Note that the long run wage per unit of effective labour is the same that the
one obtained in the case γ = 0 which means that the long run rate of output
growth is equal to (1 + n)(1 + g) - 1. This means that, when both the previous
wage and the unemployment benefit are taken into account when setting the
wage, a change in either γ or β affects the long run rate of unemployment but
keeps the long run rate of growth of output unaffected, an increase in n increases
the rate of growth of output but keeps the rate of unemployment unaffected and
an increase in g increases the rate of growth of output and decreases the rate of
unemployment.
We can not conclude that there is no relationship between growth and un-
employment in the long run in this case because there is a common variable g
which affects both rates in the long run. The higher the rate of productivity
growth, the higher the growth rate and the lower the unemployment rate in the
long run, which implies an negative relationship between growth and unemploy-
ment in the long run. Note that this happens only when previous wages are
taken into account when setting the wage. The intuition is that, in this case,
the same real wage is set independently of the rate of productivity and, then,
a change in g will affect employment. This result means that any government
policy that increases productivity will imply more growth and less unemploy-
ment. Note also that, contrary to Daveri and Tabellini’s result ( [3]), an increase
on workers’s tax rate (decrease in β) increases unemployment but keeps output
growth unaffected.
Note also that if g > ι-α and the economy converges to the steady state
the higher the γ the lower the unemployment rate which means that taking into
account only the unemployment benefit when setting the wage does not imply
the lowest unemployment rate.
7 Final Comments
Using an standard OLG model with a non competitive labour market, where
the wage is set by unions and the government pays an unemployment b enefit
taxing workers, we have analyzed under which conditions a lower unemployment
rate is associated with a higher unemployment benefit. We have found that
this situation happens if the government cares sufficiently about unemployed
workers.
We have also analyzed the long run behaviour of real wages, the rates of
growth of ouput and the rate of unemployment in three cases. We have found
that, if the government sets both the unemployment benefit and the tax rate to
employed workers and workers take into account only present variables of the
period when setting the wage, the long run rate of growth depends on the rate
16