We analyze, using an standard OLG model with a non competitive labour market, under which conditions a lower unemployment rate is associated with a higher unemployment benefit. We also study the dynamics of growth and unemployment and we check if there is no relationship between growth and unemployment in the long run. The main results are: 1) If the government cares sufficiently about unemployed workers, then a lower unemployment rate is associated with a higher unemployment benefit. 2) The relationship between growth and unemployment in the long run is weak in the sense that only the rate of growth of productivity from all the parameters of the model affects both in the long run when in wage setting process past wages and the present unemployment benefit are taken into account.Financial support from the Spanish Ministry of Education through DGICYT grant PB96- 1160-C02-02 is gratefully acknowledged.