Two social media platforms control the targeted advertisement business. The market demand for their ads is Q(P) = 180 - 6P and they each have the cost function c(qi) = 4qi where i = {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. 2. [14] Two gas stations are located side-by-side. As is customary in the industry, they are competing on price (they both have enormous signs advertising their selling price for a litre of gasoline on the roadside). Station 1 has the cost function C(q) = 4q and station 2 has the cost function C(q) = 5q2 where q and q are the number of litres sold by station 1 and station 2, respectively. The market demand for gasoline is Q (p) = 50-p where Q = 91 + 92 a. [4] Write the demand functions of the two firms. b. [4] Are the two firms selling their gas at $5 per liter a Bertrand-Nash equilibrium? Explain why or why not. c. [6] Characterize a Bertrand-Nash equilibrium. How many litres of gas will each firm sell in this equilibrium?