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<font size="2"><font face="Verdana" color="#002864" size="5"><strong>Mathematics and Economic Analysis</strong></font>
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<font size="4">William L. Anderson</font>




[Posted April 4, 2002]


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<font size="3"><img alt="Sherwin Rosen" src="http://www.mises.org/images/Rosen.gif" align="right" border="0" width="153" height="220">While
living near Greenville, South Carolina, a couple of years ago, I attended a
dinner that featured the late Sherwin Rosen of the University of Chicago as its
speaker. Rosen, who had been a colleague of F.A. Hayek's at Chicago, spoke that
evening on Austrian economics--or, at least, he attempted to talk about
Austrian economics. In a short time, he had clearly demonstrated that he
understood very little about that discipline, and he wound up giving a
caricature of Austrianism.</font>




<font size="3">During the question-and-answer session that followed, someone
asked about the effectiveness of organizations like the Ludwig von Mises
Institute. Rosen replied that the LVMI really was not particularly effective in
economic circles, especially since it represents Austrian economics, something
that, according to Rosen,"fails the market test."</font>




<font size="3">Many of us who have received mainstream training in economics
but call ourselves Austrians (or at least fellow travelers) have heard this
"market test" criticism time and again. The gist of the charge is as
follows: The economics profession over the years has accepted those ideas that
work and has rejected ideas that do not work. Whatever is"good" in
Austrian economics has already been incorporated into the greater body of
economic literature, so there is no need for a special division of
"Austrian" economics.</font>




<font size="3">Mainstream economists are especially critical of Austrians for
their lack of desire to incorporate mathematics in general, and multivariable
calculus in particular, into their economic analysis. The criticism goes
something like this: It does not matter whether or not mathematics is the most
appropriate tool to describe economic human action. Since the majority of people
in the economics profession use math for their work, it has passed the"market
test" and, therefore, is the correct tool to use. In the vernacular,
everybody uses math because everybody uses it. One hundred thousand economists
cannot be wrong, so the belief goes.</font>




<font size="3">Given this"standard" approach, it is not surprising,
then, that the"top" economic journals look more like a collection of
applied mathematics than anything resembling economics. People who do well
in math are more likely to be published in the"best" journals than
people who are not as adept in that area. Because publication in these journals
is the key to tenure and promotion in the top-flight economics departments, one
can see quickly that some people who may have a good understanding of economics
but either are not math whizzes or choose not to use math, will not be placed in
these most coveted slots, and, thus, are relegated to the"outer darkness"
of smaller and less prestigious institutions. (I do not know if there is more
"wailing and gnashing of teeth" in the"bigs" than in the
"smalls.")</font>




<font size="3">It is not surprising, then, that many in the mainstream claim
that Austrians disapprove of the extensive use of mathematics in economic
analysis because they are unable to do math themselves. My guess is that most
folks, including myself, who can survive a modern economics graduate program,
are at least competent if not proficient in mathematics, so I am not sure that
charge can stick.</font>




<font size="3">Furthermore, the most vociferous critics of math in economics,
Murray N. Rothbard and Ludwig von Mises, were both well versed in mathematics,
Rothbard entering Columbia University at age 16 as a statistics major. Rothbard
and Mises did not build mathematical theoretical models because they believed it
was inappropriate for economic analysis, not because they lacked mathematical
competence.</font>




<font size="3">What is the problem, then, of using math for economics, and
why are Austrians opposed to such a methodology? In a word, math is not an
appropriate tool to describe human action. As Mises and Rothbard often
pointed out, one cannot quantify human action. This does not mean that
people do not engage in activity in which mathematics is not important, but
rather that we cannot accurately use math to describe how humans behave.</font>




<font size="3">Take the simple"Lagrangian Multiplier" that we use
in basic graduate-school economics to"explain" consumer behavior.
Here, economists construct an equation in which one?s utility depends upon,
say, goods"x" and"y." The ability to accumulate such goods
is constrained by one?s income and the prices paid for the goods.</font>




<font size="3">In determining the"optimal" state that the consumer
can enjoy, one uses tools of multivariable calculus to reach a point where
"equilibrium" is reached. At that point, the marginal utility of good
"x" divided by the price of good"x" is equal to the
marginal utility of good"y" over the price of that good. (I have not
done the mathematical work on this page for obvious reasons.)</font>




<font size="3">The problem here is that this"solution" is nonsense. Utility
(or consumer satisfaction) cannot be measured in cardinal terms. There is
no way to take a cardinal measure of someone?s satisfaction. I can say that I
like chocolate more than vanilla, but I cannot put that preference in cardinal
numbers. An attempt to do so is nothing short of an exercise in fraud.<a title href="http://www.mises.org/fullstory.asp?control=926&FS=Mathematics+and+Economic+Analysis#_edn1" name="_ednref1">[1]</a></font>




<font size="3">When asked why they engage in such activities, economists
usually admit that they cannot take cardinal measures of individual utility, nor
can they compare the utility of one individual to another in cardinal terms.
However, they then do it anyway, saying that while their activities are
technically wrong, they pass the"market test" in economic analysis.
People, they add, will"act as though they are engaging in measurement of
cardinal utility," even if they really are not. In other words, even if
something is not true, we pretend that it is true and act accordingly.</font>




<font size="3">In The Failure of the New Economics, Henry Hazlitt
declares</font>



<font size="3">... if a mathematical equation is not precise, it is worse
than worthless; it is a fraud. It gives our results a merely spurious
precision. It gives an illusion of knowledge in place of the candid confession
of ignorance, vagueness, or uncertainty which is the beginning of wisdom. (p.
99)</font>



<font size="3">In using mathematics as the main tool for advancing economic
thought, economist must operate on the assumption that human action adheres to a
constant mathematical formula. While, as Rothbard and Mises note, that might be
appropriate for the physical sciences, it is not appropriate when
describing how humans behave.</font>




<font size="3">This is not to say that the use of logic is inappropriate in
economic science. Indeed, the Austrian methodology draws heavily upon logical
inferences in deducing economic science from the initial observation that people
act. Furthermore, mathematics is a branch of logic.</font>




<font size="3">However, while one can make logical deductions in observations
of human action, it is impossible to make those deductions with the precision
that mathematical reasoning requires. It is one thing to say (again) that I like
chocolate better than vanilla; it is quite another to claim that a bit of
chocolate gives me 6.7"utils" of pleasure and that the same amount of
vanilla yields only 4.2"utils." The former way of"measuring"
my preferences is entirely appropriate. That latter method, however, is not only
inappropriate, but also downright silly. Yet, that is what the economic"mainstream"
claims passes the"market test." One can only be thankful that
mainstream economists are not in charge of building bridges, highways, and other
structures.</font>


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William Anderson, an adjunct scholar of the Mises Institute, teaches
economics at Frostburg State University. Send him <font color="#000080" size="2">MAIL</font>.
See his Mises.org <font color="#000080" size="2">Articles
Archive</font>.


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<a title href="http://www.mises.org/fullstory.asp?control=926&FS=Mathematics+and+Economic+Analysis#_ednref1" name="_edn1">[1]</a>
In their defense, some economists say they are not actually measuring
marginal utility (which is immeasurable in cardinal terms), but rather are
taking a measurement of a rate of commodity substitution. However,
that, too, is nonsense, since it tells us absolutely nothing about consumer
behavior and preferences.


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