Human capital, income, fertility and child policy
Luciano Fanti Luca Gori
University of Pisa University of Pisa
Abstract
This paper analyses the effectiveness of child-subsidy support policies in a general equilibrium overlapping generations model with endogenous fertility, child quality choices and human capital formation. It is shown, somewhat paradoxically, that only if the preference for the quality of children is higher than the preference for the quantity of children, then a child subsidy policy gives raise to an increase in both income per-capita and fertility rates, while, on the contrary, in the case in which parents are relatively more interested to the number rather than to the quality of children, a child-subsidy support policy may just reduce fertility behaviour, and, in any case, it always depresses the level of income per-capita.
Citation: Fanti, Luciano and Luca Gori, (2008) "Human capital, income, fertility and child policy." Economics Bulletin, Vol. 9, No. 6 pp. 1-7
Submitted: February 1, 2008. Accepted: March 31, 2008.
!" # $ # % # &'!" ! ( )**+, # )**-, ! ( . / )**0, 1 . )**2 )**3" # # # # 4 $ 560* 7 $ )**- " # # 5 # # # 8 # # # # # # 9 : )**+" 8 7 ) , 7 + # # , 7 - # # # # / # 8 t t n τ β = 5" 0 > β # " # τt >0 ; $ # 5" # t N " 8 < $ # t # t c1, " c2,t+1" # nt" 5 # 9 # # 1 ! )**=" . # # #
! > 5660" # e qt" 9 , 7 $ )**+ )**- )**-#" 1 $ 0 > e " ? q≥0 4 $ 560*"
(
e q)
w Q= + @ 7 $ )**- 225" A 7 $ )**- " " Q 7 $ )**- " & / $ # # < B ht B t w # t < t s " rt+1 # t 8 {ct c t+ nt qt}Ut(
c t,c t+ ,nt,qt) ( )
=ln c t + ln( )
c t+ + ln( )
nt + ln(
e+qt)
max , , , 1, 2, 1 1, 2, 1 1 , 2 , 1 χ φ µ " #/(
)
(
)
0 1 1 1 , 2 , 1 ≥ + = − + − − = + + + t t t t t t t t t t t q s r c n q e h w s c τ β )" 1 0<χ < #/ φ,µ∈( )
0,1 # 8 1 , 1 1 , 2 1 1 + + ⋅ = + t t t r c c χ 1&C5"(
β)
φ = ⋅ + − t t t q e c n 1, 1 1&C)" t t t c n q e 1, = + µ 1&C+" D 5" )" 1&C5" 1&C+" # 0 < −φ µ 0 = q # 1 ! )**=" > # 9 # # # # 1 ! )**=" 8( )
(
β)
φχ β = e− k*8
( )
(
(
χ)
)(
φβ(
)
φββ)
χ α φ β α + − + − − = e e A n 1 1 * χ φ χ α + − + < 1 1 # 8 5" )" 9 E 0 > −φ µ ) 8 e q − − = β φ µ µ +"(
)
(
µ+χφ+µ)
β − = 1 t t t h w n -" µ χ χ + + = 1 t t t h w s 2" 1 D -" 8 ! ! ! " 8(
)
(
)
0 1+ + 2 < − − = ∂ ∂ β µ χ φ µ βt t t h w n 0 > β # 5 8 # # ; # " # 9 7 $ )**+" # $ ) 1 F )**5 2*+" ?> # C ## < $ t+1 8 ε ε − + = 1 1 t t t Bh q h 0" 0 > B ε∈
( )
0,1 + % & " C ## < α α − = 1 t t t AK L Y Yt Kt Lt =Ntht t # 0 > A α∈( )
0,1 9 < kt :=Kt/Nt yt :=Yt/Nt # α α − = 1 t t t Ak h y =" $ # 8 1 1 − = − α α t t t h k A r 3"(
−α)
α = t t t h k A w 1 6" ' ( " ! # 5" $ Nt+1 =ntNt $ $ # t t tk s n +1 = -" 2" $ # 8( )
β µχβφ − = * k 5*" . $ +" 0" 8( )
− − =Z e h φ µµβ β * 55" ε − ≡ 1 1 B Z 1 D 55" # * h # #(
)
T e β µ φ µ β > − ≡ ! " # # 9 # +1# & . # # " G # 8
( ) ( )
{
β * β * β}
* * , ,k h n n = 5)" D 5)" β 8 + + + + + + − ∂ ∂ ⋅ ∂ ∂ + ∂ ∂ ⋅ ∂ ∂ + ∂ ∂ = * ** * ** ** * β β β β h h n k k n n d dn # # # 8 5" " )" " # $ # A # D 5+" # # # # $ -" 6" 5*" 55" # 8( )
(
)(
)
(
χ µ)
β µ φ β µ φ µχβ α φ µ β α α α + + − − − − − = − − 1 1 1 1 * e Z A n 5+" 8 ! " β >βT 8( )
( )(
)(
)
(
)
[
1]
0 * * > + − − − = ∂ ∂ e e e n n φ β µ ββ µ φ α ββ T β β > ) # # 9 # 9 # # 8( )
β µχβφ α µµβφ α − − − − = 1 * e Z A y 5-" 8) " T β β > # 8
( )
( )
[
(
)
]
(
)
[
]
0 * * > − − − − = ∂ ∂ e e y y φ µ µβ ββ µβ µ φ α ββ 5-" T β β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
