We use a cake-eating model with a non-renewable resource and a backstop technology to describe the effect of migration of poor workers into a rich country with surplus labor. Migrants receive a large transfer from natives. If future migration is anticipated, natives' flow of utility increases discontinuously at the time of migration. Migration at time 0 may cause the initial flow of natives~ utility to be higher. However, the present discounted value of the stream of per capita utility falls. Thus, when migration occurs, it may benefit the current generation of natives, although it harms other generations.