GROWTH, UNEMPLOYMENT AND THE WAGE SETTING PROCESS.

The interpretation of proposition 5.2 is, if the union only cares about the
unemployment benefit of the period, β remains constant along time and there is
always unemployment, the unemployment rate remains constant along time and
depends only on α and β . Note that the higher the β the lower the unemploy-
ment rate. The intuition for this result comes from the proof of 5.2. In this case
the wage is proportional to the unemployment benefit and the unemployment
benefit is proportional to the wage, which means the same equation in terms of
the rate of unemployment for all t.

Moreover, if the wage and the unemployment benefit per unit of effective
labour at period zero are lower (higher) than the long run wage and the un-
employment benefit per unit of effective labour they increase (decrease) along
time. The rate of growth of wages and the unemployment benefit in the long
run is equal to g. The long-run rate of growth is equal to (1 + n)(1 + g) - 1
and the long run rate of unemployment is equal to ₁¹ _α^β_β, that is, there is no
relationship between growth and unemployment in the long run. Note that in
this specific OLG model when the labour market is competitive the long-run
rate of growth is also equal to (1 + n)(1 + g) - 1. This is not surprising because
the constant rate of unemployment implies that the effective quantity of labour
employed growths at the constant rate n and, then, the analysis of the model is
identically to the case of perfect competition.

Thus, the behaviour of the economic variables of this OLG model along
time when the labour market is not competitive really depends on the specific
wage setting. We want also to emphasize that the specific behaviour of the
government is also important for the results obtained. Let’s now, alternativelly,
assume that the government is commited to pay a given unemployment b enefit
s' constant along time and this quantity is provided taxing both employed and
unemployed workers at the same tax rate τt . In this case the government has no
choice, given the wage and the unemployment benefit, and, it only determines
τt in order to balance its budget. On the other hand, the utility function of the
union, if the unemployed workers are also taxed, changes to

S' = ((1 — τt)wt - γt(1 - τt-i)wt-i - (1 - γt)(1 - Tt)s')Le.

If γt = 0 for all t, it is easy to check, using the proof of proposition 3.1.1, that, if
there is unemployment, w_t = (i-_α), for all t, that is, there is real wage rigidity
along time. It is also easy to check, using equations ( 23) and ( 24), that the
rates of growth of output and employment increase.

Note then that, depending on the assumptions about the specific wage set-
ting process and the behaviour of the government, we have obtained the fol-
lowing special cases: 1) Constant rate of growth of the real wage with rates of
growth of output and employment increasing or decreasing depending on the

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