which can be rewritten in the following way:
(U
7m
^ -α(1+β) ⅜++α
(ι-mm
ι+n-mm (ι+m)
1∙'
1+n+γ* (1+m)
1
V + T7
-α(1+β) -1++α
β I-α
-Ψ β Ψ+α
(90)
>1
Since γ * ≤1, it is enough to prove that:
(U
^ -α(1+β) ψ++α
(1+Y )
m
(1-n
1+n-mm (1+m)
1+γ •
1+n+γ* (1+m)
fl—ɪ A
<1 + -I
α(1+β) ⅛++α
Д 1-α
Ψ β Ψ+α
>1
(91)
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 γt = — 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.
38
More intriguing information
1. The name is absent2. The name is absent
3. The name is absent
4. The name is absent
5. An Interview with Thomas J. Sargent
6. The name is absent
7. Benchmarking Regional Innovation: A Comparison of Bavaria, Northern Ireland and the Republic of Ireland
8. ENVIRONMENTAL POLICY: THE LEGISLATIVE AND REGULATORY AGENDA
9. The name is absent
10. The name is absent