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

486 11. Marriage, Divorce, Children
a remarried mother, who still may be forced to work part time to comply
with the interest of her new husband. As long as the courts cannot interfere
with within-household allocations (that are hard to verify) and the father
cannot transfer directly to the child, because his money transfer is fungible
and can be consumed by the mother and her new husband, it is hard to
expect that the child interests will be maintained simply by mandating a
money transfer. There is, however, one notable exception. If the mother has
sufficient bargaining power to take all the gains from marriage, then she
would solve the mirror image of problem (11.13) and maximize her utility
subject to the constraint that the new husband is just indifferent between
remaining single and remarriage. Formally, this problem is the same as
problem (11.7) that the mother solves as single and setting s = c ∗ would
indeed induce her to maintain the efficient outcome when she remarries. 26
This brief discussion illustrates that in search markets with rents that
are subject to bargaining, it is important to specify the relative bargaining
power of the parties that determines the share of the surplus that each party
gets. In the Nash bargaining model this is determined by considerations
such as impatience and risk aversion that, of course, need not be equal
across genders. More broadly, social norms such as egalitarianism and sex
roles may also affect the bargaining outcome.
Another, and potentially more fruitful, direction is to enlarge the set of
contracts that the courts are willing to enforce. In principle, child support
payments should depend on the marital status of both parents, because
the costs and benefits of post divorce transfers depend on these states. 27
In practice, child support is not contingent on marital status but there are
other payments such as alimony that are often contingent on the marital
status of the mother. Because we assume that all transfers are fungible,
the name attached to these payments does not really matter, but it does
matter how flexible they are and to what contingences they respond.
Now imagine that a father can pay different amounts to the custodial
mother depending upon whether or not she is remarried. Suppose further
that the father is forced by law to pay a fixed amount of child support
s = c ∗ but can augment it by an additional payment σ that he pays the
custodial mother only if she is single. Then, the efficient allocation within
the remarried household is determined by
max E(a|σ, σ 0 )=
hm,c
wmhm + wf − c − (1 − p)σ 0
(11.44)
26 Aiyagari et al. (2000) also discuss mandatory child support payments in a general
equilibrium framework. They show that an increase in such payments raises welfare of
parents and children.
27 In theory, the transfers should depend on the marital status of all agents that
participate in the marriage market. But this, of course, is highly impractical.