The Intensive Margin: Math vs Econ
Presumably, the content of such courses reflects what professors believe that their students must learn in order to go to graduate school and end up as academic economists publishing articles in leading journals. That fits my not very expert impression of the current state of academic economics, that it is heavy on 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 blog posts—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.
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 on subjects that smart people have been writing articles about for most of the past century—new enough, at least, to get published. One way of doing it, assuming you don't have some new and interesting economic idea, is to apply a new tool, some recently developed mathematical approach,. It has not been done before, that tool not having existed before, so with luck you can get published.
The extensive margin is the application of the existing tools of economics, and mathematics where needed, to new subjects. Examples include public choice theory, law and economics, and, somewhat more recently, behavioral economics. The same thing can be done on a smaller scale if you happen to think of something new that is relevant to more conventional topics. I have considerable disagreements with Robert Frank, some exposed in exchanges between us on this blog a while back. 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 really 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.