Two social media platforms control the targeted advertisement business. The market demand for their ads is...

 

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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? 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?

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Lets tackle each part of the problem step by step Question 1 CournotNash Equilibrium a To find the C... View the full answer