph.
Rothbard knew this. Nevertheless, take a look at the graph on page 120.
Here, we see the first compromise with sin -- as we Bible-quoting people are prone to say, "no larger than a man's hand." (We steal this from the story of Elijah and the cloud: I Kings 18:44.)
Rothbard's compromise came with a series of straight lines that connect the X's and O's. Conceptually, he inserted calculus into arithmetic. This is deadly for Austrian school economics. It is a poison pill.
With respect to Austrian school economics, there are two rules that we have to bear in mind:
"There ain't no such thing as a free lunch."
"There ain't no such thing as a legitimate line in a graph."
The X's and O's are legitimate, but the connecting straight lines are inherently anti-Austrian. Implicitly, they deny the foundational premise of Austrian school of economics: human action is a series of discrete decisions.
It gets worse on page 121.
Do you see that solid black S curve? It is black indeed. Black as sin. The other curves at least have gaps in between the hyphens. They represent the initial temptation of sin. But the solid black S-curve is sin incarnate.
The full surrender to sin appears on page 132.
"Oh! what a tangled web we weave/When first we practice to deceive!"
From this point on, the entire book is compromised. He uses curves in graph after graph.
All of these curves implicitly become subjected to the logic of calculus. Yet this logic is explicitly opposed to the Austrian school position. Calculus assumes infinitesimal changes along a line. Rothbard knew this. In another context, he wrote this:
I have tried in this paper to consider mathematical economics only in its best possible light. Actually, mathematical methods necessarily introduce many errors and inanities which cannot be developed here.The use of the calculus, for example, that has been endemic in mathematical economics assumes infinitely small steps. Infinitely small steps may be fine in physics where particles travel along a certain path; but they are completely inappropriate in a science of human action, where individuals only consider matter precisely when it becomes large enough to be visible and important. Human action takes place in discrete steps, not in infinitely small ones. . . .
The best readers' guide to the jungle of mathematical economics is to ignore the fancy welter of equations and look for the assumptions underneath. Invariably they are few in number, simple, and wrong. They are wrong precisely because mathematical economists are positivists, who do not know that economics rests on true axioms.
The mathematical economists are therefore framing assumptions which are admittedly false or partly false, but which they hope can serve as useful approximations, as they would in physics. The important thing is not to be intimidated by the mathematical trappings.
He wanted to make his book understandable in terms of the prevailing economic textbook fashion. In fact, the book is far less understandable than if he had never included a single graph.
I have committed the conceptual compromise of using supply and demand curves on occasion, but I am never going to do it again, except to show what is wrong with these curves. They add no information that cannot better be expressed verbally.
The great irony here is that Murray Rothbard was the greatest master of verbal explanations of economics in the history of the profession. In 1988, I wrote an article on this: "Why Murray Rothbard Will Never Win the Nobel Prize." I said he was far too clear for the Nobel committee ever to consider him for the honor.
His book is magnificent whenever he is not using graphs, and whenever he does not use the obscene word, "equilibrium." The concept of equilibrium assumes for explanatory reasons that men are omniscient, which means they are God. For purposes of explanation, the economist assumes that there is no uncertainty in the hypothetical world of his initial explanation of cause-and-effect. But if there is no uncertainty, there is no lack of knowledge. There are no profit opportunities to be exploited.
The Austrian school is opposed to this concept. It believes that human action is always burdened by the problem of uncertainty. It places the entrepreneur at the center of the market process. Ludwig von Mises made this clear, and Rothbard made it even clearer. Yet he constantly uses the concept of equilibrium in association with graphs that assume omniscience. He also tries to explain Austrian school economic categories in terms of equilibrium. It cannot be done. They are mutually exclusive. Mises only resorted to it once, in his discussion of time preference, which undermined his theory of the rate of interest.
Mises never used a graph with a line in it. This was not because he did not understand graphs with lines. It was because he understood fully the implications of lines, and he saw that those implications are opposed to his theory of human action. He also never used anything more than arithmetic formulas. He never invoked calculus. That was not because he did not understand calculus. That was because he understood that the assumption of calculus, namely, infinitesimal changes along a line, is incompatible with his theory of human action.
In my book, I'm going to do my best to imitate Rothbard at his best: offering verbal explanations of economic cause-and-effect. I am not going to rely on the concept of equilibrium, and I am not going to rely on graphs with lines in them.