"The rich should live simply" implies that rich people should not use luxuries which they normally use.
"so that poor people can simply live" means that if the rich lives simply, the poor people will be able to thrive
But in my opinion this is not a logical solution to poverty. If rich people don't use luxuries, the market for luxury goods like foreign holiday, decorations etc. would be non-existent. And since it is the poor people who, in turn, works in the luxury goods' industry, poor people would be unable to find that much employment.