Problem:
Mark is looking at the forecasts of expected economic growth. He plans to invest $120,000 in an investment whose return would depend on the economic conditions. It is estimated that the economy will have a high growth with a probability of 25%, normal growth with a probability of 50% and a slow growth with a probability of 25%. An investment is likely to provide an expected return of 20% if the economy has a rapid growth, 14% if the economy has normal growth and 8% if the economy grows slowly. In order to get more information, Mark has approached an economist who can provide a better estimate. The economist would charge $15,000 for providing his estimate. The economist predicts the following probabilities: High growth: 40%; normal growth: 40%; and slow growth: 20%.
Construct a decision tree and advise whether use of the services of economist is justified.