The major roles of a prototype sodium-cooled fast reactor (SFR) planned to be developed at the Korea Atomic Energy Research Institute are (a) to provide an irradiation test capability for fuel and structural materials and (b) to obtain operational experience on the systems and components. The power level of the prototype SFR should be large enough to provide an appropriate irradiation test environment. Trade-off studies were therefore performed from a neutronics viewpoint to determine the power level. Specifically, core designs were performed for power levels of 125, 250, 400, and 500 MW(thermal). The selected core performance and economic efficiency indices became insensitive to the power at [approximately]400 to 500 MW(thermal) and sharply deteriorated at [approximately]125 to 250 MW(thermal) with decreasing core sizes. For the fuel management scheme, the transuranic (TRU) core performance compared with that of the uranium core, and the sodium void reactivity, were also evaluated with increasing power levels. It was found that increasing the number of batches shows a higher-burnup performance and economic efficiency. However, increasing the cycle length resulted in a lower economic efficiency. The irradiation performance of TRU and enriched TRU cores was improved by [approximately]20% and 50%, respectively. A maximum sodium void reactivity of 5.2 $ was confirmed as less than the design limit of 7.5 $. As a conclusion of our entire study, the power capacity of the prototype SFR should not be <250 MW(thermal), and would be appropriate at [approximately]500 MW(thermal) considering the performance and economic efficiency.