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.
Generally speaking, a cost-push inflation is defined as an increase in the general price level caused by an increase in the production costs of a firm (or, in case we analize the general macroeconomic context, in the production costs of all the firms) that is charged to the consumer.As it is explained above, the labor shortage enters the game in the sense that this fact puts an upward pressure to wages and then to prices, since the firms - in order to keep their profit margin at least constant - have to raise prices to cover the increase in wages