In this paper, we study the resource allocation algorithm design for a multiuser communication system assisted by an active intelligent reflecting surface (IRS). In particular, supported by a power source, each active IRS element can adjust the phase and amplify the magnitude of the incident signal. To realize power-efficient communication, the proposed design incorporates two conflicting yet desirable objectives, i.e., access point (AP) transmit power minimization and active IRS amplification power minimization, via a multi-objective optimization problem (MOOP). In the literature, systematic algorithms that can efficiently tackle such a non-convex MOOP while preserving joint optimality are not available. To this end, we propose a state-of-the-art optimization framework by capitalizing on bilinear transformation, ϵ-constraint, and inner approximation methods. Simulation results not only reveal the power consumption tradeoff between the AP and the active IRS, but also confirm that the proposed scheme is more power-efficient than four baseline schemes.