In this work, we consider the downlink of a multi-cell multiple-input multiple-output (MIMO) system and find the jointly optimal number of base station (BS) antennas and transmission powers that minimize the power consumption while satisfying each user's effective signal-to-interference-and-noise-ratio (SINR) constraint and the BSs' power constraints. Different from prior work, we consider a power consumption model that takes both transmitted and hardware-consumed power into account. We formulate the joint optimization problem for both single-cell and multi-cell systems. Closed-form expressions for the optimal number of BS antennas and transmission powers are derived for the single-cell case. The analysis for the multi-cell case reveals that increasing the number of BS antennas in any cell always improves the performance of the overall system in terms of both feasibility and total radiated power. A key contribution of this work is to show that the joint optimization problem can be relaxed as a geometric programming problem that can be solved efficiently. The solution can be utilized in practice to turn on and off antennas depending on the traffic load variations. Substantial power savings are demonstrated by simulation.