Irrelevance of productivity difference: A case with labor union

Common wisdom suggests that firms with higher productivities earn higher profits and the higher productivities of the firms benefit consumers by increasing outputs. We show that productivity difference may not matter for outputs and profits in presence of wage bill maximizing labor unions. Our results hold under decentralized (i.e., firm specific) and centralized union-firm bargaining, for any degree of product differentiation and for any bargaining power of the firms. Hence, our results have important implications for firms' incentives for innovation.