Assignment: Economics of the Environment
Answer all questions. Show all your work. 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. 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:
ΔG/?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.
ΔT/?t = α[γG(t) - T(t)]
where T is in oC, γ measures the increase in global temperature due to increase in G and α captures the delay in temperature change due to greenhouse gases. 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
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)
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.
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).
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?
Attachment:- hw1_data.rar