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. Fiscal Insurance and Debt Management in OECD Economies2. The Value of Cultural Heritage Sites in Armenia: Evidence From a Travel Cost Method Study
3. Why unwinding preferences is not the same as liberalisation: the case of sugar
4. Rural-Urban Economic Disparities among China’s Elderly
5. The Tangible Contribution of R&D Spending Foreign-Owned Plants to a Host Region: a Plant Level Study of the Irish Manufacturing Sector (1980-1996)
6. A novel selective 11b-hydroxysteroid dehydrogenase type 1 inhibitor prevents human adipogenesis
7. Spousal Labor Market Effects from Government Health Insurance: Evidence from a Veterans Affairs Expansion
8. The name is absent
9. The name is absent
10. Constrained School Choice