GROWTH, UNEMPLOYMENT AND THE WAGE SETTING PROCESS.

proposition 3.1.1 and theorem 4.1 we have:

* - st
^-^t (1 - α)β ;

substituting s_t^* using proposition 5.1 we obtain:

-* = 1 (1 ^-^β)^-*Le ;

^t (1 - α)β Nt - Le

and simplifying w_t^* equation 54 becomes:

Lt^e

⁽¹^-^α)^β N

(1 - α)β +(1 - β) t;

that is,

ut =

1 - β

1 - αβ

From ( 22) we have:

Lt^e

1-α

^cAt ^α wt-1 Le-1

(53)

(54)

(55)

(56)

(57)

1-α

Substituting ( 55) in ( 57), if there is unemployment in period t - 1 solving for
w_t^* we obtain:

* 4l-α∕₁_vcw*-1Nt-1 ₁a ₄l-α∕₁_v cw*-1 _lα ∕_κcλ

^wt = ^cAt ⁽¹^-^α)[----N----] = At ⁽¹^-^α)[(1 + n) ] . ⁽⁵⁸⁾

Diving ( 58) by A_t we obtain:

w_t^-_-₁

w* c ~ï---

— = (1 - α)[-----A—----]^a. (59)

At ( )[(1 + n)(1+ g)] ( )

Ifwe call at the equilibrium wage per unit of efficient labor ω*, that is, ω* = A-
equation ( 59) becomes:

ω* = (1 - α)[ ---——----]^a. (60)

t ( )[(1 + n)(1+ g)^{] ()}

Solving ( 60) for ω_L^* _-_R when ω_t^* = ω_t^*_-_l = ω_L^* _-_R we obtain :

ωL в = (1 - α)¹^-α (-------—:-------)¹^-α . (61)

^l^-^r⁽ ) ((1 + n)(1 + g)) ⁽⁾

It is easy to check, drawing the phase diagram that the wage per unit of efficient
labour converges to ω_L^* _-_R. From ( 22) we have in period zero

L₀

1-α

A0 ^α Ko ,

[ t^wl ] α ;
l-α

(62)