The Role of Immigration in Sustaining the Social Security System: A Political Economy Approach

same population growth rate as the native-born population does. The number
of young native-born individuals at period t :

L_t = L_t-1(1 + n) + γ_t-1L_t-1 (1 + m)

(5)

In addition, immigrants are also assumed to contribute to, or benefit from,
the social security system in the same way as the native-born. Because the social
security system redistributes income from the young to the old, the balanced
government budget constraint implies:

bt+1Lt(1 + γ_t) = τ t+1wt+1lt+1Lt+1(1 + γ_t+1)               (6)

Re-arranging the expression yields:

bt+1 =

^τ t+ιwt+ιlt+ι[(1 ⁺ n) + Yt(1 ⁺ m)](1 ⁺ Yt+1)

(1 + γ_t)

(7)

Labor-leisure decisions of young individuals are derived, as usual, from utility
maximization, taking the prices and policy choices as given:

l_t^Ψ = wt (1 - τt)

(8)

Substituting for b_t , b_t+₁and l_t in equations (7) and (8) into equation (1), the
indirect utility functions of the young individual can be written as:

Ψ

V^y(wt,τt,τt+1,wt+1) = Log[ψ+1 wtlt(1 - τt)] +

(9)

such that,

βLog[

^τt+ιwt+ιlt+ι [1 ⁺ n ⁺ γt (1 ⁺ m)](1 ⁺ γt+ι)
(1+ Yt)

l_t^Ψ = wt (1 - τt)
l_t^Ψ₊₁ = wt+1 (1 - τt+1)

(10)

(11)

Substituting for bt in equations (7) into equation (2), yields the indirect utility
functions of the old individual:

V ^o(bt) =

τ twtlt[(1+ n)+ γ_t-1(1 + m)](1 + γ_t)
(1⁺ Yt-1)

(12)