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

8. Sharing the gains from marriage 357
does not change, and if r0.
The example allows us to examine numerically the impact of a progressive
transfer-tax system. Assume that male income is distributed uniformly on
[0, 1], while the female income is distributed uniformly on [0, 75]. Setθ =
0.025 and τ = .7. Now consider a balanced transfer scheme such that
κ(1+r) =(1−τ)(x+ry). We discuss here two separate cases, one in which
women are the majority and r =1.1 and the other when women are the
minority and r =0.9. Inthenumericalexample,x =0.5 and y =0.375.
Thus, for a marginal tax of τ =0.7, the balanced budget constraint implies
that κ =0.13 when r =1.1, and κ =0.132. whenr =0.9.Figures 8.15,
8.16 and Table 8.1 summarize the results.
When women are in the majority, their share is usually less than half
but rising in the income of their assigned husband (see Figure 8.15). The
tax-subsidy intervention moderates this increase, because in low quality
matches, the wife’s share is determined by her income, and women with low
income gain from the progressive system. When women are in the minority,
their share in the marital output declines and the progressive tax system
moderates this decline (see Figure 8.16) because in low quality matches,
the husband’s share is determined by his income, and men with low income
gain from the progressive system. The difference in slopes between the two
figures reflects the role of the non monetary gains, θ, that are captured by
the men when r>1 andbythewomenwhenr