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:
T (γt-1, kt) =
τ(kt)
0
if kt∈[F (τ ι),F (τ 1)]
otherwise
if ut(γt-1) < 1
Ψ
1+Ψ
otherwise
|
G(γt-1, kt) = |
1 Min[γ*, - mm] |
if otherwise |
kt∈[F (τ 1),F (τ 1)] 1 if ut(γt-1) < 1 |
|
1 |
otherwise |
(35)
S(πt,kt) =
(34)
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)]
otherwise n > 0
S(πt,kt, τt+1 = 0) otherwise
where x = 1 + (1ψ+αΓβ 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 ko / [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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