50W Amp for 15W Speaker
That has been a subject of debate for decades. Should the speakers be overrated or the amplifier?


If the speakers are overrated the amplifier might be strained at high volume levels and produce distortion (clipping) that not only sounds bad, it is bad for the speakers as they faithfully try to reproduce the distortion.
If the amplifier is overrated (but not by an outrageous amount like 10:1), then you get clean sound until the speakers reach their limit. The woofers may pop against their frame and the sound becomes distorted. This is a warning to back off the sound level or risk burning up a speaker.
Because there is seldom anything like a perfect match between speaker wattage ratings and that of the amplifier, the better match is to have an amplifier that is a little over rated, and be careful with the volume control. This way the amp is never strained or distorted, giving you clean sound up to the maximum volume the speaker can handle.
It is easy to burn up 15 watt speakers, but they are often very efficient and will be very loud at a safe maximum volume. A 50 watt amplifier will drive these speakers with ease and not distort from working too hard.


EDIT: For better mechanical range of the volume control, look for a gain adjust control on the amp or buy 2 RCA attenuators from most any stereo installation shop(car or home). Ones with -3db rating will cut signal level to 70.7%. Those with a -6db rating will cut sound level by 50%. Any of these options will allow you to use more of the mechanical 'rotation degrees' of the volume control before you reach the limit of the speakers. (To avoid confusion, I am referring to signal level, not power levels.)