Thus there are two different "optimal" levels of sexual activity for Martin, depending on what one means by "optimal." If we want to minimize the prevalence of AIDS, then there is a certain optimal increase in Martin's sexual-activity level. If, on the other hand, we want to maximize the difference between the benefits of sex and the costs of AIDS, then there is a different (and larger) optimal increase in Martin's activity level. Of these two notions of "optimal," economists will have a strong preference for the latter.

(It should also be noted that there is a difference between minimizing the long-run prevalence of AIDS and minimizing the short-run rate of infection; this offers yet a third possible interpretation of the word "optimal.")