of the young. Due to the fact that "Effect One" is stronger than "Effect Two",
larger immigration quotas which increase next period tax rate (since it decreases
next period capital per (native-born) worker6 ), raise next period future social
security benefits. This additional positive effect of immigration quotas on the
indirect utility of the young raises the preferable immigration quotas leading to
no restriction on immigration.
The reason for the additional strategy (i.e. the "demographic steady" strat-
egy) in the "combined strategy" equilibrium, results from the additional state
variable- the capital per (native-born) worker, which influences next period pol-
icy variables. When the capital per (native-born) worker is an additional state
variable, the decisive young voter does not have to engage in a strategy of influ-
encing next period policy variables only by changing next period decisive voter’s
identity through immigration quotas (meaning by admitting a limited amount
of immigrants). Because both current policy variables, the tax and the migra-
tion quota, influence the amount of capital per (native-born) worker; which, in
turn, influences next period policy variables. Moreover, the young can use the
"demographic steady" strategy (instead of the "demographic switching" strat-
egy), which is optimal for low enough capital per (native-born) worker7 . This is
due to the fact that low capital per (native-born) worker adds a positive effect
on the indirect utility of the young in the case of the "demographic steady"
strategy: it decreases the current wage income of the young which by reduc-
ing the amount of next period capital per (native-born) worker, leads to an
increase in the next period tax rate and benefits (since "Effect One" is stronger
than "Effect Two"). This raises the young future income, meaning that for low
enough capital per (native-born) worker the "demographic steady" strategy is
the dominant strategy.
The equilibrium paths depend on the population growth rates and the amount
of capital per (native-born) worker:
1. The population growth rates of the native-born and immigrant popula-
tions are positive, n, m > 0. In this case, the number of next period young
6 A larger immigration quotas increases the number of young who save leading to higher
aggregate capital accumulation in the next period. But since we assumed that m > n,
immigration quotas increases even more the number of next period young. Thus the amount
of next period capital per native-born work force decreases.
7 The reason that the "demographic steady" strategy is optimal for a closed range of capital
per (native born) worker instead of every capital per (native born) worker lower than some
threshold, is that the tax rate is assumed to be positive and smaller than one. Since the tax
rate is a function of the capital per (native born) worker, it means that the capital per (native
born) worker should also be in a specific range (see the second part of the proof in appendix
III).
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