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Globalization makes it easier to relocate production and thus employment across countries. Therefore, it is often asserted that labour demand becomes more elastic, causing wage mark-ups to fall and thus erode the effective market power of trade unions. We explore this issue in a general equilibrium model where the elasticity of labour demand is endogenized and related to the facility by which production can be relocated across countries. Wages and employment increase unambiguously as a result of product market integration, but it is ambiguous whether wage mark-ups decrease or increase. A numerical illustration suggests that the elasticity effect – even when the wage mark-up falls – is of second order relative to the gains from trade. [ABSTRACT FROM AUTHOR]