We consider rate allocation for video users in the case where the available bandwidth fluctuates. Simply minimizing the objective distortion or optimizing the stability of video qualities does not optimize subjective quality. We formulate a utility-based solution, considering that a user's preference of video quality often varies over a range with upper and lower thresholds of quality. Our iterative pricing-based resource allocation procedure reallocates the bandwidth not only between different users within a time slot but also between different time slots, such that no user suffers quality degradation on average by participating in the multiplexing process. Experimental results show that, compared with equal resource allocation and existing rate allocation solutions, the subjective result becomes increasingly better with the increase of bandwidth fluctuation rate or bandwidth fluctuation range. Moreover, as the number of users increases, the results improve.