Two social media platforms control the targeted advertisement business. The market demand for their ads is () = 180 6 and they each have the cost function () = 4 where = {1,2}. a. [8] Initially, the two firms compete on quantity. Find the Cournot-Nash equilibrium price and output of each firm. How much profit does each firm earn? b. [8] Suppose that the two firms decide to form a cartel. What will the firms' profits be under a collusive arrangement (assume that they split the joint profit evenly)? Why are their profits different than in part (a)? c. [4] Is the cartel a stable arrangement in a one period interaction? Show supporting calculations. Hint: Consider the profit maximizing output of one of the firms if its competitor produces the cartel output