rate but has two conflicting considerations regarding the desired immigration
quotas. One one hand, if there is full openness towards immigration: there will
be more young working people in period t + 1, and therefore, the tax revenue
that which will be collected from a larger work force and needed to support
retirement benefits, will increase. The young decisive voter in period t, who
will be old in period t + 1, would benefit from the more generous social security
benefits. On the other hand, if the immigration policy is excessively large, the
decisive voter in period t + 1 will be a young voter. This voter will want to see
the tax rate in period t + 1 reduced to zero; hence no social security benefits
whatsoever in period t + 1. There is a threshold level of immigration quotas,
γt = -n/m, which is exactly the level of the immigration policy that would
equate the number of old and the number of young in period t + 1. Thus, by
choosing the immigration quotas at this level, the decisive voter in period t would
finely balance the two conflicting forces on period t + 1 social security benefits,
so as to maximize these benefits. Observe that this young voter’s preferable
immigration quotas is chosen strategically, aimed to influence the identity of the
decisive voter in the next period from young voter to old.
If the old-young ratio is higher or equal to one (ut ≥ 1), the decisive voter
in the next period is an old voter. This voter will naturally vote for the most
liberal immigration policy possible, because only the current social security
benefits matter to this voter. The immigration quota is therefore equal to its
maximum level (i.e., one). The tax revenue is set at the "Laffer point", where
the tax rate is equal to ψψ+ι, because this way the current social security benefits
are maximized.
There are three possible equilibrium paths depending on the population
growth rates of the native-born and immigrant populations.
The first equilibrium path is the one where the population growth rate of the
native-born and the immigrant population growth rate are both positive; that
is, n, m > 0. In this case, the level of social security benefits is zero. This is due
to the fact that for every level of immigration, the number of next period young
voters exceeds the number of next period old voters. Therefore, the decisive
voter in the current and all the following periods is the young voter, and her
preferences are for zero labor tax. The young voter is indifferent concerning the
level of immigration because it has no influence on her current income, nor on
the next period decisive voter’s identity. The resulting equilibrium path is one
in which there is a majority of young voters, and the social security system is
dismantled, for ever.
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