Is competition or collusion in the product market relevant for labour market?

In non-union models, there is an ambiguous relationship between collusion on the product market and the resulting impact on the labour market. We can derive some conclusions by assuming a dual labour market with qualified and unqualified workers and taking into account the efficiency effect when employing qualified workers. The framework adopted here consists of two firms competing to hire workers on the qualified labour market, and then competing (or colluding) on the product market to sell their production. While qualified workers are heterogeneous in their specialization, firms sell imperfect substitute goods on the product market.