Automation leads to population shrinkage?

The video below has got me thinking. In a world with tons of automation, the only reasonable thing to happen, imo, is to decrease the number pf people that we have sitting around. A fully automated world can't give us enough jobs to support our current numbers. For a while at least, the efficiency that automation brings can be used to gain economic superiority over other countries, I suppose, but that will only be useful for so long. What would a future with so few jobs look like? Would we have to restructure out entire economy in order to help the "working class" that can no longer work?