You first need to establish the benefits function B. For each firm it is equal to the amount produced (q1 for firm 1 and q2 for firm 2) multiplied by the price P, minus cost C. It is
B1 = P.q1 - C1 = (69 - q1 - q2)q1 - C1
B2= P.q2 - C2 = (69 - q1 - q2)q2 - C2
As firma Will maximize benefits we need the derivative in q1 and q2 for firms 1 and 2 respectively. This will give us
69 - 2q1 - q2 = 0
69 - q1 - 2q2 = 0
Note that the derivative of cost is null as marginal cost is null.
Thus,
q2= 69 - 2q1
Replacing on the second equation:
69- q1 - 138 + 4q1 = 0
-69 + 3q1= 0
q1= 69/3=23
Replacing in the q2 equation:
q2=69- 46= 23
To find the money they make replace in benefits function. First we find piece P=69-23-23=23. Thus:
B1=23*23-C1
B2=23*23-C2
As we don't have a value for C1 and C2 we can't compute a number for benefits. If you have these values you will have the benefits.
