How Imperfect Competition in the Labor Market Affects Long-Term Unemployment Policies ?

We consider a continuum of unemployed workers ranked according to their unemployment duration. There are two industries, a high and a low technology one, which compete imperfectly on the labor market. Once employed, each individual must bear a training cost, which is proportional to his unemployment duration, the training cost being larger in the high technology industry. There is a duration dependence since the long-term unemployed may never find a job. In this framework, we study different types of second best policies that either subsidy the training cost or the wages and we compared them.