Imagine that you were the governor of Massachusetts 15 years ago and needed to decide if you should support the "Big Dig" highway and bridge construction project.
The Big Dig is estimated to take seven years to complete. The project will require $45 million in construction materials per year and $20 million in labor costs per year. In addition, the construction will disrupt transportation within the city for the duration of the construction. The transportation disruption lengthens transport times for 100,000 workers by 30 hours per year. All workers are paid $15 per hour (assume that there are no distortions and that the wage reflects each worker's per-hour valuation of leisure).
The Big Dig, when finished, will ease transportation within the city. Each of the 100,000 workers will have their transport time reduced by 35 hours per year as compared to the preconstruction transport time. In addition, part of the Big Dig project involves converting the space formerly taken up by an elevated highway into a large park. The Commonwealth of Massachusetts has determined that each worker will value the park at $40 per year. We will assume that no one else will use the park.
We also assume the government has a 5% discount rate and that the workers live forever. The benefits to the Big Dig begin in year 7, assuming the project begins in year 0 (i.e., the project runs for 7 years, from t = 0 to t = 6).
a. Should you, as the governor, proceed with the project? Formally show the cost-benefit analysis.
b. It occurs to you, after completing the calculation in part (a), that it is possible that the cost estimates are uncertain. If the construction materials estimate is $45 million with 50% probability, and $100 million with 50% probability, should the project proceed? Assume that the government is risk neutral.