Article dans une revue: We investigate the welfare cost of business cycles implied by matching frictions. First, using the reduced-form of the matching model, we show that job finding rate fluctuations generate intrinsically a non-linear effect on unemployment: positive shocks reduce unemployment less than negative shocks increase it. For the observed process of the job finding rate in the US economy, this intrinsic asymmetry increases average unemployment, which leads to substantial business cycles costs. Moreover, the structural matching model embeds other non-linearities, which alter the average job finding rate and consequently the welfare cost of business cycles. Our theory suggests to subsidizing employment in order to dampen the impact of the job finding rate fluctuations on welfare.