The Theoretical Case Against Curves in Economics

Gary North

October 10, 2008

If I ran the Mises Institute, I would sponsor a conference of scholars on this topic: "Great Methodological Blunders in the History of Economic Thought." I would invite each participant to make a case for the greatest blunder.

High on the list would be Walras' use of simultaneous equations. Because it assumed away the problem it was intended to solve -- the free market's allocation problem -- by beginning with omniscience, it led the craft guild of economists down the primrose path to irrelevance. The guild has never found a conceptual way to get from here -- non-omniscience -- to there: resource allocation. The guild has preferred to remain in the rarified world of assumed omniscience and simultaneous equations, the better to resemble physics. They fully understand the law governing the acquisition of tenure in tax-funded universities. This is characterized accurately by this saying. "When an economist dies, he is reincarnated into one of two forms. A good economist returns as a physicist. A bad economist returns as a sociologist."

I have long had a different view of the use of simultaneous equations. I have interpreted this as a benefit to Austrian School economists. Our members rarely use simultaneous equations. We therefore can better communicate our ideas to non- economists, who have either money or power to dispense. Meanwhile, neoclassical economists can barely communicate with each other. They use higher mathematics to prove the case for this or that, but hardly anyone inside the profession bothers to read his colleagues' unreadable journal articles. This grants, if not a monopoly, then at least an oligopoly to Austrians. Never look a gift horse in the mouth, I always say. This may not be an axiom of Austrian economics, but it ought to be raised to corollary status.

My target is the use of curves in graphs. This practice goes back to William Stanley Jevons in the early 1870's. Curves were adopted by Alfred Marshall in his textbook. His famous supply-demand scissors have become ubiquitous. From the first high school textbook in economics to the latest issue of Econometrica, we find graphs filled with curves and lines.

When Austrians imported the simple supply-demand graph, they imported a Trojan horse. It was filled with methodologically ruthless Greeks -- not just Greeks in general, but Parmenideans. The disciples of Parmenides do not cooperate with the followers of Heraclitus. Heraclitus sought to water the crops with water diverted from the river famous for never being the same each time you stick your foot into it. Everything flows in Heraclitus' world. This is the realm of entrepreneurship. Nothing flows in Parmenides' world. His is the realm of simultaneous equations.


Assuming Away Time

The supply-demand scissors rely on the phrase, "other things remaining equal." When we draw a demand curse, it goes downward and to the right. We say, "when the price falls, more is demanded." But what we say is not what the graph necessarily teaches. The price does not fall. It takes time for a price to fall. But the graph is timeless. This is why the verbal methodology of Austrianism reflects the truth of action over time. The curves of neoclassical economics do not correspond with action over time. They are analogous to Walras' simultaneous equations. Simultaneity is the key to understanding one of the two main errors of neoclassical economics. Simultaneity denies entrepreneurship. (The other main error is omniscience: no unexploited profit opportunities. Omniscience denies entrepreneurship.)

A demand curve assumes that no change has taken place, other than a lower price. The curve implicitly asks the reader to believe the following: "If you were to offer a good for sale at varying prices, in the same moment of time, here is how buyers would respond to each price." Timelessness is mandatory in the graph in order to maintain the assumption, "other things remaining equal." This is because time changes other things. The rule of the real world is this: "You cannot change just one thing." So, the graph dwells in Parmenides' timeless world, not Heraclitus's world of change.

A demand curve assumes the following about buyers: (1) their tastes do not change; (2) they think that the same item is being offered for sale at various prices (no counterfeit goods); (3) they think that each price is universal -- no better price elsewhere. The graph therefore assumes two things; (1) a representation of timelessness is valid for describing events in time; (2) we can change only one thing.

If a person is told that he can buy an item at a significantly lower price than he could before, he may think -- probably will think -- "What's the catch? This has to be a fake." He refuses to purchase at the lower price. The information he possesses about past prices affects his decision. A curve assumes infinite knowledge about past prices, for a price line contains an infinite number of infinitesimal prices. There is no escape from time in real-world price-taking. The graph assumes away time. It therefore assumes away the process of actual decision-making regarding prices.

On the other hand, he may buy it after all, if he thinks it is stolen. He may respond exactly as Mordecai Jones insisted he would in The Flim-Flam Man (1967). "You can sell a man anything if he thinks it's stolen." He had a phrase: "You can't cheat an honest man." He believed everyone is dishonest, so all mankind was his target. But his point was clear: a seller has to offer a believable reason for selling a high-quality good at a very low price. Otherwise, there would be no sale.

If the continuous line continues down and to the right, the buyer at any point before the final sale at the lowest price must be assumed to be ignorant of past pricing -- higher on the curve -- so as not to forecast a lower price in the future, and therefore refuse to buy. The curve, like the graph itself, must be timeless.

A curve -- demand or supply -- assumes the following scenario: (1) a person or group of people will universally respond in a totally predictable way to separate price offers that (2) are made at the same time, (3) yet each offer must be considered by the price-taker -- he is implicitly assumed by the graph to be a price-taker -- in complete isolation from all the other price offers, (4) which are infinite in number and infinitesimal in size and can therefore legitimately be represented by a curve. In short, the supply and demand curves are neverland incarnate.

First-year economics students are never informed of any of this, and when a few of them earn doctorates, virtually all of them remain oblivious to what their favorite chart silently but necessarily assumes. The phrase, "other things remaining equal" seems to be necessary to economic reasoning, but it is nonetheless preposterous when applied literally to the real world. The phrase assumes regarding human action that which can never be true of human action, namely, that you can change just one thing. In short, the timeless logic of Parmenides remains logically inapplicable to the changing world of Heraclitus. This remains true after 2,400 years. Or, put in a more familiar phrase, the more things change, the more they remain the same.

It may be that human beings cannot think economically without Parmenidean timelessness, where other things always remain equal. So, we resort to the use x's and o's to illustrate what we have implicitly assumed about price-taking but have not proven and cannot prove regarding the world of time. But to take the next step involves us in a unilateral surrender to neoclassical economics.

Assuming Away Choice

In Man, Economy, and State, Rothbard offered this critique of neoclassical economics. I quote it at length because I cannot figure out a way to cut any of it and still retain its power -- a problem with citing much of what he wrote.

This illustrates one of the grave dangers of the mathematical method in economics, since this method carries with it the bias of the assumption of continuity, or the infinitely small step. Most writers on economics consider this assumption a harmless, but potentially very useful, fiction, and point to its great success in the field of physics. They overlook the enormous differences between the world of physics and the world of human action. The problem is not simply one of acquiring the microscopic measuring tools that physics has developed. The crucial difference is that physics deals with inanimate objects that move but do not act. The movements of these objects can be investigated as being governed by precise, quantitatively determinate laws, well expressed in terms of mathematical functions. Since these laws precisely describe definite paths of movement, there is no harm at all in introducing simplified assumptions of continuity and infinitely small steps.

Human beings, however, do not move in such fashion, but act purposefully, applying means to the attainment of ends. Investigating causes of human action, then, is radically different from investigating the laws of motion of physical objects. In particular, human beings act on the basis of things that are relevant to their action. The human being cannot see the infinitely small step; it therefore has no meaning to him and no relevance to his action. Thus, if one ounce of a good is the smallest unit that human beings will bother distinguishing, then the ounce is the basic unit, and we cannot simply assume infinite continuity in terms of small fractions of an ounce.

The key problem in utility theory, neglected by the mathematical writers, has been the size of the unit. Under the assumption of mathematical continuity, this is not a problem at all; it could hardly be when the mathematically conceived unit is infinitely small and therefore literally sizeless. In a praxeological analysis of human action, however, this becomes a basic question. The relevant size of the unit varies according to the particular situation, and in each of these situations this relevant unit becomes the marginal unit. There is none but a simple ordinal relation among the utilities of the variously sized units.

Yet in the previous chapter, with Figure 14, he introduced his first graph using supply and demand curves. Before this, in Figures 5 and 6, his graphs used discrete little circles (supply) and x's (demand) to reveal the shape of the things we like to call curves but which cannot possibly be curves. We find it difficult to speak of anything except curves, in a way that we do not feel equally constrained about speaking of alternatives to simulations equations. With Figure 13, he made the transition, filling in the spaces in between the circles and the x's with straight lines. Then, on the next page, Figure 14 makes the transition.

Most of the graphs after Figure 14 are traditional. They employ curves. The epistemological problem with curves for economists is a blessing for physicists. They invite the calculus. They assume continuity.

In high school geometry classes, most of us are first introduced to Parmenides' timeless logic by way of Pythagoras. We are told that a line is a series of infinitely small dots. The brighter people in the class think, "then an inch-long line has as many infinitely small dots as a mile-long line." These are the sort of people who gravitate toward Zeno's paradoxes. They may eventually discover this one: "If a Keynesian is half way to tenure, and an Austrian is behind him, the Austrian will race to overtake the Keynesian. But in the time it takes the Austrian to get halfway to the Keynesian's position on the tenure track, the Keynesian will have moved ahead. Thus, the Austrian will never overtake the Keynesian." Of course, the same would be true if an Austrian were initially ahead of a Keynesian on the tenure track. But theory must be in contact with reality at some point, so this alternative description of the initial positing is not ever considered.

To draw a curve to represent economic action -- timeless economic action -- we implicitly make the following two assumptions, each clearly false: (1) there can be price changes that are infinitesimal; (2) people respond to price changes that are infinitesimal. How often does an economics teacher warn his students of these two assumptions? Rothbard warned readers about the methodological dangers of mathematics, but not the methodological dangers of the assumptions undergirding a curve, which are the same as the assumptions undergirding the use of calculus in economic theory.

When we enroll in our first class in economics, we have already been conditioned into accepting the usefulness, despite the obvious logical impossibility, of lines. So, when we see our first graph with a line in it, we make the transition without thinking about it. Very few economists ever think through what the line assumes: that the methodology of the science of economics is the same as the methodology of physics. There are no decisions in physics. There are no decisions in neoclassical economics, either. Everyone is an omniscient price-taker. No one is an entrepreneurial price-forecaster. Even if there were entrepreneurs, they could not get their grubby hands on any capital. They would have no more influence on the outcome than some down-on-his-luck tout has on the racetrack's odds.

From the moment an economist takes the easy way out at the blackboard and rapidly draws lines rather than circles and x's, which take longer, he has run up the white flag of surrender to the neoclassical camp. He has substituted convenience for methodological rigor. He has not made clear to his students, graph by blackboard graph, that the lines assume away what Austrian economists insist are the fundamental issues of economics: uncertainty, entrepreneurship, and change. The lines assume away human action.

The graph also assumes that buyers are price-takers and suppliers are price-takers. This means that there is no entrepreneurship in the traditional graph which illustrates supply and demand. There is no entrepreneurship because entrepreneurship takes place over time: buy low now; sell high later. There is also no entrepreneurship for one of two other reasons: either everyone is omniscient (no profit opportunities) or else everyone is totally ignorant of other markets and other prices (no perceived profit opportunities). It is not clear from the graph which of these reasons should be accepted, but one of them must.

Rothbard vs. Mises

Consider Mises. He used only one graph in his career. That was very early: Socialism (1922). He never did it again.

Consider Hayek. He used a few graphs with curves in Prices and Production (1931), his first book, and The Pure Theory of Capital (1941). Nowhere else.

Consider Kirzner. He used graphs with curves throughout his intermediate economics textbook, Market Theory and the Price System (1963). He did not allow it to be reprinted, and he never revised it. He never again used a graph, let alone a graph with a curve in it.

Consider Gordon. In his book, An Introduction to Economic Reasoning, David Gordon offers only graphs without curves. In his chapter on supply and demand, he uses mostly x's. Two graphs use discontinuous hyphens rather than curves. These graphs convey the fundamental principles of supply and demand.

This is why Rothbard's use of curves is strange. He clearly identified the methodological error involved in the adoption of higher mathematics in economic reasoning, yet he also adopted a teaching tool that fairly cries out, "Calculus spoken here." The moment we use the conceptual apparatus of "function," we have surrendered Austrianism's central premise: human action.

At the second Austrian conference, which was held in 1975 in Connecticut, Percy Greaves in a presentation called Rothbard on something he had written which was not sufficiently Misesian. After the lecture, Rothbard chortled: "This is the sort of criticism I appreciate." I hope he would have accepted mine with similar verve.

A Recovery Program

It is so easy to adopt curves in our supply and demand graphs. We may say to ourselves, "I can quit any time," but somehow we never do.

We need to attend regular meetings in which we stand in front of our peers and say, "Hi. I'm [first name only], and I'm a neoclassical economist." The audience responds: "Hi, [name]." Then we give our testimonies.

Thirty meetings for thirty days. Easy does it. One day at a time.