Corporal punishment for certain offences would actually be far less costly, in economic and social terms, and far less inhumane than prison.
For example, take the situation of a man, the sole support of his family, who steals a stereo.
Put him in prison and you not only risk throwing his family on to the welfare rolls, but you also send him to the best training ground for future criminals.
Give him a flogging and you can send him back to work to pay restitution and support his family the next day.
Property criminals who reoffend should be isolated from society in a "criminals only" zone, from which no escape is possible and into which no resources are put except erecting and maintaining the fence.
This sounds like something similar to a gulag, without the routine barbarism of the administration and the political prisoners. Northern Alaska sounds like a perfect place for it.
Someone stealing a stereo isn't likely to be holding down a job or being responsible to his family any way and most likely they're already living on welfare --- someone like that should be in prison but shouldn't be placed with the extremely violent population.