Assignment: Economics of the Environment

1. Suppose that the market demand curve for coal is given by P = 80 - Q, and the marginal cost of producing it is MC = Q where P is the price of coal per ton and Q is quantity in thousands of tons.

a. (i) How much will be supplied by a competitive market?

a. (ii) Show your result graphically.

b. Compute the consumer surplus and producer surplus if coal is supplied in a competitive market.

c. (i) How much will be supplied if there is only one supplier of coal (monopoly)?

c. (ii) Show your result graphically.

d. Compute the consumer surplus and producer surplus if coal is supplied by a monopoly. Compare the consumer surplus, producer surplus and total surplus between the two types of markets.

2. Consider the market for electricity where demand (in megawatt hours) is given by Q = 50 - P and the private marginal cost of generating electricity is $10 per megawatt hour. Suppose further that pollution is generated in the production of electricity in direct proportion to the amount of electricity generated and the health damage from the pollution is $15 per megawatt hour.

a. Suppose electricity is produced by many competitive producers. What price will be charged, and how much electricity is produced?

b. Suppose electricity is produced by a monopolist. What price will be charged, and how much electricity is produced?

c. In parts a. and b., what is the consumer surplus and producer surplus from electricity generation? In parts a. and b., what is the net surplus, after taking pollution damage into account?

3. In the figure below, identify a point D such that Z and Y are Pareto preferred to D but S is not.

4. In the figure below, the slope of the production possibility frontier is increasing (getting steeper) as garbage disposal decreases and production of wine increases. Does this make sense? Explain.

5. A politician states that "total surplus is not maximized in a free-market." Critique this statement.

6. Consider an air basin with only two consumers, Huck and Matilda. Suppose Huck's demand for air quality is given by Q_H = 1 - P where P is Huck's marginal willingness to pay for air quality. Similarly, Matilda's demand is given by Q_M = 2 - 2P.

The supply of air quality is given by Q = P where P is the marginal cost of supply.

a. Graph the individual demand curves and aggregate demand curve for air quality.

b. What is the efficient amount of air quality?

7. Consider an airport that produces noise (N) that decays as distance (d) from the airport increases, where distance is in miles. The relationship between distance and noise is given by the following equation.

N = 1/d²

Fritz works at the airport and his damage from noise is $1 per unit of noise. His cost of commuting is $1/mile (each way). The closest he can live to the airport is d = 0.1 miles.

a. Write an expression for Fritz's total cost (noise and transportation).

b. How far will Fritz live from the airport? What are his total costs?

c. Suppose Fritz is compensated for the noise damages. How far will Fritz live from the airport? How much will he be compensated?

8. When sulfur dioxide is emitted into the air, it is transported over long distances and is converted to sulfuric acid. This gradually falls to the ground, either as rain or snow. This is called acid deposition. In what way could acid deposition be considered a rival bad?

9. Identify whether each of the following resource categories is a public good, a common-pool resource, or neither. Explain each answer.

a. A pool of whales in the ocean to whale hunters.

b. A pod of whales in the ocean to whale watchers

c. Bottled water

10. Consider a small exchange economy with two consumers, Ned (N) and Stark (S) and two commodities, food (F) and electricity (E). The preferences of the two consumers are given by the following equations:

U_N = F_N × E_N
U_S = F_S × E_S

The initial endowments of the goods are: Ned has 12 units of food and 2 units of electricity while Stark has 8 units of food and 18 units of electricity.

a. Draw an Edgeworth box for this economy. Be sure to label the axes, (including the endowment point).

b. Draw in the efficient lens that corresponds to the initial endowment. Explain this lens.

c. For an allocation in this economy to be Pareto efficient, it must maximize the utility of Ned given the utility of Stark. Is the initial endowment Pareto efficient? Why or why not?

d. Now assume Ned gets to choose a new allocation to maximize utility, subject to the constraint that Stark's utility be no lower than at the endowment point. Illustrate this situation on a separate graph.