trouble resolving efficient value of x
I've got a problem where I have two firms, i and j both cooperating in performing r&d. The level of r&d expenditure for each firm is given by xi and xj and is symmetric as the two firms have the same cost function - if you can find xi, then the same result is valid for xj. Where I'm having trouble is finding the collusive result - what is the combined level of r&d?
As you can see, what I've tried to do is return to the original profit function and get it all in terms of one x but something is going wrong.
I have the answer from the textbook (see the bottom of attached document), but can't manage to reach it - if someone could help me with the working I would be very much in their debt.