Capacity and Entry Deterrence under Asymmetric Information on Demand

I consider a two period model with an incumbent firm and a potential entrant each of whom produces a homogeneous good. There is a demand uncertainty and the information regarding the demand is asymmetric: the incumbent possesses private information concerning the state of demand while the entrant only knows the probability distribution. I show that under certain cost structure of the incumbent (which is common knowledge), using capaciy as a signalling device, the incumbent can reliably convey the information to the potential entrant regarding the state of demand; while in some other cost environment such a signalling has no effect. Outcomes are more desirable where signalling truly reveals and more importantly convince the entrant about the true state of demand compared to those where signalling does not reveal.