In this paper, we study the bandwidth efficiency (throughput) and the energy efficiency of relay networks considering both the physical layer and the medium access control (MAC) layer. Due to wireless signal power attenuation with transmission distance, using a relay for packet transmissions can lead to more energy-efficient wireless networking at the expense of requiring multihop transmissions. To understand the potential benefits of using a relay, the energy–throughput tradeoff needs to be analyzed. In a decentralized wireless network, not only the physical layer but also the MAC layer should be considered. At the physical layer, the transmit power determines the area which contains nodes that might be contending for channel access at the MAC layer. At the MAC layer, gaining access to the channel entails transmitting various signals at the physical layer. This uses energy and takes time, which impacts the bandwidth efficiency. We analyze the energy consumption and the throughput of relay networks as a function of the transmit power. We determine the conditions in which wireless communication using a relay has better energy efficiency or bandwidth efficiency than direct transmission.