And how is this not hot?
I consider a world where individuals live a maximum of two periods. All individuals live for certain in period 1, and there is a chance, p, of surviving until period 2. Each individual receives utility from certain income, y, in each period, as well as their choices of number of sexual partners in each period: sigma1 and sigma2. Total utility in period i is u(y, sigmai), and we will assume that u(.) is concave in both y and sigmai. In a world without HIV, total lifetime
utility can be written:
Utot = u(y, sigma1) + pu(y, sigma2) (1)
Income is fixed in each period so the only choices individuals make are about sexual behavior. The first order condition defining the choice of sigmai is usigmai(y, sigmai) = 0. Note that optimal choice of sigmai can vary with y, even in the framework without HIV. The direction of this relationship will depend on the sign of usigmay. If the cross partial is positive, richer people will have more sexual
partners; if it is negative, they will have fewer. For example, if sexual partners cost money, this will deliver a positive cross partial, which would imply that richer people have more partners.
How is that not hot? I mean, sex, partial derivatives and utility maximization. I defintely have a crush.