Considering Cournot competition, this note shows that, if the firms differ in labor productivities, the equilibrium wage rates under a centralized labor union are not independent of the number of firms and product differentiation if the labor union charges a uniform wage rate. However, if the centralized labor union can discriminate wage rate between the firms, the equilibrium wage rates do not depend on the number of firms and product differentiation. Hence, the wage rigidity result of Dhillon and Petrakis (2002) may not be robust with respect to the asymmetry in firms, which is perhaps more common than symmetry considered by them. The effects of the number of firms and product differentiation on the equilibrium wage rate are also shown.
