Pre-print, Working paper: We develop a theoretical framework analyzing responsible firms (REFs) that prioritize worker welfare alongside profits in labor markets with search frictions. At the micro level, REFs' use of market power varies with labor conditions: they refrain from using it in slack markets but may exercise it in tight markets without harming workers. Our macro analysis shows these firms offer higher wages, creating a distinct high-wage sector. When firms endogenously choose worker bargaining power, there is a trade-off between worker surplus and employment, though this improves with elastic labor supply. While REFs cannot survive with free entry, they can coexist with profit-maximizing firms under limited competition, where their presence forces ordinary firms to raise wages.