In this paper we analyse the impact of both the number of immigrants and their human capital on the welfare of the host economy. We will show that in the presence of ‘social increasing returns’ in human and physical capital accumulation, arising from a labour market characterized by a costly search and by randomness of the matching technology, immigrants’ skill level may influence the investments in human capital of natives as well as the investments in physical capital. We will find that the immigrants’ human capital interacts with social increasing returns making them stronger or weaker according to the level of immigrants’ human capital relative to that of natives. If immigrants have a higher level of human capital, increasing returns are accelerated, while if immigrants’ human capital is lower, increasing returns are weakened if not reversed. The consequence of this behaviour is that in the first case immigration has a positive impact on native welfare and there is a positive interrelation between the skills of natives, the skills of immigrants and the firms’ level of physical capital. In the second case immigration may have a negative impact on the welfare of natives, on the skills of native workers and on the physical capital of firms.