A treaty between the United States and Canada guarantees that one-third of the water in the Niagara River should f low over the falls. One-third can be removed from the river to generate hydro-electric power by Canada and another third by the United States. Until 2013, Canada had a canal and a tunnel for extracting water upstream of the falls and taking it to two generating stations downstream. A second tunnel was completed in 2013, increasing the water supply to the power stations. Put yourself in the position of a decision maker during the planning for the second tunnel. You have three options: (i) Do nothing, (ii) dig a second tunnel to bring additional water to the two existing power stations, and (iii) dig a second tunnel and construct a third power station. Suppose that the geologists and engineers reach a consensus that the second tunnel will cost $1.4 billion with a probability of 0.7 and $2.3 billion with a probability of 0.3. The engineers estimate that the third power station will cost $0.4 billion with a probability of 0.4 and $0.6 billion with a probability of 0.6. The second tunnel by itself will bring in revenues of $2.1 billion and the second tunnel plus the third generating station will bring in revenues of $2.5 billion.

a) Based on expected profits (revenues minus costs), which of the three options should you take?

b) How much would the revenue from option (iii) need to be (to two significant figures) for you to change your decision?

c) What other factors should be taken into account in addition to expected profits?