Question

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

Answer 1

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