A new road is to be built through the Himalayan mountains to the ancient valley of Zarksa. The road will provide access to the valley for tourists, who currently have to travel on mules in a journey...

A new road is to be built through the Himalayan mountains to the ancient valley of Zarksa. The road will provide access to the valley for tourists, who currently have to travel on mules in a journey that can take up to five days. At some point the road will have to cross the river Yeli and a bridge will be built for this purpose. However, the road builders have yet to decide on the exact location where the road will cross the river. Two options are being considered: Yeli Gorge and Bana.

If the Yeli Gorge location is chosen it is provisionally estimated that there is a 0.6 probability that the geological conditions will be favorable to the bridge construction and the construction costs will be $40 million. However, should the geological conditions prove unfavorable, the construction costs will soar to $70 million. There is no doubt about the geology at the Bana site and it can be assumed that a bridge built here will be certain to cost $50 million. Before making the decision on the bridge location, the road builders hear that a specialist firm of geologists will carry out a detailed survey of Yeli Gorge and report on whether the conditions are favorable or unfavorable. However, their methods are not perfectly accurate and only have an estimated 75% probability of giving a correct indication.

(a) Assuming that the road builders want to minimize expected costs determine the expected value of the imperfect information from their survey and interpret your result.

(b) If the geologists’ survey was certain to give a correct indication, what would be the value of the information from the survey?