collected, and thus the social security benefits she receives. The old preferable
tax rate is the "Laffer point" tax rate, where the tax revenues, and therefore
the social security benefits, are maximized. The tax rate at that point is equal
to
Ψ
Ψ+1 ∙
The young individual prefers naturally that the current tax rate is as low as
possible, namely zero. Concerning immigration quotas, the young preferences
are ambiguous. On one hand, a larger quotas increases next period social se-
curity benefits per old individual. This is due to the fact that larger quotas
increases the number of young in the next generation (some of these are off-
spring of the current immigrants) more than it increases the number of the old
(who happen to be the current young) in the next period. This is due to the
assumption that immigrants have a higher population growth rate than that of
the native-born (m > n). Thus, the number of next period old recipients of
social security increases but the total sum of next period social security benefits
increases even more. This means that next period social security benefits per
old individual (bt+1) are higher the larger is the immigration quotas.
On the other hand, since immigrants gain the right to vote in the second
period of their life, when old, the level of immigration quotas which affects
the ratio of next period old to young voters also influences the identity of next
period decisive voter. Lowering current immigration quota decreases the number
of next period old voters less than it decreases the number of next period young
voters (because we assumed m > n). Thus, voting for a low enough level
of immigration quotas (below a certain a threshold level), would change the
identity of the decisive voter from young to old in the next period. This will
lead the current young voter which will be old in the next period, to favor the
largest possible quota (due to its effect on next period transfer payments) which
yet change next period decisive voter’s identity from young to old in the next
period.
3.0.1 A Political-Economic Equilibrium
We employ a subgame-perfect Markov equilibrium of perfect foresight, as our
equilibrium concept (see Krusell and Rios-Rull (1996)):
Definition 1 A subgame-perfect Markov equilibrium is defined as a vector of
policy decision rules, Ψ = (T, G), where T : [0, 1] -→ [0, 1], is the taxation
policy rule, T (γt-1), and G : [0, 1] -→ [0, 1], is the immigration quotas policy
rule, G(γt-1), such that the following functional equation holds:
1. Ψ(Yt-1) = argmax∏t Vi(Yt-i, ∏t, ∏t+ι) subject to ∏t+ι = Ψ(Yt), where