# Question: this problem asks you to analyze environmental quality as a...

###### Question details

*This problem asks you to analyze environmental quality as a
public good, but using a slightly different approach than was used
in the class example. In class we measured environmental quality by
the percent abated (20%, 60% etc), this time we will measure
environmental quality in terms of the quantity of pollution abated.
I ask you to go into some detail about your calculations, to
illustrate your understanding intuitively and technically*.

The Valley of Grimes is inhabited by
three people and a strange natural formation that pollutes the air
with sulfur dioxide (SO_{2}). Air quality is measured in
terms of the concentration of SO_{2} per cubic meter of
air, expressed as μg/m^{3}, where μg is a microgram, or
one-millionth of a gram, and m^{3} represents cubic meters.
The Valley of Grimes currently experiences an ambient air quality
for SO_{2} of 1500 μg/m^{3} per time period.

Assume the three individuals (1, 2,
and 3) value pollution abatement (A) according to the following
identical marginal private benefit (marginal willingness-to-pay,
P_{i}) schedules:

P_{1} = 60 - (A/10)

P_{2} = 60 - (A/10)

P_{3} = 60 - (A/10)

where A is micrograms per cubic meter
(μg/m3) of SO_{2} abated

P_{i} is $
per μg/m^{3}

Assume the marginal (social) cost of
reducing ambient SO_{2} is constant at $30 per
μg/m^{3}, that is MSC = $30, drawn as a horizontal
line.

Your diagrams will have $ per unit abated on the vertical axis and quantity of pollution abated (A) on the horizontal axis.

- (
*3 points*) Think about air quality in general terms—not the specifics of the problem

above--is air quality a public good or a private good? Discuss your logic.

- (
*12 points*) Derive the aggregate MSB curverelated ways: (1) by constructing a table, (2) by deriving the MSB mathematically and (3) by drawing a graph. You will be doing a "vertical summation" of the individual consumer’s marginal benefit curves. Note that I have expressed*three**price*as a function of abatement for each individual. Then for any given quantity of abatement add the three individuals' marginal values, by adding P_{1}(A) + P_{2}(A) + P_{3}(A), where "P_{1}(A)" means that P_{1}is a function of A.

- (
*5 points*) Solve for the socially efficient level of air quality. [Recall that by "socially efficient level" of air quality, you will find the level that maximizes net social benefits, (TSB-TSC).] In your answer, be sure to state the rule. Show all work and discuss your reasoning. Draw a diagram showing your solution.

- (
*5 points*) Calculate the net social benefit to society at the socially efficient level of air quality you found in part (c). Calculate both TSB and TSC and subtract to get net social benefits. Also illustrate in a graph.

- (
*5 points*) Now show that the allocation where all of the pollution is abated (that is clean up all 1500 μg/m^{3}of SO_{2}per time period), would yield less net social benefits than what you found in part (d). Illustrate in a graph.