Migration of young workers (as distinct from retirees), even when driven in by the generosity of the welfare state, slows down the trend of increasing dependency ratio. But, even though low-skill migration improves the dependency ratio, it nevertheless burdens the welfare state. Recent studies by Smith and Edmonston (1977), and Sinn et al (2003) comprehensively estimate the fiscal burden that low-skill migration imposes on the fiscal system. However, an important message of this paper is that in an infinite-horizon set-up, one cannot fully grasp the implications of migration for the welfare state just by looking at the net fiscal burden that migrants impose on the fiscal system. In an infinite-horizon, overlapping generations economy, this net burden could change to net gain to the native-born population.