I have read about cats that if you need a mouser you should not worry about feeding it too much. Cats will catch mice even if well fed. Feeding it too little means it will start to scout for food far away from your place, thus catching mice elsewhere.
Domestic cats are somewhat unique in that they don't exhibit contra-freeloading. That is they prefer not to work to working. I guess they consider catching mice "play". :-)
Completely true. Our girl cat was a killing machine. Multiple gophers each weekend -- always presented them as presents. But she loves to eat and takes advantage of the fact the other cat doesn't eat as much. She's a pudgeball now and hasn't caught much in awhile (some of that is due to age...).