MICROECONOMICS

Question 3 [19 marks) Beta and Alpha, the brick manufacturing companies in Namaniland, should decide whether to invest in the production of new brick-making technology. Both companies must make huge expenditures to construct a production plant for new brick-making technology. The payoffs that each company gets when it enters and decides to produce either high or low output bricks are given below. Consider in the game that Yht]. Aipha High output Low output High output 120; 120 10; 150 Beta Low output 70+Y; 7UY 30; 30 a) Determine the values of onr which both companies have a dominant strategy. Find the Nash equilibrium. (4 marks) b) Determine the values of Y for which only a single company has a dominant strategy. Find the Nash equilibrium. (3 marks) c)Without using mixed strategies. what are the values of Y such that neither company has a dominant strategy nor states the Nash equilibrium? (2 marks) d) Suppose the market demand for the two companies is given by P = 120 Q and the marginal cost is R20. Construct a payoff matrix where the strategies available to each of the companies are to produce the IGournot equilibrium quantity or half the monopoly quantity. Determine the Nash equilibrium. {10 marks}