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

484 11. Marriage, Divorce, Children
the outcomes if all couples do not have children, it still may influence the
equilibrium outcome through the impact on the incentives to have children.
Thus if b1 is reduced from 0.25 to 0.05 then the equilibrium without children
disappears and the only equilibrium is with children.
The last panel of Table 11.1 illustrates the impact of changes in the
utility of the father, as δ rises and he suffers less from living apart from the
child. Such an increase in proximity raises the utility of the father directly,
but it also raises his willingness to transfer money to the custodial mother
and, consequently, the child and mother gain too. Notice that for δ =1, the
father would like to have a child but the mother prefers not to have a child
if all other couples do not have a child. This conflict could, in principle, be
resolved by ex ante contracting at the time of marriage.
11.8 Further issues
In this concluding section we discuss some departures from the standard
contract that we analyzed and examine their implications.
11.8.1 The custody assignment
If the father has the custody, he will spend only the minimal amount of
time on child care because, under our assumption that wf(1 + α) >β,any
hour spent on child care could be better used in the market. He will spend
on the child good c ∗ and spend the remainder of his income on the adult
good. This is true whether or not he receives transfers from the mother.
Therefore, the mother has no incentive to transfer to the custodial father,
as any additional dollar is spent on the adult good and αα(wf − c ∗ ) is sufficient to ensure that mother custody is better for
the child. In this case, the father also prefers that the child will be with