This is a misconception similar to how people thought computerization will cause shortage of jobs back in the 70s. Automation will not cause shortage of jobs. It might cause shortage of obsolete jobs but new jobs for design, service, management will always pop-up.Lol no, they definitely will not face shortage of labour, especially with how much automatiom is ongoing.
Also, going down to 1 billion really isn't all that bad, especially if it can somewhat sustained.