Abstract We develop a model of international trade with heterogeneous firms and monopsonistically competitive labour markets. We show that due to monopsonistic competition our model makes sharply different predictions about the effects of the export of goods and the offshoring of tasks. Trade in goods is unambiguously welfare increasing as domestic resources are reallocated to large firms with high productivity and firms with low productivities exit the market thereby reducing the monopsony distortion present in autarky. Offshoring, however, gives firms additional scope for exercising monopsony power by reducing their domestic size and therefore can lead to welfare losses.