A city engineer has complied the following data on a flood d

A city engineer has complied the following data on a flood damage project to control the flood, the construction of a small dam will cost $100,000. Based on the estimated damage data collected, check if is worth building a dam

Solution

1. The probability of flood damage is 0.3 if the flood damage is $ 200000. Then the estimated damage is $ 200000*0.3 = $60000.

2. The probability of flood damage is 0.5 if the estimated flood damage is $ 100000. Then the damage is $100000*0.5 = $ 50000.

3. The probability of flood damage is 0.3 if the estimated flood damage is $ 200000. Then the damage is $ 50000*0.1 = $ 5000.

4. The probability of flood damage is 0.1 if the estimated flood damage is $ 0. Then the estimated damage is $ 0*0.1 = $ 0.

The construction of a dam is a viable proposition even if the annual estimated damage is $ 50000, as the lifespan of a flood control dam is now 100 years. The investment on constructing a dam will then be recovered in 20 years. If the estimated damages are more, the investment can be recovered earlier. Further, apart from the economic costs, there are social costs of shifting and rehabilitating a part of the population and the pain of leaving homes which have not been considered here.