We consider the communication problem in a multi-hop relay network where the intermediate relay nodes cannot transmit and receive at the same time. The motivation for this assumption comes from the fact that current radios operate in TDD mode when the transmitting and receiving frequencies are the same. We label such a node radio as a 'cheap' radio and the corresponding node of the network as a 'cheap' node. In this paper we derive the capacities of the degraded cheap relay channel and the multi-hop network with cheap nodes. The proof of the achievability parts in coding theorems are presented based on the jointly typical sequences, while the proof of the converses are derived from the direct application of the upper bounds derived in [7].