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

in a pay-as-you-go system³ .

The utility of the representative young individual, as before, is logarithmic.

_lΨ+1

U^y(wt,τt,st,rt+1,bt+1) = Log(wtlt(1 - τt) - st - ψ^t + 1) +
βLog(b_t+₁ + (1 + r_t+₁)s_t)            (16)

U ^o(s_t-1, r_t, b_t) = b_t + (1 + r_t)s_t-1                      (17)

where rt is the interest rate, and st is the savings of the young at period t.

The production function is a Cobb-Douglas production function which is
assumed to use both labor and capital as its factors of production:

Yt = N_t^1-aK_t^α                            (18)

where Kt is the aggregate amount of capital and Nt is defined as in the previ-
ous section. The wage rate and interest rate are determined by the marginal
productivity conditions (capital is assumed to depreciate completely at the end
of the period):

wt = (1 - a)(1 + γt)^-alt^-akt^α
rt = α(1 + γt)^1-alt^1-akt^α-1 - 1

where kt is capital per (native-born) worker. The balanced government budget
constraint is derived as in the previous section:

^τ t+ιwt+ιlt+ι[(1 + n) + Yt (1 + m)](1 + γt+ι)
^{(1 +} Yt)

The saving-consumption decision of young individuals are made by maxi-
mizing their utility while taking the prices and policy choices as given, and the
labor-leisure decision is given as in the previous section:

st = ɪ ββ ^ψ wtlt(1 — τt)  ⁺—-ʌ          (22)

^t 1+ β V Ψ + 1 t t^V t^J 1 + rt+1)              ^{V 7}

l_t^Ψ = wt (1 - τt)

The market clearing condition requires that the net domestic saving generates
net domestic investment:

³ To isolate the unique role of social security, the reader can compare the equilibrium types
derived in appendix 7.4. The appendix assumes a similar model, but without a social security
system.

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