The Role of Immigration in Sustaining the Social Security System: A Political Economy Approach

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

U^y(wt,τt,bt+ι) = Log[wtlt(1 - Tt) - ɪ-j-] + βLog[bt+ι]        (1)

U^o(bt) = bt                                     (2)

where U^y and U^o 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 l_t 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 L_t 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.

<<   5   6   7   8   9   10   11   >>

More intriguing information