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Tutorial 8 Globogym has a monopoly over the market for personal training and faces a demand curve modelled as P = 400 0.2:}I where P is the price of a training session and Q is the number of Sessions provided. Their total cost function is given by TC = 1000 + 40!). 3.1 Is Globogym a natural monopoly in this scenario? Justify your answer carefully. What does this suggest about the number of rms in this market? [4] 3.2 What are the prot-maximizing price and quantity of sessions in this market? Show all your calculations. How much prot does the company make in equilibrium? [6] Let's assume that the Average Joe's gym enters the market as a competitor providing personal training sessions. In the rst year of operations, Globogym and Average Joe's made their decisions about pricing simultaneously. Each firm chooses either pricing high or pricing low, and their interaction is represented in the game table below. The payoff to Globogym is represented in the table by In, and the payoff to Neotel is represented by It}. Average Joe' s 3.3 Do either of the two telecommunications rms have a dominant strategy in this interaction? If so, what are these dominant strategies? [2] 3.4 What is the Nash Equilibrium of the game above? Clearly, show the logic you use to reach your conclusion. What type of game is this? [4] 3.5 Suppose the two rms could incentivize or punish each other, could the two rms nd their way to the socially optimum outcome? How would they do this? [4] After observing the strategic interaction between Glohogym and Average Joe's. the government decides to pass a law that states that the two terms must pre-commit to the quantities of training sessions they will supply to the South African market