# However in determining mr there is an important

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MC. However, in determining MR, there is an important difference related to how the output of the other firm is treated. State this difference and explain why it makes sense. (4 pts). 3. Consider a game in the Canadian airline industry. A particular route is currently served by incumbent Air Canada (AC). WestJet (WJ) is considering entering the route. If WJ enters AC has two possible strategies at its disposal: Fight the entry, or Accommodate (the entrant). WJ has the option to enter or not enter the route. Dollar numbers are in thousands of dollars per week. In the absence of competition, AC makes monopoly profits of 150. If WJ enters and AC accommodates (by maintaining price and sharing the market), then AC earns 100 and WJ earns 80. If WJ enters and AC decides to fight, then AC makes 70 and WJ suffers a loss of 20. a) Construct a game tree representing this situation and indicate clearly the outcome predicted by game theory. (4 pts)

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11 b) Now assume that to deter entry, AC buys an additional aircraft and threatens WJ with a price war in case of entry. This new purchase reduces AC's profits by 40 in all situations except when it fights the entry. Assuming that WJ can foresee this situation before it makes its entry decision, redraw the game tree for this new situation and identify the sequential Nash equilibrium outcome. Use your results from parts (a) and (b) to briefly explain the statement: “commitment makes a threat credible”. (7 pts) c) Suppose AC hears a rumor that WJ likes to take on risk and will enter the market with probability p even if it is not profitable to do so. However, WJ will always enter if it can profit from doing so. For what range of values of p will AC not invest in the additional fleet and thus not threaten a price war? (4 pts) 4. A manager must choose one of four advertising strategies, with the following characteristics. Strategy Return with Bad Luck Probability of Bad Luck Return with Good Luck Probability of Good Luck A 3 0.7 10 0.3 B 4 0.6 7 0.4 C 1 0.2 6 0.8 D 2 0.5 10 0.5 a) Calculate the expected return and the standard deviation of the return for each of the four strategies. (Use a spreadsheet for these calculations). (4 pts) b) Assume the decision maker cares only about the expected value and about the risk as measured by variance (or standard deviation) and is risk averse. Can you say which project would be chosen? Can we eliminate any of the projects from consideration? Explain briefly. (4 pts) c) Now suppose you are told that the decision maker is risk averse and has a utility function over income with the following values: U(0) = 0; U(2) = 6; U(6) = 12; U(10) = 14. You are also told that the utility function is a smooth function. Draw a diagram illustrating the utility function by showing the four points just given and then connecting these points. Also show the risk premium associated with strategy D. You will not be able to calculate this risk premium. Just show it on the diagram. Put numerical values on the axes corresponding to the information given. Determine the expected utility associated with Strategy D and show it on the diagram (7 pts)
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