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

s = _k 11+n + 7t(1 + m) ʌ                 (24)

^{t t+}4     (1 + Yt)     J                    ( )

Solving for bt+1 from equations (21) and (22), and substituting bt+1 in equations
(16) , the utility indirect function of the young can be written as follows:

V^y(wt^,τt^,rt+ι^,τt+1) = Log (1+=βΨ+1 wtlt(^{1 - τ}t)(^{1+ βf} (^τt+1⁾⁾)         _λ

(25a)

^+βLo^g (ι+βΨ+1 wtlt(^{1 - τ}t⁾⁽¹ + ^βf(^τt+1^{))(1 + r}t+1)J

where f (τ,+1) = _{1 ι} ^α-_ο1^+βτt —, such that,
1⁺ α 1+β ^{T t} + 1

k = β Ψ ^{(1 +} Yt)^wtlt(^{1 - τ}t^{)(1 - f} (^τt+1))
^t+1   1 + β Ψ + 1      1+ n + γ_t(1 + m)

lt^Ψ = wt (1 - τt)                             (27)

l_t^Ψ₊₁ = wt+1(1 - τt+1)                         (28)

and substituting b_t from equation (21) and k_t from equation (24), in equations
(17), the indirect utility function of the old can be written as follows:

V ο(γ,-_l,k,,W,,r,,T ,)= ^T ■^Wt|.^[(1+n)++.^-_-1)^+m)](1+Yt) +          29

(1 + rt)k ( ¹⁺ⁿ++t,^-_t¹_-(1+^m* )                                      ⁽

such that,

l_t^Ψ = wt (1 - τt)

As in the previous analysis, the old individual favors a positive level of tax
rate at a "Laffer Point" (τ* = ψ^ψ+1 ), and the largest immigration quotas.

The preferences of the young, which will be discussed in the next section,
differ from the baseline model as they are influenced by capital accumulation
and endogenous factor prices effects.

4.0.2 Political-Economic Equilibria

The Markov sub-game Perfect equilibrium definition for the extended model is
as follows:

Definition 3 A Markov perfect political equilibrium is defined as a vector of
policy decision rules, Ψ = (T, G), and private decision rule, S, where T :
[0, 1] -→ [0, 1], is the tax policy rule, τt = T(γ_t-1 , kt), and G : [0, 1] -→ [0, 1],

16

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