It's better to feed one cat than many mice

"It's better to feed one cat than many mice." ---Norwegian Proverb

Please explain the meaning.

The mice referred to are not pet mice but pest mice. It is worth having a pet cat to avoid a rodent infestation.

Yes, it means, I think, that it is sometimes necessary to make some small expenditure (on keeping a cat) in order to avoid a much larger one (dealing with a plague of mice) in the future.

DFG