The main purpose of this paper is to provide theoretic insights into capacity and resource allocation for the downlink of the multicarrier system. Throughout the paper, our objective is to maximize the total throughput (bits/sec/hertz). We assume that multiple users may simultaneously access a subcarrier with the code division multiple access. We show that the user with the best channel gain should be always assigned the corresponding carrier. Further, we quantify the conditions under which either single-user or multiple-user occupancy of a carrier is optimal. For the single-user case, the so called water-filling downlink power allocation is required. On the other hand, for the multiple-user case, careful consideration is needed in selecting users and powers. The optimal resource allocation improves the throughput, for which we also suggest sub-optimal algorithms of a lower complexity. However, our general conclusion is that the single-user transmission together with the equal-power allocation is still a good strategy.