Is it possible for there to be a shortage of labour in an economy when there is cost-push inflation?
The definition of cost-push inflation is an increase in aggregate prices driven by an increase in the cost of labour and/or production inputs.
A shortage of labour could put upward pressure on wages, yielding this type of inflation. So, yes, it is possible. However, it is not necessarily true that cost-push inflation is caused by a labour shortage and it is also not true that a labour shortage will always cause cost-push inflation.