GROWTH, UNEMPLOYMENT AND THE WAGE SETTING PROCESS.



*

If w* = wt-1

If wt = (1-α)


for all t solving this difference equation backwards we get:

*

wt*


w0*


(1 - α)t.


(48)


Subtituting At = A0(1 + g)t and ( 48) in ( 23) we obtain:

yt =


c(1


α) α


[w* ] 1-αα

I-Ao -I


[(1+g)(1-α)]


1-α t
α


1.


(49)


If w


,*


= (1 - α)w


then, using ( 24), lt becomes:


lt =


c(1


,w*  1-α

( At ) α


1=


.1-α,          ,

cAt α (1 - α)


wt


... 1-α

*----


1.


(50)


Subtituting At = A0(1 + g)t and ( 48) in ( 50) we obtain:

lt =


c(1


[ w* ] 1-α

I- Ao -I


[(1+g)(1-α)]


1α t


1.


(51)


We have that ut (=)(>)ut-1 if and only if lt


using ( 51):


> (=)(<)n which becomes,


c(1


α)1


[w* ] —

[ Ao ] α


[(1+g)(1-α)]


1-α t
α


> (=)(<)n.


(52)


From ( 49) and ( 51) we have that yt and lt decrease if and only if [(1+g)(1 -

α)] 1-α 1 that is, if and only if g < —. From ( 52) if c(t-αLα - 1 n we
"                          [ A0 ] α

have that ut increases for all t 0. If not there will exist some t > 0 such that
lt < n.

From ( 49) and ( 51) we have that yt and lt are constant if and only if [(1 +

g)(1-α)] 1αα = 1 thatis, if and only if g = ɪ. From ( 52) if c(1w-*αΓZ -1 < n
“                     [ At] α

1+α                                             1+α

then ut increases. If c(t*α)-α--1 = n then ut is constant. If c(1w*α)-α--1 > n

[ ^°- ] ~α~                                        [ ^o ] ~α~

[Ao]                                                                           [Ao]

then ut decreases.

From (49) and ( 51) we have that yt and lt increase if and only if [(1+g)(1 -

α)] 1-α 1 that is, if and only if g> —. From ( 52) if c(1w-α)-+Γ - 1 n we
α                      [
Ao] α

have that ut decreases for all t 0. If not there will exist some t > 0 such that
lt > n.

Proof of Proposition 5. 2 If γt = 0 it is easy to compute, using the proof of
theorem 4.1 that w't
= 0 and then wtcwtt. Now, if there is unemployment from

21



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