There are two companies in the market. Firm A has the advantage of being able to select profit$-$maximizing output before firm B$.$ The inverse demand function of the market is P $=500-2$Q$.$ And firm A$\text{'}$s cost function is C$($a$)=2$Qa$,$ and firm B$\text{'}$s cost function is C$($b$)=4$Qb$.$

Instead of considering antitrust matters, explain whether it would be beneficial if Firm A and Firm B merged. If it would not be beneficial, give why and specifically give how much it would be beneficial if it would be beneficial.