A 50 kW carrier is to be modulated to a level of 85%. What is the carrier power after modulation?
Assuming plain old amplitude modulation, the average power will just stay constant regardless of modulation index unless the transmitter experiences nonlinearities (e.g. clipping). The transmitter will transmit at 50 kW + 50 kW * 85% = 92.5 kW during positive peaks of the signal and at 50 kW - 50 kW * 85% = 7.5 kW during negative peaks, but it averages out in the long run to 50 kW.  

Double sideband suppressed carrier and single sideband transmitters are a different story, as the power output does change with the modulation index in those cases.