Economics of the environment homework

ECN 236 – Economics of the Environment

HW # 1 – due date: September 7, 2017

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Answer all questions. Show all your work. You will get 0 points for just writing down the

answer. Group work is encouraged BUT each student should turn in their individual homework.

1. Go on the internet and put together a data-set of agricultural profits by U.S. states for a

particular year. Find data on average annual temperature in each state. For each state you should

have two numbers: agricultural profits and average annual temperature. Plot these data (profits

on vertical axis and temperature on horizontal axis). Is there a relationship between agricultural

profits and average temperature? What can you conclude about the overall effect on profits of a

3°C increase in the temperature? Are there additional variables that might be needed to fully understand the relationship between temperature and profits?

2. We will develop a simple model that relates greenhouse gas accumulation and temperature.1

Let 𝐺 be the level of greenhouse gases (in billions of tons) and 𝐸 be the level of emissions from factories in a particular time period. A certain fraction of the greenhouse gases is “cleaned” by

the environment (assimilative capacity of the environment). The following expression shows

how 𝐺 evolves over time:

∆𝐺

∆𝑡 = 𝛽𝐸(𝑡) − 𝛿𝐺(𝑡)

where 𝛽 represents the transformation of 𝐸 into 𝐺, 𝛿 represents the assimilative capacity of the environment and 𝑡 = time.

Let 𝑇 be the increase in global temperature due to greenhouse warming. The temporal relationship between 𝑇 and greenhouse gases (𝐺) is given by the following expression. ∆𝑇

∆𝑡 = 𝛼[𝛾𝐺(𝑡) − 𝑇(𝑡)]

where 𝑇 is in °C, 𝛾 measures the increase in global temperature due to increase in 𝐺 and 𝛼 captures the delay in temperature change due to greenhouse gases.2 The values of these

parameters are given in the following table.

Parameter Value

𝛽 0.50 𝛿 0.005 𝛼 0.02 𝛾 0.003

a. Steady-state is defined as the long-run equilibrium where climatic impacts of industrial

activity have stabilized. All emissions and concentrations of greenhouse gases are

therefore constant. That is, in steady-state, neither 𝐺 nor 𝑇 are changing. Using the values

1 For a more complicated model, see Nordhaus, William D. 1991. “To slow or not to slow: The economics of the greenhouse effect.” The Economic Journal, 101(407): 920 – 937. 2 The average climate responds slowly to increases in greenhouse gases and estimates of the delay range from 6 to

95 years.

ECN 236 – Economics of the Environment

HW # 1 – due date: September 7, 2017

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of the parameters, derive expressions for the steady-state of emissions (𝐸) and the steady- state of temperature (𝑇).

b. Define marginal damages as the decrease in global GDP in dollars due to increase in

temperature. The data on Moodle (HW1_data.xlsx), contains information on total

damages as a function of temperature increases. Using the data, plot marginal damages

against changes in temperature.

c. (i) The steady-state uncontrolled level of emissions are 12 billion tons of carbon. Using

your answers to a. and b., compute the steady-state of 𝐺, 𝑇 and marginal damages per ton of carbon.

c. (ii) Suppose 10% of 12 billion tons of carbon are controlled. Using your answers to a.

and b., compute the steady-state of 𝐺, 𝑇 and marginal damages per ton of carbon.

c. (iii) Suppose 20% of 12 billion tons of carbon are controlled. Using your answers to a.

and b., compute the steady-state of 𝐺, 𝑇 and marginal damages per ton of carbon.

c. (iv) Repeat exercise c. (iii) for higher control levels (30%, 40%, …, 90%). Tabulate

your answers. Using these answers and your answers to c. (i) – c. (iii), plot marginal

damages per ton of carbon as a function of percentage of emissions controlled.

d. (i) Controlling emissions is expensive and these costs increase as abatement increases.

The data on Moodle (HW1_data.xlsx) contains information on total cost of abatement

and control levels. Plot the relationship between marginal control costs and control

levels. Interpret the shape of the function.

d. (ii) Put the plots of c. (iv) and d. (i) on the same graph. What level of emissions control

balances marginal cost of control with marginal damages?

3. Explain the four myths identified by Fullerton and Stavins (1998) on how economists think

about the environment.

4. For each of the following social choice methods, which of Arrow’s axioms are violated and

why.

a. Pareto criterion

b. majority – rule voting

c. Pulling a choice out of a hat (at random)

ECN 236 – Economics of the Environment

HW # 1 – due date: September 7, 2017

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5. Suppose we have a small island with three residents and a volcano, Mount Doom that

generates air pollution. Two people live upwind of the volcano and are unaffected by the

pollution. One person, Frodo, lives downwind and is affected by the air pollution.

For $21,000 we can clean-up the volcano with a patented “smoke guzzler”. The two-upwind people are willing to pay $1,000 each to get rid of the smoke whereas Frodo would be willing to pay $15,000. Consider two plans to finance the “smoke guzzler”.

Plan A: Each resident will pay $7,000 (head – tax) Plan B: Frodo, who is affected by pollution, pays $21,000

Compare each plan to the status quo and indicate society’s choice using (a) Pareto criterion, (b)

majority rule and (c) potential Pareto improvement.

6. In the figure below, using the Pareto criterion, identify the points that are socially preferred to

W. Explain your answer.

ECN 236 – Economics of the Environment

HW # 1 – due date: September 7, 2017

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7. Borda Count is a common way of making a choice among more than two alternatives. Each

member of the society assigns a rank to the social alternatives with 1 corresponding to first

choice, 2 corresponding to second choice and so on. The ranks each alternative gets are summed

over all individuals. The alternative with the lowest sum wins. For example, suppose there are

three individuals and their rankings between three environmental commodities 𝐴,𝐵,𝐶 are given below.

Rank Person 1 Person 2 Person 3

1 𝐴 𝐵 𝐴 2 𝐵 𝐶 𝐶 3 𝐶 𝐴 𝐵

In the example above, choice 𝐴 has a score of 1 + 3 + 1 = 5; choice 𝐵 has a score of 2 + 1 + 3 = 6; and choice 𝐶 has a score of 3 + 2 + 2 = 7. Since 𝐴 has the lowest score, 𝐴 will be chosen.

Set up an example to show that Borda Count violates independence of irrelevant alternatives.

Hint: introduce a fourth alternative in the example above.

8. A society consists of two individuals, Alex and Menza, who consume two goods, food (𝐹) and national parks (𝑅). The following table ranks their preferences for different bundles of 𝐹 and 𝑅.

Alex’s preferences

Rank Food National parks

1 2.1 1.0

2 1.0 2.0

3 2.4 0.7

4 1.7 1.3

5 2.0 1.0

Menza’s preferences

Rank Food National Parks

1 1.4 1.4

2 1.0 2.0

3 1.6 1.3

4 1.8 1.1

5 2.0 1.0

a. For Alex, all bundles containing less than 0.9 units of national parks are inferior to (1.0, 2.0) --

- bundle ranked second for Alex. Given Alex’s rankings, draw an indifference curve that goes

through (1.0, 2.0).

ECN 236 – Economics of the Environment

HW # 1 – due date: September 7, 2017

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b. For Menza, all bundles containing less than 1.2 units of national parks are inferior to (1.0, 2.0)

--- bundle ranked second for Menza. Given Menza’s rankings, draw an indifference curve that

goes through (1.0, 2.0).

Three social choices are available for these two individuals where the allocations of food and

national parks are given below.

Alex’s allocation Menza’s allocation

Social choice Food National parks Food National parks

A 2.0 1.0 2.0 1.0

B 1.7 1.3 1.8 1.1

C 1.0 2.0 1.0 2.0

c. Between social choices A and B, which option does our two-person society prefer. Explain

d. Is there a way to shuffle around the total amount of food and national parks in choice A so that

your answer to c. is reversed? Does this imply that the compensation principle is flawed?