$1.$ Maintaining monopoly power: entry deterrence $$vs$$ buyout Consider the market for a homogeneous good with demand given by P$($Q$)=344$Q$.$ Let there be a single incumbent firm $($I$)$ in the market and a single potential entrant $($E$).$ Each firm i $=$ I or E has access to the same technology characterised by cost function Ci$($qi$)=2$qi $+$ F$,$ with $2<$ F $<16($the constraint $2<$ F ensures that entry deterrence is preferred to accommodation and F $<16$ ensures that both firms can reap positive profits under Stackelberg competition$).$ Find the stackelberg equilibrium and then show steps to find the the minimum quantity that the incumbent needs to produce to keep the entrant out of the market $($the limit quantity$)?$