That is not due to work shortage - but due to shortage of work that can be done by socialistic, highly (unproductively) unionized and unqualified work-force.
Eastern Germany will stay like that until the workforce that was raised in socialism gets out of the way. Eastern Germany has more in common with Poland, Czech and Slovakia than with western Germany and France.
I'm from ex-socialist country and it is the same situation here - plenty of high value added opportunities are available - but nobody to take advantage of them.