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

is by increasing s. Specifically,
11. Marriage, Divorce, Children 471
∂a(s, yh)
= λ(u
∂s
0 m(s) − γ
) ≥ 0, (11.19)
wm
∂a(s, yh)
= 1−λ(1 + α) > 1,
∂yh
∂q(s, yh)
= u
∂s
0 ∂a(s, yh)
m(s) − > 0,
∂s
∂q(s, yh) ∂a(s, yh)
= − ≤ 0.
∂yh
∂yh
An increase in the transfer s raises the utility that the mother would receive
as single and improves her bargaining position in the newly formed
household. Consequently, the remarried mother works less and spends more
time with the child, which raises the utility of the child. 12 However, an
increase in s also has the unintended effect of raising the new husband’s
utility, who "eats" part of the transfer. An increase in the net income of the
new husband raises his gain from marriage a(s, yh)−yh because the mother
spends less time with the child and more time in the market. The mother
is willing to do such a sacrifice of child quality because she is compensated
by a higher level of adult consumption, jointly with the new husband.
The result that remarried mothers work more in the market may seem
counterfactual. 13 We emphasize that market work is just one way of transferring
resources from the child to the new husband and the crucial assumption
is the availability of a linear transfer in some non-trivial range.
For instance, the mother may spend less time with the child and more time
with the new husband in joint leisure activities. As long as such substitutions
are available at a fixed rate of exchange, the results are the same as
if the remarried mother would spend time working in the market.
11.4 Transfers, the interim perspective
Following separation, the parents can be in four different states, depending
on the new marital status of their ex spouses:
1. Both parents are single, which happens with probability (1 − p) 2 .
12 ∂a(s,y
Note that h)
=0if s =ĉ, ∂s
∂a(s,yh) =1if s = c ∂s
∗ and 1 > ∂a(s,yh) > 0 for
∂s
ĉ