GROWTH, UNEMPLOYMENT AND THE WAGE SETTING PROCESS.

Le =     (¹ - ^а)в     N

0   (1 - α)β +(1 - β) N0.

Substituting ( 62) in ( 63) and solving the equation for w* we obtain:

that is:

*   ∩ u(^{1 - α})^{β + (1 - β}) KO iα               {(ir∖

^ωo = <^{1 - a)[}—.— A^,   ∙           ⁽⁶⁵⁾

From ( 53) we obtain : s_t^* = β(1 - α)w_t^* and defining the equilibrium unem-

ployment benefit per unit of efficient labor, σ*, as σ* = At we also have

σt^o = β(1 - α)ωt^o∙                            (66)

Substituting ( 58) and ( 61) in ( 66) we obtain:

σ* = β(1^-α)(1 - α)(^2-α)[⅛-]^α;
(1 + n)

and

σ*-R = β(1 - α)^2-α (—C—)¹-^α .               (68)

^-                  (1 + n)

Finally, substituting ( 61) in ( 23) we obtain that y_L^o _-R = (1 + g)(1 + n) - 1
and the rate of growth of employment is always equal to the rate of population
growth because the rate of unemployment is constant with time.

Proof of Proposition 6. 1 We define equation 31 as F (ωt, ωt-1 , ut) = 0 and
equation 32 as G(ω_t, ω_t-1, u_t-1, u_t) = 0 which implicitly define the system:
ω_t = f1 (ω_t-1, u_t-1), u_t = f2 (ω_t-1 , u_t-1). Linearizing this system around the
steady state and simplifying we obtain the fol lowing jacobian matrix:

, which means a unique eigen

value λ = 1 and, then, the system does not converge to the steady state. If
γ < (1 - α)(1 + g) then 0 < u < 1. In this case one can compute that the eigen
values will be real numbers if and only if

α1

^γ< 4(Γ+Σ)^{[(1 - a)(1 + g) - γ}]U∙
23

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