We consider the downlink of Cell-Free Massive MIMO systems, where a very large number of distributed access points (APs) simultaneously serve a much smaller number of users. Each AP uses local channel estimates obtained from received uplink pilots and applies conjugate beamforming to transmit data to the users. We derive a closed-form expression for the achievable rate. This expression enables us to design an optimal max-min power control scheme that gives equal quality of service to all users. We further compare the performance of the Cell-Free Massive MIMO system to that of a conventional small-cell network and show that the throughput of the Cell-Free system is much more concentrated around its median compared to that of the small-cell system. The Cell-Free Massive MIMO system can provide an almost $20-$fold increase in 95%-likely per-user throughput, compared with the small-cell system. Furthermore, Cell-Free systems are more robust to shadow fading correlation than small-cell systems.