We present a model of a monetary economy with two systems of wage setting: a decentralized system and a centralized system. In the decentralized system there is a union per firm that sets the firm's wage. In the centralized system there is a unique union that sets a common wage for all firms. We find that, when there is unemployment, the equilibrium wage set in the centralized wage setting system is lower than the one set in the decentralized wage setting and that both depend on the size of the unemployment benefit and on the degree of pro-workerism of the government. When the unemployment benefit is a given quantity, we find that monetary policy has real effects in both systems and implies nominal wage rigidity in the centralized system. On the contrary, when the unemployment benefit grows with the size of the economy, monetary policy has no real effects and implies real wage rigidity in both systems.Financial support from the Spanish Ministry of Education through DGICYT grant PB96-1160-C02-02 is gratefully acknowledged.