We first estimate country- and sector-specific technology frontiers within the EU, and show that countries that joined the Union in 2004-7 clearly stand below the lower envelope frontier of the older members in their use of skilled and unskilled labor. We interpret this as due to past barriers to technology adoption, barriers that are likely to be removed by the integration process. With the narrowing of the technology gap bound to follow, it is likely that firms and physical capital will be attracted to these economies by improved profitable prospects. Could such a technological upgrading trigger massive enough relocation of firms and outflows of capital to be detrimental to the welfare of workers in older EU member countries? We provide a quantitative exploration of this issue using a calibrated intertemporal multisector general equilibrium model of the EU27. We show that the results depend crucially on the value of the intertemporal substitution elasticity in households' preferences: a strong enough increase in the EU-aggregate stock of productive physical capital is necessary for the capital outflows not to be achieved at the expense of workers in old-member states. Though maybe not the most likely, the threshold value of this elasticity below which the EU-integration wave could turn into a non-Pareto-improving move is shown to lie within a statistically feasible interval.