**Econ 3363: Environmental Economics**

** Problem Set 2**

**Environmental Quality as a Public Good, the Pollution Control Model & **

**the Equimarginal Principle Applied to Emissions Reduction**

**Directions: ** You may work in groups of 1-2 students. You may only be in one group. Turn in one solution document per group—each member will earn the same score. Answer all questions. Clearly label answers. Please write or type on ** one** side of each sheet of paper. You may edit this

Need help? Contact the TA, Ryan McGregor at rpmcgregor@uh.edu

.

**(30 points, as indicated)***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__.

In your answer you will be asked to draw graphs. Please put $ per unit abated ($/A) 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 for this type of problem the, “socially efficient level” is that level that maximizes net social benefits, (NSB = TSB-TSC).] In your answer, be sure to state the “rule.” Show all work and discuss your reasoning. Draw a graph that shows your solution.

- (
*5 points*) Algebraically 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.

**2**. (**10 points, as indicated**) Consider the pollution control model discussed in chapter 5 of our class textbook by Field and Field (8^{th}edition),*Environmental Economics: An Introduction*.

- (
*4 points*) Draw two graphs with the first showing that the socially efficient amount of emissions is 0 and the second showing that the socially efficient amount of emissions is the free-dumping level.

- (
*6 points*) Explain why the same model yields such different predictions. What is the source of the difference between your 2 graphs?

**3**. (**14 points, as indicated**) The following table shows for 3 firms how each firm’s marginal abatement cost (MAC) is related to emissions. Assume the free-dumping level of emissions for each firm is 10 tons/week. Furthermore, assume that each firm emits the free-dumping level, so total emissions are 30 tons/week. Suppose a local government hopes to reduce the total emissions by 50% per week. The government proposes 2 policies:

- an equi-proportionate reduction in emissions (that is each firm must reduce

emission by 50%)

- an emissions reduction policy based on the equi-marginal principle.

- (
*4 points*) Discuss the two policies by answering the following questions. i) Do the two policies have the same new overall emissions target? What is the new target(s)? ii) what is the difference between an equi-proportionate reduction in emissions and an emissions reduction based on the equi-marginal principle?

- (
*3 points*) Calculate the total abatement costs implied by Policy 1. Show and explain your calculations.

- (
*3 points*) Calculate the total abatement costs implied by Policy 2. Show and explain your calculations.

- (
*4 points*) Which policy proposal is better and why?

** **

**COVER SHEET**

**ENVIRONMMENTAL ECONOMICS Homework 2**

** **

**DATE____________________**

**STUDENTS IN GROUP (up to two) **

Name (printed) |
PeopleSoft-ID |

*Directions*: Fill out the above table and place as the first page of your solutions.

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