strategy dominates.
In the first type of Markov sub game Perfect equilibrium (referred to by
"demographic switching strategy" equilibrium) policy rules do not depend on
the capital per (native-born) worker state variable.
Proposition 4 There exists an equilibrium with the following feature:
T(γt-1)=
τt = 0
T.= Ψ-
1 t 1+Ψ
if ut(γt-1) < 1
otherwise
(31)
G(Yt1) = I γt = Min[γ'∙ -m] if
t-1 γt = 1 otherwise
ut(γt-1) < 1
(32)
S(πt,kt) =
S(πt,kt,τt+1 = 1+Ψ) if ut(Yt-i) < 1
S(πt,kt,τt+1 = 0) otherwise
S(πt,kt,τ t+1 = ι+ψ )
S(πt,kt, τ t+1 = 0 )
n<0∩
if
m+n>
if m + n < 0
otherwise n > 0
where γt is restricted to be between zero and one, and γ*
(33)
is given explicitly in the
appendix. The equilibrium paths depend on the population growth rates and on
the initial amount of capital per (native-born) worker the economy is endowed
with. There are three main types of equilibrium paths which are similar to the
previous section:1. if n > 0, 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 "de-
mographic switching" equilibrium path, where some positive level of immigration
always prevails while there is an alternate taxation/social security policy; in pe-
riods where the decisive voter is old, the economy is fully opened to immigration
and there is a positive level of taxation (the "Laffer point" tax rate); whereas
in periods where the current decisive voter is young, there is no taxation/social
security benefits and a more restrictive policy towards immigration.
The proposition is proved in the appendix.
The intuition is the same as in section 2. Because the decision rules in
type one equilibrium do not depend on the capital per (native-born) worker,
the Markov sub game Perfect equilibrium of the base line model is essentially a
reduced form of this equilibrium. The equilibrium paths depend on the native-
born and immigrant’s population growth rates as in the baseline model, but
naturally are also quantitatively influenced by the amount of initial stock of
18
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