This paper investigates a novel communication paradigm employing movable antennas (MAs) within a multiple-input single-output (MISO) non-orthogonal multiple access (NOMA) downlink framework, where users are equipped with MAs. Initially, leveraging the far-field response, we delineate the channel characteristics concerning both the power allocation coefficient and positions of MAs. Subsequently, we endeavor to maximize the channel capacity by jointly optimizing power allocation and antenna positions. To tackle the resultant non-convex problem, we propose an alternating optimization (AO) scheme underpinned by successive convex approximation (SCA) to converge towards a stationary point. Through numerical simulations, our findings substantiate the superiority of the MA-assisted NOMA system over both orthogonal multiple access (OMA) and conventional NOMA configurations in terms of average sum rate and outage probability.