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

2.5.2 Intact families
2. The gains from marriage 95
We have three regimes, depending on the parameter values. We always
assume:
w b >w a ,α>β
implying that the high wage spouse, b, hasacomparative advantage in
market work and the low wage person a has comparative advantage in
home production:
w b
β
> wa
α
(2.23)
If both wages are high relative to efficiency at home production, (if w a >α
and, consequently, w b >β) then both parents will work full-time in the
market and use only market goods for caring for the child. Conversely, if
both wages are low relative to efficiency at home production (if w b 0. Specifically, t a =1and t b =0and c k = wb −α
2 . The utility of
the child is then uk = wb +α
2 and the utility possibility frontier facing the
parentsisgivenby
u a + u b = (wb + α) 2
. (2.25)
4
Incase2wehavetheconverse:
w b