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

10. An equilibrium model of marriage, fertility and divorce 453
Finally we can consider high values of θ,suchthatθ≥θc. Equality for equation
(10.10) requiresequatingV1with W1,1 (θ) evaluated for θ ≥ θc(that
is, the third region of equation (10.17)). This gives
θm = 1
1
p(Y + β) −
2 2 (q∗ − c) − Y (10.59)
This case requires θm >θc which gives:
p(Y + β) < 3(q ∗ − c) − 2a (10.60)
Properties of the proportion of singles, U(θm(p),θc(p)), in the example
(proof of 10.21)
The proportion of singles at the beginning of the second period consists of
those who did not marry in the beginning of the first period, G (θm (p)),
and of the divorcees at the end of the first period among the married.
The proportion of divorcees depends on the location of θm. IfV1 is low
and intersects W1,0 (θ) below h0 − a, then all of the married for whom
θm