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

404 9. Investment in Schooling and the Marriage Market
Efficiency
We can now demonstrate that in our model individuals’ pre-marital investments
are efficient. Consider,first, a mixed equilibrium in which some
married men are more educated than their wives and consider a particular
couple (i, j) such that the husband is educated and the wife is not. The
question is whether by coordination this couple could have gained by, for
example, changing investments and allowing redistribution between them.
If woman j had gotten educated, the partners together would have gained
ζ 22 − ζ 21 in terms of marital output but the cost of schooling for woman
j would have been her forgone earnings in the first period ζ 01 plus her
idiosyncratic non-monetary cost, μ j. The couple would gain from such a
shift only if μ j + ζ 01 ζ 21 − ζ 11, or equivalently,
μ i >z21 − z11 + R m . (9.28)
But, in the assumed marriage market configuration, z21 − z11 = V2 − V1
and, by assumption, man i chose to invest and marry. Therefore, by 9.17
μ i