The Intensive Margin
I was told, by an undergraduate at a top school who had been considering majoring in economics and decided not to, that the required courses had turned out to contain a great deal more mathematics than economics. That report was confirmed by a senior faculty member at the same school with whom I raised the issue. He agreed with me that the situation was an unfortunate one.
The content of such courses presumably reflects what professors believe their students must learn in order to go to graduate school, publish articles in leading journals, have a successful career as academic economists. That fits my not very expert impression of the current state of academic economics, that it is heavy with what Gordon Tullock used to refer to as "ornamental mathematics," advanced tools used to demonstrate the author's mathematical sophistication but contributing little to the substance of the analysis.
I have not been much involved with the world of journal submissions for a long time — I prefer to write books and posts, although I have occasionally been asked to referee articles — so am in a poor position to make blanket judgments. But some years back, reading an interesting article by Akerlof and Yellin on why changes that should have reduced the number of children born to unmarried mothers had been accompanied instead by a sharp increase, I was struck by the fact that they had used game theory to make an argument that could have been presented equally well, perhaps more clearly, with supply and demand curves. Their analysis was simply an application of the theory of joint products — sexual pleasure and babies in a world without reliable contraception or readily available abortion. Add in those technologies, making the products no longer joint, and the outcome changes, making some women who want babies unable to find husbands to help support them due to the competition from women who don’t want babies. The argument uses nothing Marshall did not know, arguably nothing Smith, who discusses wool and mutton as joint products, did not know.
Assume, for the moment, that I am right that both economics in the journals and economics in the classroom emphasize mathematics well past the point where it no longer contributes much to the economics. Why?
The answer, I suspect, takes us back to Ricardo's distinction between the intensive and extensive margins of cultivation. Expanding production on the intensive margin means getting more grain out of land already cultivated, expanding it on the extensive margin means getting more grain by bringing new land into cultivation.
In economics, the intensive margin means writing new articles — new enough, at least, to get published — on subjects that smart people have been writing articles about for most of the past century. An example would be the question of why involuntary unemployment sometimes exists and what can be done about it. That is an important question, sufficiently important so that many non-economists seem to consider dealing with it the chief business of economists. But it is also a question which quite a lot of very good economists have been working on for a long time, which makes it difficult to say anything both new and interesting about it.
Another example would be game theory. I like to defend my disinterest in being more than an observer of that field by explaining that, when I am looking for problems to work on, problems that stumped John Von Neumann, one of the most brilliant thinkers of the Twentieth Century, go at the bottom of my pile.1
One consequence of the difficulty of such questions is that anything new is likely to be either uninteresting or wrong. That is an implication of what I have referred to elsewhere as the rising marginal cost of originality, a principle I usually illustrate with examples from city planning and architecture. My favorite example of the latter is, for those familiar with it, the Coombs building at Australian National University, a truly inspired piece of bad design in which I once spent part of a summer.
One solution to the problem, assuming you don't have any new and interesting economic ideas on the subject, is to apply a new mathematical tool to an old problem. It has not been done before, that tool not having existed before, so with luck you can get published, whether or not the new tool adds anything useful to analysis of the problem.
The extensive margin, in contrast, is the application of the existing tools of economics, including mathematics where needed, to new subjects. Examples include public choice theory, law and economics, and behavioral economics. A recent example I am fond of is the work Peter Leeson has done on applying economics to making sense of 18th century piracy; curious readers will find it in his book The Invisible Hook. Because nobody, so far as I know, had thought of doing it before, Leeson was able to produce interesting results by applying conventional economic analysis to a subject that specialist historians had researched but economists knew very little about, to the benefit of both fields.
I have considerable disagreements with Robert Frank, some exposed in exchanges between us on my blog. But when, in Choosing the Right Pond, he showed how the fact that relative as well as absolute outcomes matter to people could be incorporated into conventional price theory he was working new ground and, in the process, teaching the rest of us something interesting.
My conclusion is that, if you want to do interesting economics, your best bet is probably to work on the extensive margin — better yet, if sufficiently clever and lucky, to extend it.
On the Use of Mathematics in Economics: A Letter
Balliol Croft, Cambridge
27. ii. 06
My dear Bowley,I have not been able to lay my hands on any notes as to Mathematico-economics that would be of any use to you: and I have very indistinct memories of what I used to think on the subject. I never read mathematics now: in fact I have forgotten even how to integrate a good many things.
But I know I had a growing feeling in the later years of my work at the subject that a good mathematical theorem dealing with economic hypotheses was very unlikely to be good economics: and I went more and more on the rules—(1) Use mathematics as a shorthand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life. (5) Burn the mathematics. (6) If you can't succeed in 4, burn 3. This last I did often.
I believe in Newton's Principia Methods, because they carry so much of the ordinary mind with them. Mathematics used in a Fellowship thesis by a man who is not a mathematician by nature—and I have come across a good deal of that—seems to be an unmixed evil. And I think you should do all you can to prevent people from using Mathematics in cases in which the English Language is as short as the Mathematical.....
Alfred Marshall
Which leaves me wondering how much of the economics of the next century went into Marshall's fireplace.
Eugene Wigner, himself a brilliant man, is reputed to have said "There are two kinds of people in the world: Johnny Von Neumann and everybody else."
Really appreciate this analysis — your framing of the “intensive margin” as ornamental rather than insight-driven hits the nail on the head. I’d like to extend that critique upstream, into the K-12 system and the college admissions pipeline, where the groundwork for this ornamental math culture is laid far earlier — even as early as pre-K.
In many high schools — elite or not — Calculus has become a symbol of college readiness, not because of its intrinsic value, but because of what it signals. States now push calculus access as an equity goal. Counselors warn students they’ll be shut out of competitive majors without it. Parents and teachers treat it as the gateway to a “real” future. The result is a kind of fetishization: math not as a tool, but as a ticket.
Why? Because at the college level, high-level math courses are routinely used to screen students out of capacity-limited programs like CS, pre-med, and yes — Economics. Even when the skills aren’t essential to the major, calculus becomes a blunt gatekeeping instrument. So students rush to AP Calc in high school, not because it’s enlightening, but because the system quietly made it mandatory.
Which brings me to Econ itself. Some departments may be dressing themselves in the same quant-heavy prerequisites not out of curricular necessity, but out of academic competition — or just prestige mimicry. If CS and Engineering use math to assert rigor, Economics seems to be borrowing the same costume — emphasizing formalism not because it clarifies thought, but because it signals seriousness.
Take four schools: University of Washington (Seattle), UC Berkeley, University of British Columbia, and UC Santa Barbara. All have selective Econ majors with seat caps. All require multiple college-level calculus courses. And all have created conditions where high school students now feel pressured to prep early — often through AP Calc or higher — to stay competitive in admissions.
So the ornamental math you describe isn’t just an internal affliction of academic economics — it’s a cultural export, baked into the broader educational signaling system. We’re not teaching students to think like economists. We’re teaching them to mimic the inputs elite institutions have learned to reward.
Since David mentioned Neuman and Wigner, I would like to leave this here.
Enrico Fermi famously asked "Where are they?" Leo Szilard had an answer. “They are among us,” he said, “but they call themselves Hungarians.” Plausible because Hungarians are weirdly super-intelligent. In fact, they have been suspected of being "Martians."
The following bit is from the wiki:
“The Martians” was the name of a group of prominent scientists (mostly, but not exclusively physicists and mathematicians) who emigrated from Hungary to the United States in the early half of the 20th century. They included, among others, Theodore von Kármán, John von Neumann, Paul Halmos, Eugene Wigner, Edward Teller, George Pólya, and Paul Erdős. They received the name from a fellow Martian Leó Szilárd, who jokingly suggested that Hungary was a front for aliens from Mars.