If the sum of the native-born and immigrant population growth rates is
negative, m + n < 0, the number of next period old voters always exceeds
the number of next period young voters. Thus, along the equilibrium path a
majority of old will always prevail, which validates a permanent existence for
the social security system and a maximum flow of immigrants.
The third equilibrium path obtains if the native-born and immigrant pop-
ulations growth rates are: n < 0, and m + n > 0 . This equilibrium path is
characterized by an alternate taxation/social security policy over two consecu-
tive periods. Some positive level of immigration always prevails. This is due to a
"demographic switching" strategy of the current and next period young voters.
The reason is that when there is a majority of old, their preferable immigration
quota is at the maximum and the tax rate is at the "Laffer point". Because
m +n > 0 and the old decisive voter allows as much as possible immigrants, the
number of next period young voters exceed the number of next period old vot-
ers. Thus, in the next period the decisive voter must be the young. This voter
opts for a zero tax rate, and does vote strategically on immigration levels. This
means setting immigration at the threshold level , γt = -n/m. The identity
of the next period decisive voter will change from young to old (a possibility
of such demographic changes exists because the native-born population growth
rate is negative while the immigrant population growth rate is positive). This
creates a cycling effect of an alternate taxation/social security policy, with a
certain level of immigration, depending on the identity of the decisive voter.
4 The Extended Model: Private Saving, Capital
Accumulation and Endogenous Factor Prices
The base line model assumes zero private savings; hence no capital accumu-
lation at all. In this section, we introduce private saving. This means that
intertemporal transfers are both through private savings and through the social
security system. The aggregate savings of the current young population gener-
ates next period aggregate capital. The latter is used as a factor of production,
along with the labor input in the next period. The production function exhibits
constant return to scale. Another feature of the extended model is the wage
rate, as well as the rate of interest, are endogenously determined along the equi-
librium path. Social security benefits are financed, as before, by a payroll tax
14