Massive MIMO is attractive for wireless information and energy transfer due to its ability to focus energy towards desired spatial locations. In this paper, the overall power transfer efficiency (PTE) and the energy efficiency (EE) of a wireless-powered massive MIMO system is investigated where a multi-antenna base-station (BS) uses wireless energy transfer to charge single-antenna energy harvesting users on the downlink. The users may exploit the harvested energy to transmit information to the BS on the uplink. The overall system performance is analyzed while accounting for the nonlinear nature of practical energy harvesters. First, for wireless energy transfer, the PTE is characterized using a scalable model for the BS circuit power consumption. The PTE-optimal number of BS antennas and users are derived. Then, for wireless energy and information transfer, the EE performance is characterized. The EE-optimal BS transmit power is derived in terms of the key system parameters such as the number of BS antennas and the number of users. As the number of antennas becomes large, increasing the transmit power improves the energy efficiency for moderate to large number of antennas. Simulation results suggest that it is energy efficient to operate the system in the massive antenna regime.