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1 SUGGESTED ANSWERS TO SPECIMEN EXAMINATION PAPER 2 Question 1 a) Heraton Attendance Rev (\$) Cost (\$) Profit (\$) Prob. 50 15 000 19 000 –4 000 0.2 100 30 000 24 000 6 000 0.5 150 45 000 29 000 16 000 0.3 EMV \$7000 Atlantic Attendance Rev (\$) Cost (\$) Profit (\$) Prob. 60 18 000 17 200 800 0.4 100 30 000 22 000 8 000 0.5 140 42 000 26 800 15 200 0.1 EMV \$5840 So the Heraton venue maximizes expected profit. b) Typical reservations: – The EMV criterion ignores the attitude to risk of the decision makers and applies a ‘long run average’ payoff to a one-off decision. – The EMV criterion ignores non-monetary attributes, such as the quality of facilities and comfort of the venues. – The probability distributions are estimates and subject to biases emanating from the use of heuristics like anchoring and adjustment and availability. – Three point probability distributions can only approximate the ‘real’ probability distributions. c) i) Profit (\$) Utility –4 000 0 800 0.6 6 000 0.88 8 000 0.92 15 200 0.99 16 000 1 (see next page)

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2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -5000 0 5000 10000 15000 20000 Profit \$ Utility The utility function indicates risk aversion ii) Consider the fact that the decision maker is ‘indifferent between earning a profit of \$15 200 for certain and taking a gamble which had a 0.99 probability of yielding a profit of \$16 000 and a 0.01 probability of yielding a loss of \$4000.’ If the probability of winning the gamble was 0.933, then its expected value would be equal to the certain sum on offer, \$15 200. Hence a risk-neutral decision maker would be indifferent between the certain money and the gamble at this probability. However, the Academy's treasurer requires a probability of winning the gamble of 0.99 before he/she is indifferent, indicating risk aversion. Similar arguments apply to the other statements made by the treasurer. d) Heraton Attendance Profit (\$) Utility Prob. 50 –4 000 0 0.2 100 6 000 0.88 0.5 150 16 000 1 0.3 Exp utility= 0.74 Atlantic Attendance Profit (\$) Utility Prob. 60 800 0.6 0.4 100 8 000 0.92 0.5 140 15 200 0.99 0.1 Exp utility= 0.80 Thus the treasurer should prefer Atlantic University, the least risky option.
3 e) – it is difficult to obtain a utility function for a group of decision makers like the directors of the Academy; – elicited utilities are sensitive to the framing of questions – questions framed in terms of gains tend to lead to risk averse responses, those framed as losses tend to lead to risk seeking responses; – utility elicitation takes the decision maker from the real decision to a world of hypothetical gambles. Preferences expressed in relation to these gambles may not apply when the real decision is faced. Question 2

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