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

280 6. Uncertainty and Dynamics in the Collective model
utilities when married). A second requirement is that utility be transferable
after divorce; here, we have therefore assumed quasi-linear preferences for
singles. Finally, the slopes of the two Pareto frontiers (before and after
divorce) must be equal.
While these requirements are indeed satisfied in the example just given,
they are in fact quite unlikely to hold in reality. For instance, the assumption
of quasilinear preferences if single is totally ad hoc . Assume, on the
contrary, that preferences if single have the same general form as when
married - that is, that:
u i ¡ ¢ i i
s q ,Q = Fs (Q) q i 1 + G i ¡ ¢ i i
s Q, q−1 + θ ,i= a, b
The question, now, is whether commodity Q, which was publicly consumed
when the couple was married, remains public after divorce. In many cases, it
does not; for instance, housing typically stops being jointly consumed after
the separation. CIW show that, in that case, the second requirement is not
satisfied in general. In other situations, the commodity remains public, in
the sense that it still enters both ex-spouse’s utilities; this is the case for
children consumption, for instance. However, the utility adults derive from
children’s well being may well change after divorce, especially for the parent
who does not have full custody. Technically, the F i s function is now different
between spouses, which violates either the second or the third requirement.
All in all, CIW argue that, in general, these requirements are unlikely to
be fulfilled - therefore that the Becker-Coase result is unlikely to hold.
An important implication is that the claim, frequently encountered in the
literature, that the Becker-Coase theorem is a consequence of the efficiency
assumption is incorrect. Whenever any of the CIW requirements is violated,
the neutrality result does not hold true. Then the general model developed
in the previous subsection, which only assumes efficient behavior (including
for divorce decisions), remains valid; but one can find situations in which
couples would split under unilateral divorce but not under mutual consent
- and also, more surprisingly, cases in which this intuition is reversed, in the
sense that divorce occurs under mutual consent but not under unilateral
divorce. Figure 6.3, borrowed from Clark (1999) and CIW, illustrates the
latter case. With mutual consent, each partner has a "property right" on
the allocation within marriage, represented by M. This point is contained
in the divorce frontier and both partners can be made better of by renegotiating
the divorce settlement and leaving the marriage. In contrast, with
unilateral divorce partners have property rights on their divorce allocation,
represented by D. This point, however, is contained within the marriage
frontier and the partners can find an allocation within marriage that will
sustain the marriage.