He accuses AE of scorning the continuous when everybody else uses it, but blithely using it themselves.
First, he quotes their rejection of it:
Mises and Rothbard have a final related objection to standard neoclassical utility theory: the assumption of continuity. Quoting Rothbard, "[H]uman 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." The implications are broader than they may initially appear, because as a mathematician will tell you, you can't differentiate a function that isn't continuous. This means that if Mises and Rothbard is correct, the pervasive use of calculus in economics must be rejected in toto.
Then, in a dashingly brilliant stroke, he shows how the Austrians themselves use continuity in their ubiquitous supply and demand curves:
One obvious problem arises here. Without continuous preferences, it is also highly unlikely that e.g. supply and demand can ever be equal. If you draw the supply and demand curves continuously, then they are (almost) bound to intersect. But if you draw them as a discrete set of points, supply and demand in general don't have to intersect. Thus, the argument against calculus based upon the rejection of continuity also argues against even the use of simple algebraic constructs - like intersecting supply and demand lines - that fill Rothbard's works.
Of course, one could say that the unrealism of continuity is only minor. But this is precisely the reply that Rothbard considered and rejected: "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... The crucial difference is that physics deals with inanimate objects that move but do not act."
You can't have it both ways, guys, explains Caplan:
Rothbard thereby runs into a serious contradiction. If the assumption of continuity is not a harmless fiction, then it is incumbent upon him to remove all of the supply and demand intersections in his works, and to state that supply equals demand only under extremely rare conditions (for without continuous pricing, the odds that supply and demand actually intersect are very slim). This position is certainly coherent (and since Mises used no diagrams, it would be less work for him to adhere to it), but rather peculiar. Alternately, Rothbard could concede that assuming continuity rarely alters substantive results, and accept both supply and demand intersections and the use of calculus as methodologically kosher in economics.
Dang, he really hit a home run here, it looks like. Let's see his key point once again, the one that goes for the jugular:
Without continuous preferences, it is also highly unlikely that e.g. supply and demand can ever be equal.
And why not, we ask? He explains for the simple minded:
If you draw the supply and demand curves continuously, then they are (almost) bound to intersect. But if you draw them as a discrete set of points, supply and demand in general don't have to intersect.
And indeed he repeats this argument, to make sure we get it:
...supply equals demand only under extremely rare conditions (for without continuous pricing, the odds that supply and demand actually intersect are very slim).
That's his whole argument, really, that without continuous pricing, the odds that supply and demand actually intersect are very slim.
And now it's clobbering time. I see two egregious errors Caplan is making.
1. The first thing is to understand that supply and demand curves are not made by gathering data from the real world. There is no actual data of how many units people actually bought or sold at, say, $1 a bushel, at $2 a bushel, etc. [Doing this has inherent problems, and of course Rothbard has every right to reject it, and never uses it when discussing supply and demand]
Not only that, the curves are not even meant to represent what happened in the real world, but rather what is going on in the minds of people. It represents what people are "willing and able" to buy and sell at various prices. Henry Hazlitt spells this out:
All valuation begins in the minds of individuals. We are accus-
tomed to saying that market value is determined by supply and
demand, and this is as true of money as of other commodities. But
we should be careful not to interpret either supply or demand in
purely physical terms, but rather in psychological terms. Demand
rises when people want something more than they did before. It
falls when they want it less. Supply is more often thought of in a
purely physical sense, but as an economic term it also refers to
psychic factors. It may vary with price. At a higher price producers
may make more of a commodity, or be ready to offer more of the
existing stock for sale.
Since nobody has learned to read minds yet, we see that every supply and demand curve in the world must be hypothetical. And indeed, that is what they are, teaching aids to explain hypothetical situations. They are intended to teach general principles, and most of them don't use any numbers at all.
That being said, we can now ask ourselves, "What should a supply and demand curve look like?" The answer is of, of course "Whatever the teacher wants it to." He is using it to illustrate a situation he has made up.
We see now the blunder Caplan has made. He is asking "Why do supply and demand curves intersect?" The answer is "Because the teacher wants them to." He claims "...without continuous pricing, the odds that supply and demand actually intersect are very slim."
To which we reply, "Odds in which universe? The one the teacher made up? He can make up whatever he wants, choosing whatever helps him explain his point.
"The real world? Supply and demand curves are not trying to summarize a historical event in the real world, nor to predict the numerical future of a real world." They are perfect examples of what Mises was talking about when he wrote [quoted here] that true economics principles are qualitative, not quantitative.
Now there is one point on the whole curve that does have a basis in reality, sometimes. If we are talking about the supply and demand curve of some point in the past, say the month of January 2012, then we can sometimes gather up the data and see how much was actually bought and sold, and at what price. Since buying and selling actually took place at some price, and a given amount was bought and a given amount was sold, we know one point on the supply and demand curve. At price X [the one that actually happened] supply Y will be given out for sale [the amount that actually was sold], and the demand will also be for Y [because that was the amount actually bought].
So that the odds in such a case, of a supply and demand curve of a true situation in the past, has odds of 100% of intersection, whether pricing is continuous or no. Bryan, really!
2. That was Caplan's first mistake. His second one is his implicit assumption that the real world market usually is in equilibrium. He states that according to Rothbard "supply equals demand only under extremely rare conditions." This is, if anything, a merit, because according to AE, that is exactly the situation. Here's a line from our good friend, Wikipedia: "...the Austrian School and Joseph Schumpeter maintained that in the short term equilibrium is never attained..."
Now for a thought or two about Caplan's paper in general. Most of it is over my head, so I have no idea if is right or wrong. But in the two areas I've discussed in this humble blog, the calculation problem and continuity, he has so missed the boat, I begin to wonder how much of the rest of his paper will hold up to close scrutiny.