This paper studies the optimal duration of unemployment benefits in a basic job search model where a risk neutral unemployment insurance agency can not monitor the search effort of risk-averse workers. Unemployment assistance is taken as exogenous by the unemployment agency who chooses op- timally the tax rate, the level of unemployment benefit and the maximum date of their exhaustion. We deal with non-stationarity complexities and show that the solution of the agency's problem always exists with, at some conditions, a finite optimal duration of unemployment benefits.