GROWTH, UNEMPLOYMENT AND THE WAGE SETTING PROCESS.

Theorem 4.1 There exists w^,_t and w” _t such that if wC < w^,_t then an equilibrium
with unemployment always exists and it is unique.

If γ_t = 1 and wt_t ≤ wC < w” _t there exists an equilibrium with unemployment
and an equilibrium with full employment, if w”t ≤ w_t^c there exists a unique
equilibrium with full employment.

If 0 ≤ Yt < 1 and w^,_t ≤ wtc there exists an equilibrium with unemployment
and an equilibrium with full employment.

The representation of these situations are given by Figures 1.a, 1.b and
2.a, 2.b and 2.c. We denote the equilibrium with unemployment as w*_u =
w^t(wt-i,τt-i, Yt,βt), τfu = τt(βt), and s*,u = ^t(wt-ι, τt-ι,Yt,βt)∙ The special
case γt = 1 is analyzed in the next section. When 0 ≤ γt < 1 we can prove the
following theorem.

Theorem 4.2 Comparative Statics. The sign of the equilibrium partial deriva-
tives is given by the following table:

If u_t < ^1-βt then:

— < ¹¹ ∂Tτ < 0 ∂^t > 0 .

∂βt        ∂βt        ∂βt

If u_t > ^1-_α^βt then:

^dwLL < 0  ^dτ- < 0  ^d^- < 0

∂βt < 0  ∂βt < 0  ∂βt < 0 .

If (1 - τt)wt-1 > st then:

^d^L > 0  ^dTt = 0  ^d^- < 0

∂γt > 0   ∂γt   0   ∂γt < 0 .

If (1 - τt)wt-1 < st then:

— < 0 ∂τL =0 ∂sL > 0 .
∂γt         ∂γt         ∂γt       .

The interpretation of Theorem 4.2 is the following. First, the more proem-
ployed workers the government the lower the equilibrium wage and, by ( 23)
and ( 25), the higher the output growth rate and the lower the unemployment
rate. Second, if the unemployment rate is low enough, u_t < ^1-_α^βt, then the more
proemployed workers the government the higher the unemployment benefit, that
is, we will have more employment and a higher unemployment benefit with a
more proemployed workers government. Note that the unemployment rate de-
pends on βt , this means that, in principle, we can not say when this situation
happens. A sufficient condition is to have ^1-_α^βt > 1, that is, β_t < 1 — α. We
can interpret this result as follows: if the government is really prounemployed
workers and it becomes more proemployed workers the economy will have less
unemployment and a higher unemployment benefit, that is, if the government
cares sufficiently about unemployed workers a lower unemployment rate is asso-
ciated with a higher unemployment benefit. Finally, if the real wage after taxes
of the previous period is greater that the unemployment benefit of the period
the higher the union cares about the wage of the previous period the higher
the equilibrium wage rate and the unemployment rate and the lower the growth
rate and the unemployment benefit.

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