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

which can be rewritten in the following way:

Since γ ^* ≤1, it is enough to prove that:

Denote by k(y) the following function:

1 1 ∖ ^-α(^1+β)⅜+α             /      -       Z - ∖ ^-α(¹+^β)⅛⁺+α∖

^kfe)=U; )      Г . U )     ) I

(92)

Since the derivative of k(y) by y is positive for — mm ≤ y ≤ 1, it means that
k(γ*) > k(— mm). Thus, the optimal strategy of the young in that case is to set
the immigration quota to be γ_t = — mm, which completes the proof. ■

References

[1] Becker, G.S., Mulligan, C., 2003. Deadweight costs and the size of govern-
ment. The Journal of Law and Economics 46, 293—340.

[2] Benhabib, J., 1996. On the political economy of immigration. European
Economic Review 40, 1737-43

[3] Bergstrom, T.C., Hartman, J.L., 2005. Sustainabillity of pay-as-you-go so-
cial security, Cesifo Working Paper No.1378.

[4] Bohn, Henning, , 2005. Will Social Security and Medicare Remain Viable
as the U.S. Population is

[5] Aging? An Update, in: Robin Brooks and Assaf Razin (eds.), The Politics
and Finance of

[6] Social Security Reform, Cambridge University Press, 44-72

[7] Boldrin, M., Rustichini, A., 2000. Political equilibria with social security.
Review of Economic Dynamics 3, 41-78.

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