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

368 8. Sharing the gains from marriage
Y + uH
Y + p.uH
Y
u(M)
FIGURE 8.6. An Increase in the Risk of Pregnancy
gain for single women) but nevertheless positive. On the other hand, when
the excess supply of women is ‘large’, married women do not benefit from
the new technology, because the marginal woman does not use it. Hence
the consequences of the new technology for married women’s welfare are
intimately related to the situation that prevails on the marriage market.
Finally, men cannot gain from the introduction of the new technology.
When the excess supply of women is large, their utility is not affected.
When the excess supply of women is small, so that the marginal wife does
not want a child, the total welfare of the household is increased, but so
is the reservation utility of the wife; the husband is left with the same
consumption, but loses the benefit he would have received from an unwanted
birth. The intermediate case is even more spectacular. Here, all
marriages result in a child being born, so the total surplus generated by
marriage is not affected by the innovation. What changes, however, is the
intrahousehold allocation of the surplus. The new technology improves the
reservation utility of the marginal woman, hence her share of resources increases.
Stability requires this shift to be reproduced in all couples. All in
all, the new technology results in a net transfer from the husband to the
wife, which equals the expected gain of the marginal single woman, that
is p (y − y 0 − u (r)), without any change on the fertility of married couple
(who actually do not use the new technology).
We thus conclude that in our model an improvement in the birth control
Increase in
female surplus
u