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SUGGESTED ANSWERS TO SPECIMEN EXAMINATION PAPER 1 Question 1 a) Swing weights are: DISTANCE: 100, PARKING: 30, RESIDENTS: 55 ACCESSIBILITY: 15 so normalized weights are: DISTANCE: 0.5, PARKING: 0.15, RESIDENTS: 0.275 ACCESSIBILITY: 0.075 So Hodge Street score = (0.5 × 100) + (0.15 × 0) + (0.275 × 20) + (0.075 × 10) = 56.25 b) 0 10 20 30 40 50 60 70 80 0 50 100 150 Costs \$m Aggregate benefit score Lakeside Hodge St Egbert Heath Jones St The Causeway Lakeside and Jones Street are on the efficient frontier. c) Assuming a linear trade-off between costs and the aggregate benefits score: Swing Extra cost Extra Cost/benefit point \$m benefits \$m Jones St to Lakeside 35 35.5 0.99 The board is prepared to pay \$1.20 million for each extra benefit point so they should choose Lakeside. 1

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d) Because swing weights also reflect the differences between the worst and best performances on each attribute. Probably all of the sites had very similar levels of accessibility – so although accessibility per se was important, it had little importance in discriminating between the sites. Question 2 a) See decision tree on the following page: the company should choose the low price and, if there is a competitor, it should respond by advertising the product on television. b) -1 -0.5 0 0.5 1 1.5 2 00 . 20 . 40 . 60 . 8 p (competition if low price chosen) Profit \$m Low price High price 1 If p (competition if low price chosen) exceeds about 0.38 then the high price should be chosen. This assumes that the probability of competition at the high price remains unchanged. c) Utilities would allow i) the attitude to risk of the decision maker to be taken into account and ii) (if multi-attribute utilities are used) other objectives to be addressed in addition to profit. However: – elicited utilities are sensitive to the way questions are framed (e.g. risk averse responses are often derived from lottery questions involving gains, risk seeking responses, when losses are involved); – it is difficult to establish a utility function for a group of decision makers as this involves interpersonal comparisons of strength of preference; 2
Decision tree for question 2 0.4 Profits High sales \$m 1 Advertise 1 –0.8 0.6 Low sales 0.1 –2 Competitor –2 1 –0.8 0.7 High sales 0 Lower price 0 Low price –0.9 0.3

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