In an industry with two firms, represent the output for these single product firms as q1 q2. the two firms decide to form a cartel and set their level of output to maximise total profits for the industry. consider the situation where the industry inverse demand function curve which the two firms face is:
demand function P=25-2Q

where Q is output of the who firms. firms have different cost structures.
firm 1: C1=Q1
firm 2: 0.25Q^2 (2 at the bottom of Q and also to the power of 2)

determine profit maximising cartel, amount of profit earned, output and profit share for each firm. ensure you have found maximum by deriving the second order sufficent conditions.