Both spectral efficiency (SE) and energy efficiency (EE) are key performance evaluation metrics in the wireless communication systems, however, they are always conflicting with each other. Therefore, recent works shift their main focus on how to achieve an EE-SE trade-off. In this paper, the EE-SE trade-off problem in downlink large-scale MIMO systems is investigated, which is formulated as Pareto optimal set based multiple objective optimization problem with respect to the transmit power and the number of available antennas at the base station (BS). Then with the help of Cobb-Douglas production model in economics, a unified EE-SE trade-off metric is derived to convert the multi-objective optimization problem into a single-objective one. Furthermore, it is theoretically proved that the EE-SE trade-off metric can be maximized by optimizing the transmit power and the number of available antennas in the downlink large-scale MIMO systems. Simulation results validate that it is flexible to achieve the EE-SE trade-off with different priority levels. (C) 2017 Published by Elsevier Ltd.