Pierre André Chiappori (Columbia) "Family Economics" - Cemmap

362 8. Sharing the gains from marriage
costs of) out-of-wedlock children, due to the fact that they do not live in
the same household. On the other hand, married men’s utility is of the form
UH(cH,k)=cH +uHk, where the parameter uH > 0 is identical for all men
in the economy. Women differ in their preferences toward children. Specifically,
female utility functions take the quasi-linear form U(c, k) =c + uk.
Here, each woman is characterized by the individual-specific tasteparameter
u, which is distributed according to the density f over the interval
[0,U]. We assume that any woman (single or married) who wants a child
can have one. However, if she plans to have no children, unwanted births
may still occur with some probability p, which depends on the available
contraceptive technology and the legality of abortion.
The quasilinear structure of the male and female preferences implies that
utility is transferable within marriage. For each spouse, the utility depends
on the couple’s fertility decision and on the share of composite good that
he or she receives.
As before, we normalize the mass of men to be 1, and we denote by r
the total mass of women on the market; here, we assume that r>1, that
is that women are on the long side of the market. Male income is denoted
by Y . Women without children have income, y; however, if a woman has
children, her income drops to y 0 ,withy 0