Simple answer: Merges are (almost) always good for the producers in IO-models. In this simple model you face a Stackelberg game to be solved by backward induction. For BS the output of MS is given. Thus:
If you optimize this profitfunction for the output of BS you have this company's optimal outputlevel ( ) with respect to what MS has chosen. Using this outputlevel (MS will antizipate this level, too.) you can now optimize the MS profits:
Now you know what both Q will be and therefore what the total Q will be. This will yield both companies profits. You will see that the sum of both profits is lower then the profit in a monopoly and therefore a merge would be profitable.