18 gauge wire from battery

Fellas, I feel like I need to explain this better... based on the following assumptions:
I assume this is a typical aftermarket radio, and typical aftermarket radio wiring. (Kenwood, JVC, Sony, Alpine, Pioneer, Clarion, Jensen, Dual, Blaupunkt, Soundstream, et al)
I assume the speakers are being driven by the radio, not an external amplifier.
If these assumptions are correct, there will be a yellow wire for constant power, and a red wire for switched power coming out of the radio.
ALL aftermarket radios use the YELLOW wire to provide the current for the internal amplifier that drives the speakers. This wire also provides a constant power for the memory functions, and the ability to operate certain functions when the key is off. (Ejecting a CD for example)
This means that the yellow wire will need at least a 10A fuse to properly power the radios internal amplifier. The yellow wire is NEVER just for memory functions. You can prove this for yourself if you connect an ohm meter from the yellow wire to the radios chassis mounted main 10A fuse. If you put a 2 or 5 amp fuse in this lead, the draw from the internal amp will blow it.
The RED wire is simply used to turn the radio on and off with the vehicles ignition, and is a low current draw connection. (less than 1 amp)

I'm absolutely certain of the above statements, if the stated assumptions are true. Engineering audio products is what I do for a living, and I test dozens of radios every year.