When a parallel external magnetic field is applied to underdamped Josephson-junction arrays, constant-voltage steps appear in their current-voltage characteristics. These steps correspond to different numbers of rows being switched to a new resonant state. If the number of switched rows is larger then a threshold number, the array radiates coherent microwave radiation. When the array is biased on a step, the number of radiating rows stays fixed and we can change the input power, P-DC, by changing the bias current. We measure the output power, P-AC, as a function of P-DC This dependence is linear at high powers with a slope alpha, while at low powers P-AC vanishes nonlinearly with P-DC. For a given array, the slope a is larger for steps that correspond to a larger number of switched rows. We present a systematic study of the dependence of the slope a on the size of the array and discuss its implications for obtaining optimal DC-to-AC conversion efficiency.