Problem #1 (20 points)
The board of directors of Tolford sports club are searching for a location for their new stadium and they are using the Simple Multiattribute Rating Technique (SMART) to help them with their decision. Five possible sites are being considered and the decision between them will be based on five attributes: (i) the COST of developing the site; (ii) the DISTANCE of the site from downtown Tolford; (iii) the amount of space for car PARKING; (iv) the extent to which choosing the site would cause inconvenience for local RESIDENTS; and (v) the ACCESSIBILITY of the site from the highway network.
The board has assigned scores for each site to measure its performance on the non-monetary attributes. These are shown below, together with the development costs of the sites (note that 0 is the score for the worst site on a given attribute and 100 a score for the best site on that attribute).
| Site | Distance | Parking | Residents | Accessibility | Cost($m) |
| Egbert Heath | 10 | 100 | 70 | 50 | 80 |
| Lakeside | 40 | 80 | 100 | 100 | 65 |
| Jones Street | 60 | 10 | 0 | 0 | 30 |
| The Causeway | 0 | 60 | 40 | 60 | 100 |
| Hodge Street | 100 | 0 | 20 | 10 | 75 |
The board then considered a hypothetical site that had the worst performance on all the non-monetary attributes. They were then asked, if they could make just one improvement to this site so that it was as good as the best site on this attribute, which improvement would they make? They agreed that they would most prefer to “improve” the DISTANCE from downtown Tolford. Similar improvements in relation to the attributes PARKING, RESIDENTS and ACCESSIBILTY were thought to be, respectively, 30%, 55% and 15% as important as this. It can be assumed that the attributes are mutually preference independent.
(a)The aggregate scores of the first four sites in the above table for the non-monetary attributes are shown below:
| Site | Aggregate
Score |
| Egbert Heath
Lakeside Jones Street The Causeway |
43.0
67.0 31.5 24.5 |
Calculate the score for the Hodge Street site.
(b)Determine the sites which lie on the efficient frontier, when the development costs are brought into consideration, and explain how you arrived at your answer.
(c)The board would be prepared to pay $18 million to improve the space for PARKING from that equivalent to the worst site for parking to that equivalent to the best, all else remaining equal. Stating any assumptions you have made, determine which site they should select.
(d)The attribute that the board considered to be most important was assigned the lowest weight in the analysis. Explain why the decision model might still accurately reflect the board’s preferences.
Problem #2 (20 points)
A unit trust fund manager has to make regular assessments of the future performance of share prices, both in general, and in relation to particular companies.
(a)Discuss how the fund manager might use the following heuristics in making the assessments:
(i)Availability
(ii)Representativeness
(iii)Anchoring and adjustment
(b)Discuss the biases that might arise from the use of each heuristic.
(c)Tversky and Kahneman have carried out the most widely cited research into heuristics and biases in human judgment under uncertainty. To what extent does their research provide evidence of the widespread occurrence of biased judgments by decision makers like the fund manager?
Problem #3 (20 points)
The BAC Import Company has decided to market Z-games in the USA. The game, an electronic device the size of a mobile phone, has been a great success in Japan. However, sales of the game in the USA are not expected to last for more than a year; after this period the novelty of the game is likely to have subsided. For simplicity, potential sales levels are categorized as being either high or low. BAC has an initial decision on what price it should charge for the game and two prices are being considered: a low price ($4) and a high price ($8). The table below shows the estimated profits that would be achieved for each price and sales level.
| Sales Level | (Profits) | ||
| High | Low | ||
| Low price
High price |
$2 m
$4 m |
-$1m
$1m |
|
If the low price is chosen it is thought that there is only a 0.1 probability that a competitor will enter the market. If there is no competitor then it is thought that the chances of high sales will be 0.9. However, if there is competition then BAC will have to decide whether to respond by either advertising on television or lowering the price even further. Advertising would lower profits by $1m, but would give an estimated 0.4 probability of high sales. Lowering the price would reduce profits by $2m, but would give a 0.7 probability of high sales. (Only one of these two responses to competition would be used).
If the high price is chosen then the probability of competition is estimated to be 0.8. In the absence of competition it is thought that there would be a 0.5 probability of high sales. If there is competition then either advertising on television or lowering the price would be carried out, as above. These would have estimated probabilities of generating high sales of 0.1 and 0.3, respectively. (These two responses would have the same effect on profits as before.)
(a)Assuming that BAC’s objective is to maximize expected profit, identify the policy that the company should adopt.
(b)Determine how sensitive your recommended policy is to changes in the estimated probability of competition when a low price is initially chosen.
(c)Discuss whether the use of utilities, rather than profits, would have improved your decision model.
