In this paper, we investigate the capacity region of a multiuser shared channel with time-varying transmission power, whose typical examples are the Forward Packet Data Channel (F-PDCH) of, IS-2000 1xEV-DV system and the High Speed Downlink Shared Channel (HS-DSCH) in 3GPP High Speed Downlink Packet Access. (HSDPA) system. The concavity of the throughput yields the property that additional power contributes more to a weaker user having a lower channel gain than to a stronger user. Noting this property, we consider a power-balanced policy which tries to balance the received SNR of each user by serving a weaker user with higher transmission power. Then, we establish the equivalence of the power-balanced policy and the Pareto optimal policy which yields a throughput vector at the boundary of the capacity region. This enables to characterize the capacity region explicitly, and also renders an easy means to maximize the total throughput while meeting each user's requirement.