Though Alex has already blogged about the Kremer/Snyder paper on vaccines versus cures, there are, I think, a couple of comments worth adding.
According to Kremer and Snyder, monopoly sellers would rather sell cures than vaccines. To get this result, they need some heterogeneity: we all have different probabilities of getting sick (though we all find it equally costly to get sick).
But what if you introduce the opposite kind of heterogeneity? (That is, we all have different costs of getting sick, even though we all face the same probability of getting sick.) Then it’s a nice little exercise for your students to show that the cure and the vaccine are equally lucrative monopolies (ignoring the positive externalities of the vaccine).
A more important observation: In the Kremer/Snyder setup (still ignoring positive externalities), it’s a good thing for sellers to invest in cures rather than vaccines. The reason cures are more profitable is that they in essence allow perfect price discrimination. So with cures, there’s no deadweight loss due to monopoly; with vaccines there is.
The analysis changes if you assume, say, that a vaccine prevents a four-day illness, but a cure only cuts two days off your illness. Then vaccines might or might not be socially preferable to cures—but in that case, willingness-to-pay for vaccines versus cures would double. This gives sellers an incentive to produce vaccines. The incentive isn’t perfect, but it goes in the right direction.