4. Consider a market where there are only two producers (a duopoly). First producers cost function is 24+ y and the second producers cost function is: 24+ y2. They face a demand p=120-y.y1 and y2 are output levels for the individual producers and y is the combined output of both producers. a) Assume the two agents do not co-operate. What are their level of output, price and profits. (3 marks) b) Suppose that now they form a cartel and work together. What are their level of output, price and profits. (3 marks) 2 c) Repeat part b) this time assuming that producer two produces the output agreed upon in part b) but producer one secretly breaks the agreement (cheats) and chooses the optimal level of output independently. (2 marks) d) Present results from parts a), b) and c) as a normal form game (the payoff matrix), what are the dominant and dominated strategies for both players, what is the Nash equilibrium? (2 marks) e) Do the above results suggest a need to regulate cartels? If yes, why? If not, why not? How would you change the underlying framework of the question to necessitate regulation of cartels? (8 marks)