solve $in$ detail and explain fully

Question $6$:

Consider a homogenous product duopoly $in$ which the two firms, $1$ and $2,$ compete $by$ choosing

their respective quantities, $Q_1$ and $Q_2.$ Market demand $is$ given $byP=100-Q,$ where $Pis$ the

market price per unit and $Q=Q_1+Q_2.$ Firm $2\text{'}s$ total costs are given $byT{C}_2=200+Q_2,$

while firm $l\text{'}s$ total costs are $T{C}_1=100+2Q_1.$

$(a)To$ which firm would the ability $to$ move first $be$ most valuable?

$(b)Is$ there $an$ incentive for the two firms $to$ merge $to$ form a monopoly? Explain fully.

$(c)$ Would a government wish $to$ set policy $to$ block such a merger? Explain fully.