GROWTH, UNEMPLOYMENT AND THE WAGE SETTING PROCESS.

for all t solving this difference equation backwards we get:

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

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

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

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

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

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

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

1+α                                             1+α

then u_t increases. If c(t*^α)-^α--1 = n then u_t is constant. If c(1_w*^α)_-^α--1 > n

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

^[Ao^{]                                                                           [}Ao^]

then u_t decreases.

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

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

have that u_t decreases for all t ≥ 0. If not there will exist some t > 0 such that
l_t > 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 wtc ≥ wt_t. Now, if there is unemployment from

21

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