In this paper, we analyze the dynamics of a very small economy which tries to attract foreign investments. For that purpose, we model the intertemporal behavior of a small jurisdiction using taxes and attractive public infrastructures as policy instruments, for given policy choices of the rest of the world. Applying Pontryagin's maximum principle, we then characterize the potential steady states which are attainable. These results give some insights into the policy behavior that may guarantee the long run survival of very small economies.