If 0 < u < 1 and γ
inequality holds if and
0 <a< 1 b < 0
c>0 0<d<1
< 4(i+α) [(1 — α)(1 + g) — γ] then 70 holds.
only if γ < α(1-+5α+g). If 0 < u < 1 then
Last
J=
such
. In this case the two eigen values λi, λ2 are
that λ1 + λ2 = a + d > 0 and λ1 λ2 = ad — bc > 0. These two inequalities imply
λ1 > 0 and λ2 > 0. Now if λ1 + λ2 = a + d < 1 then we have that 0 < λ1 < 1
and 0 < λ2 < 1 which implies convergence to the steady state if both are real.
Using 69 we obtain:
λ1 + λ2 =
2Y + [(1 - α)(1+ g) — γ]U
γ + α[(1 - α)(1 + g )- γ] u '
(71)
Using 71 we have that λ1 + λ2 < 1 if and only if:
γ< ∩~^2[(1 — α)(1 + g) — γ]1. (72)
αu
If 0 < u < 1 and γ < (1 α) [(1 — α)(1 + g) — γ] then 72 holds. Last inequality
holds if and only if γ < (1 — α)2(1 + g). Finally we define
Y' = min( α(1-α5(α1+g) , (1 — a)2(1 + g)).
References
[1] Aghion, P. and Howitt, P. (1994); ”Growth and Unemployment”, Review
of Economic Studies, 61, 477-494.
[2] Bean, Ch. and Pissarides, Ch. (1993); ”Unemployment, consumption and
growth”, European Economic Review, 37, 837-859.
[3] Daveri, F. and Tabellini, G. (1997), ”Unemployment, Growth and Taxation
in Industrial Countries”, Discussion Paper Series, No 1681, International
Macroeconomics, CEPR.
[4] Diamond, P. (1965); ”National Debt in a Neo-classical Growth Model”,
American Economic Review, 55, 1126-1150.
[5] Layard, R. , Nickell, S. and Jackman, R. (1991); ”Unemployment”, Oxford
University Press.
[6] McDonald, I.M. and Solow, R. M.(1981); ”Wage Bargaining and Employ-
ment”, American Economic Review, 71, 896-909.
[7] Oswald, A.J. (1985); ”The Economic Theory of Trade Unions: An Intro-
ductory Survey”, Scandinavian Journal of Economics, 87(2), 160-193.
[8] Pissarides, C.A. (1990); ”Equilibrium Unemployment Theory”, Basil
Blacwell, Oxford.
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