The government is considering building a bridge to connect Havelock Island with the main- land. 50,000 citizens live on the island and the government will hire the 25,000 employees it needs for the construction entirely from the population of the island; it will pay them an hourly wage rate of $25. The project will require 1 million sacks of asphalt, 0.5 million bars of steel, and 250,000 labor hours. In the future, the bridge will have to undergo annual maintenance at $10 million per annum. The bridge will provide a better, safer alternative to the ferry system that is currently being used by the inhabitants of Havelock Island. It will save them 250,000 hours of commuting time every year, and result in 3 lives saved every year. Reduced usage of the ferry will also help conserve marine life in the area. The government has the following information at its disposal: the market price of a sack of asphalt is $5, the market price of a bar of steel is also $5. The citizens of Havelock Island have two employment options: working on the construction project or working some other job at a minimum wage of $10. Studies have found that the value of one hour saved is $22.70. Other studies have used the concept of compensating differentials to find that the value of a human life is $9.6 million. Government revealed preferences show that the value of statistical life is $9.93 million. Using the above information, showing all steps of your calculations, and listing any assump- tions that you make [Hint: you will have to make at least two], conduct cost-benefit analysis for this project. Then, provide your recommendation: should the government build the bridge or not?
Solution
The Govt.will take the decision to build the bridge only if the value of benefits associated with it are more than the expenditure involved in building it.
Firstly calculating the Cost / Expense associated with building the bridge:
Estimated labor cost for constructing the bridge = 25,000 (no.of labor) * $25 (wage rate) * 25,000 (no.of hours)
= $15,625 million
Material Cost
(a) Estimated Cost of Steel that will be used = $ 5 (per unit cost) * 1 million (no.of units) i.e., $5 million
(b)Estimated Cost of Asphalt that will be used = $ 5 (per unit cost) * 0.50 million (no.of units) = $2.50 million
Annual maintenance cost = $10 million
Total cost of constructing the bridge = $15,642.50 million
Assumption 1 : The life span of the bridge is 20 years:
Assumption 2 : Even if the people of island do not choose to work for bridge construction,they utilitize / get the entire time (25,000 hours) to take up some other job
Calculating the benefits generated from the bridge
Given that the workers will get only $10 as minimum wage if they choose some other job than bridge construction
Benefit from working for bridge construction = 25,000 (no.of labor) * (25-10) * 25,000 (no.of hours)
= $9375 million
Cost of saving 3 lives per year = 3 * ($9.93 million ) i.e., $29.79 million
Therefore for 20 years,the value is : $595.80 million
Here,I took value of human life based on value of statistical life
Given that the value of 1 hour saved in travel = $22.70 ; No of hours saved per year = 2,50,000
Total value of saved hours = 2,50,000 * 22.70 i.e., $ 5.675 million
For 20 years the value is : $113.50 million
So, Total benefits accrued for 20 years = $10,084.30 million
So,since the cost associated with the bridge is more,the GOVT. should not build the bridge
The government is considering building a bridge to connect Havelock Island with the main- land. 50,000...