Question #110526

Consider a community consisting of 20 households who depend on a common well for its supply of water. Clean-up and chemical treatment is required to ensure safety of water from the well. The marginal benefits to each household from clean-up and treatment is given by the equation,

MBx=100-4X

If the marginal clean-up and treatment cost is 100 + 20X where X represents the number of clean-ups and chemical treatment per year,

1. Determine the social optimal number of clean-ups and chemical treatment per year.

2. Compute the net social welfare benefit to each household if the households share the cost of clean-ups and treatment

3. Compute the total social welfare benefit to each household if half of the households pay half the cost of clean-ups and treatment

4. Compute the amount of free riding from the two groups in 3 above

MBx=100-4X

If the marginal clean-up and treatment cost is 100 + 20X where X represents the number of clean-ups and chemical treatment per year,

1. Determine the social optimal number of clean-ups and chemical treatment per year.

2. Compute the net social welfare benefit to each household if the households share the cost of clean-ups and treatment

3. Compute the total social welfare benefit to each household if half of the households pay half the cost of clean-ups and treatment

4. Compute the amount of free riding from the two groups in 3 above

Expert's answer

1."20\\times(100-4x)=100+20x"

2000-80x=100+20x

1900=100x

x=19

2."20\\times(100-4\\times19)-(100+20\\times19)=2000-76-100-380=1444"

"\\frac{1444}{20}=72.2"

3."100+20\\times19=480"

"\\frac{480}{2}=240"

4."6\\times(100-4x)=0"

600-24x=0

x=25

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