Movable antennas (MAs) have recently garnered significant attention in wireless communications due to their capability to reshape wireless channels via local antenna movement within a confined region. However, to achieve accurate antenna movement, MA drivers introduce non-negligible mechanical power consumption, rendering energy efficiency (EE) optimization more critical compared to conventional fixed-position antenna (FPA) systems. To address this problem, we develop in this paper a fundamental power consumption model for stepper motor-driven MA systems by resorting to basic electric motor theory. Based on this model, we formulate an EE maximization problem by jointly optimizing an MA's position, moving speed, and transmit power. However, this problem is difficult to solve optimally due to the intricate relationship between the mechanical power consumption and the design variables. To tackle this issue, we first uncover a hidden monotonicity of the EE performance with respect to the MA's moving speed. Then, we apply the Dinkelbach algorithm to obtain the optimal transmit power in a semi-closed form for any given MA position, followed by an enumeration to determine the optimal MA position. Numerical results demonstrate that despite the additional mechanical power consumption, the MA system can outperform the conventional FPA system in terms of EE.