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

capital per (native-born) worker. The larger the initial stock of capital, the
higher is the amount of capital accumulated every period.

The second type of Markov Perfect equilibrium of the extended model (re-
ferred to as "combined strategy" equilibrium) is specified as follows:

Proposition 5 Under several conditions on the parameters of the model, which
are specified in the appendix, there exists another equilibrium type, with the
following features:

Ψ

1+Ψ

otherwise

(35)

S(πt,kt) =

S(∏t,kt,τt+ι = τ(kt+ι) ) if kt∈[F(τι),F(τ 1)] if u(_γ   ) < 1

S(∏t,kt,τt+ι = ɪ) otherwise                       ^t-1      . m + n > 0

S(∏t,kt,τt+ι = τ(kt+ι)) if kt∈ [g(F(τ1)),g(F(τ 1))] otherwise '    ∩ n< 0

S(πt, kt , τt+1 = 0) otherwise                                                         (36)

S(∏t,kt,τt+ι = ₁+_ψ)                                          if m + n< 0

S(∏t,kt,τt+ι= τ(kt+1)) if kt∈[F(τ1),F(τι)]

S(πt,kt, τt+1 = 0) otherwise
where x = 1 + (¹ψ+αΓ^β and g(F), F(τ) and τ ₁ are given in the appendix. The
equilibrium tax rate, τ(kt), is a decreasing function in kt . The equilibrium paths,
depends on the native-born and immigrant population growth rates and on the
initial capital the economy is endowed with: 1. if n > 0 and ko ∈ [F(τ ₁), F(τ ₁)],
there is a "demographic steady" equilibrium path, characterized by a positive tax
rate which depends on the capital per (native-born) worker state variable and
migration quota is set at its maximum. If k_o / [F(τ ₁),F(τ ₁)], there are at least
few periods in which there is no taxation/social security benefits and there are
some restrictions on immigration. 2. if m + n < 0, migration quota is set
at its maximum, and there is a positive level of taxation/social security benefits
(the "Laffer point" tax rate). 3. if n < 0 and m + n > 0, there is a range of

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