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

Uy(wtt,st,rt+1,bt+1) = Log(wtlt(1 - τt) - st - ψt + 1) +
βLog(b
t+1 + (1 + rt+1)st)            (16)

U o(st-1, rt, bt) = bt + (1 + rt)st-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 = Nt1-aKtα                            (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-aktα
rt = α(1 + γt)1-alt1-aktα-1 - 1

(19)


(20)


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

bt+1 =


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

(21)


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 tV tJ 1 + rt+1)              V 7

ltΨ = wt (1 - τt)

(23)


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.

15



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