We set up a partial equilibrium model of Cournot competition, where firms can strategically choose their outsourcing intensity. This decision is based on a trade-off between lower marginal production costs and higher fixed costs. In this model, a lower number of identical firms leads to higher market concentration and higher outsourcing activities. The theoretical hypothesis of a positive correlation between market concentration and international outsourcing is confirmed by rank correlation coefficients and a fixed effects panel data analysis using data on the intermediate goods imports to output ratio and market concentration in the EU12 countries. In the fixed effects regression analysis we show that market concentration has to be treated as an endogenous variable to avoid biased and inconsistent estimates.