Suppose a community could spend $3,000 on a levee that would decrease the probab

Question

Suppose a community could spend $3,000 on a levee that would decrease the probability of flooding in a three-house neighborhood from 3% to 2%. A flood would destroy all three houses, and flood insurance is not available. The market value of the three houses is known to be $90,000, $180,000, and $360,000 respectively.

a) Is the levee socially efficient? What is its benefit to cost ratio?

b) Design a taxing scheme (to pay for the levee) that could generate unanimous support for the levee.

c) Could you have an alternative taxing scheme to your answer in part b that has majority support but not unanimous support?

Explanation / Answer

a.

Average cost of houses = Total cost / Number of houses

                                       = (90,000 + 180,000 + 360,000) / 3

                                       = 630,000 / 3

                                       = $210,000

The benefit is the decrease in probability of flooding the three-houses.

It is (3% - 2% =) 1%

Percentage decreasing = (1/3) × 100 = 100/3%

Benefit = Average cost of houses × Percentage decreasing

            = $210,000 × 100/3%

            = $70,000

Answer: The levee is socially efficient, since the benefit $70,000 is above the cost of levee $3,000.

Benefit to cost ratio = Benefit / Cost

                                 = $70,000 / $3,000

                                 = 23.33: 1 (Answer)

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