You could say that this stereotype will be self-fulfilling. If everyone assumes that you can't do math, the marginal benefit of learning more math is zero, right?
Well, maybe that's right on a homework problem. But how about the real world? In the real world, there are ways of showing that you are counter-stereotypical. For example, a libertarian economist could write his dissertation on game theory under Avinash Dixit. Will people still assume that the libertarian economist can't do math? I think not.
In more general terms, even if people look down on the average member of your group, it's hardly clear that your marginal incentive to do better is worse than anyone else's. In fact, as my Dixit example illustrates, if people think your group is bad in some way, the marginal benefit of counter-stereotypical behavior is probably unusually BIG. The expected mathematical ability of a non-libertarian who writes under Dixit goes from very good to excellent. The expected mathematical ability of a libertarian who writes under Dixit goes from poor to excellent. These look like incentives for a self-reversing prophesy to me.
If I'm right, though, shouldn't all statistical discrimination undo itself? Sure, if groups were really the same to begin with. But they're not. Libertarians go into economics to think big thoughts, not solve equations. It would be amazing if their average mathematical ability could equal that of people who go into economics because they like solving equations. The result: Even though libertarians have a stronger incentive to learn math, they are still less proficient.
Overall, it seems like my example generalizes. If taxis are reluctant to pick up young, black males, then young, black males probably have an unusually large marginal benefit of wearing a suit. Outside of a simple-minded homework problem, statistical discrimination is a reason to try harder, not a reason to give up.