The issue has been raised by Alex Tabarrok and Bryan Caplan. I'm fine with schools experimenting with this sort of thing, but for much different reasons than Bryan and Alex are talking about. If they want to grow certain fields at their university, or if they want students to pay more for things that are relatively more costly to teach I'm fine with that. I'm also fine with the standard cross-subsidization that universities do.
But I don't like the idea of setting tuitions to deal with positive externalities associated with certain degrees, for much the same reason that I don't like "staple act" proposals (where green cards are automatically given to foreign STEM majors), or any other idea focused around generating more scientists and engineers just because they're good for society.
The positive externalities associated with science and engineering are not really analogous to the negative externalities of pollution that frame a lot of the way we think about externalities. There's a lot more diffusion and diversity in scientific outputs. Work on relativity a century ago was truly an externality because a lot of the economic benefits from it several decades later had no hope of being captured by the people working on it. But you didn't have to work on relativity. You could work on other physical problems that didn't stray far from classical mechanics (flight, rocketry) or from electricity or radio.
Or think about biology majors. You could work on a cure for malaria. That would do tremendous good for the world, far exceeding ability to pay. Or AIDs. But that's not the sort of stuff a lot of biology majors work on. There's other biology work to do.
This is very different from pollution. If we tax gasoline there's pretty much a one-for-one relation between gasoline produced and pollution produced (given a certain combustion technology being used). If we produce a biology major with skills relevant to pharmaceuticals there's a pretty good chance they're just going to add one more worker to the labs that produce anti-depression, anti-erectile dysfunction, and anti-baldness pills.
They'll be doing the non-spillover work by and large precisely because that's the most remunerative work (which is not surprising because that's the whole problem posed by positive spillovers in the first place).
This bugs me a lot about Romer's New Growth Theory models as well. He just sort of assumes that if you generate more researchers you're going to get more externalities. There's no consideration at all of the labor market for these researchers. When they graduate, what are they going to be paid to do? Why would they necesarily be paid for something that by definition doesn't have as big of a payoff? I'm hoping that one of my dissertation chapters will tackle exactly this question with regard to New Growth Theory.
So what's my solution?
I've said this a couple times before but I think it's pretty straightforward: if you're dealing with a demand-side externality, use a demand-side solution. With respect to the STEM labor market this is a demand-side externality, not a supply-side externality. So the solution is to pay scientists and engineers to do the work that they would not do otherwise. Internalize the externalities. If people are not demanding enough public infrastructure or AIDs research or particle accelerators, buy those things. That is where the externality is, not in the supply of these workers. Decades of research has shown that STEM workers are very responsive to wages (just like all workers). So if there is a demand deficit because of externalities, provide that demand and then let labor markets work.
That's not to say nothing goes wrong on the supply-side. There are all sorts of credit constraints and asymmetric information problems associated with educational investments. Those may deserve attention. But I can't really think of any major supply-side externalities specific to STEM. The STEM-specific problems, as far as I can tell, are all on the demand-side. So use a demand-side solution.