In this paper, we outline a baseline DSGE model which enables a straightforward analysis of wage bargaining between firms and households/unions in a model with both staggered prices and wages. Relying on empirical evidence, we assume that prices can be changed whenever wages are changed. This feature of the model greatly reduces the complexity of the price and wage setting decisions; specifically it removes complicated interdependencies between current and future price and wage decisions. In an application of the model we study the interaction between labor-market institutions and monetary policy choices, and the consequences for welfare outcomes. Specifically, we focus on the relative bargaining power of unions. We find that, for a standard specification of the monetary policy rule, welfare is substantially affected by the degree of relative bargaining power, but that this effect can be neutralized by optimal discretionary policy.