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

454 10. An equilibrium model of marriage, fertility and divorce
Therefore, we equate W1,0 (θ) evaluated in the first region of equation
(10.17) with W1,1 (θ) evaluated in the intermediate region of equation
(10.17), implying
and
θm =
⎧
⎪⎨
⎪⎩
θc = p(Y + β) − Y − a +2c − q ∗ − q 0 , (10.64)
−Y
if p(Y + β) >a+ q0 + q∗ − 2c
p(Y +β)−a+2c−q ∗ −q 0
3 − Y
if a + q0 + q∗ − 2c ≥ p(Y + β) ≥ c + q∗ − 2q0 − 2a
p(Y +β)
2 − q∗−c 2 − Y
if p(Y + β) ¡ q∗ − q0¢ and c< q∗ +q 0
2 ensure that
interval £ ¤
∗ 0 0 ∗ c + q − 2q − 2a, a + q + q − 2c is non-empty.
The aggregate number of singles associated with a given p is
⎧
⎪⎨
U(θm(p),θc(p)) =
⎪⎩
10.6 References
G(h1(p)+a)+G(θc(p))
2
if p(Y + β) >a+ q0 + q∗ − 2c
(G(h1(p)+a)+G(θm(p)))
2
if a + q0 + q∗ − 2c ≥ p(Y + β) ≥ c + q∗ − 2q0 − 2a
G(θm(p))
if p(Y + β)