This paper studies two power control problems in energy harvesting wireless networks where one hybrid base station (HBS) and all user equipments (UEs) are operating in in-band full-duplex mode. We consider minimizing the aggregate power subject to the quality of service requirement constraint, and maximizing the aggregate throughput. We address these two problems by proposing two distributed power control schemes for controlling the uplink transmit power by the UEs and the downlink energy harvesting signal power by the HBS. In our proposed schemes, the HBS updates the downlink transmit power level of the energy-harvesting signal so that each UE is enabled to harvest its required energy for powering the operating circuit and transmitting its uplink information signal with the power level determined by the proposed schemes. We show that our proposed power control schemes converge to their corresponding unique fixed points starting from any arbitrary initial transmit power. We will show that our proposed schemes well address the stated problems, which is also demonstrated by our extensive simulation results.