A city is considering replacing its fleet of gas-powered cars with electric cars. If the replacement is successful, the city will experience savings of $1.5m. If the replacement plan fails, the cost to the city will be $675,000. A third possibility is that less serious problems occur and the city will just breakeven ($0). The city estimates these three outcomes have probabilities of 0.3, 0.3, and 0.4.
a. Draw a decision tree for this problem.
b. Suppose the city could get perfect information regarding the outcomes of the replacement, what is the most it should pay for this information?
c. The city could also, at a cost of $75,000 implement a pilot program involving renting a small number of electric cars and running them for a few months. The pilot program would either have positive or negative results. Other cities in the country have used this kind of pilot program. Their experience suggests the following: When the pilot is positive, the probabilities of success, failure, and break-even of the actual replacement program become: 0.4, 0.14, and 0.46. When the pilot is negative, the probabilites of success, failure, and break-even become 0.07, 0.66, and 0.27. The city currently estimates the probability of positive results with the pilot at 0.7.
(i) Should the city utilize the pilot program? What should it do if the program result is positive? Negative?
(ii) What is the most they would spend on the pilot program.