are like native-born in all respects (in particular, they have the same rate of
population growth).
We assume that the utility of the representative young individual is loga-
rithmic 1 , given by:
lΨ+1
Uy(wt,τt,bt+ι) = Log[wtlt(1 - Tt) - ɪ-j-] + βLog[bt+ι] (1)
Uo(bt) = bt (2)
where Uy and Uo are the utility functions of young and old individuals, β ∈ [0, 1]
is the discount factor, and Ψ > 0 a labor- disutility parameter (also equals to the
labor supply elasticity with respect to the wage rate). The transfer payments
to the old at period t, bt , are financed by collecting a flat income tax rate,
τt ∈ [0, 1], from the young individual’s wage income at the same period, wtlt ,
where lt denotes hours worked.
Labor is a single input in the production of a homogenous final good. The
production function is linear:
Yt = Nt (3)
where Yt and Nt are period t output and labor supply, respectively. Com-
petitive equilibrium wage rate, which is equal to the marginal productivity of
labor, is constant and normalized to unity. A worker can be either native-born
or immigrant, perfectly substitutable, and with equal productivities. The im-
migration quotas is expressed as a certain percentage of the number of young
individuals in the native-born population, γ ∈ [0, 1] 2 . Labor supply is:
Nt = Ltlt(1 +γt) (4)
where Lt is the number of young individuals in the native-born population (old
people do not work).
Immigrants have the same preferences as the native-born population, but
different population growth rates. We assume that the native-born population
has a lower population growth rate, n ∈ [-1, 1], than that of the immigrant
population, m ∈ [-1, 1], so that, n < m. We also assume that the immigrant’s
descendants are completely integrated into the economy and therefore have the
1 Note that this type of utility function implies that there are no income effects on the
demand for leisure (Greenwood, Hercowitz, and Huffman (1988)).
2 A ceiling for γ is set equal to one, which means that the number of immigrants cannot
surpass the number of native born.
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