Abstract We study how unionization affects competitive selection between heterogeneous firms when wage negotiations can occur at the firm or at the profit‐centre level. With productivity specific wages, an increase in union power has: (i) a selection‐softening; (ii) a counter‐competitive; (iii) a wage‐inequality; and (iv) a variety effect. In a two‐country asymmetric setting, stronger unions soften competition for domestic firms and toughen it for exporters. With profit‐centre bargaining, we show how trade liberalization can affect wage inequality among identical workers both across firms (via its effects on competitive selection) and within firms (via wage discrimination across destination markets).