What is the natural equilibrium and the maximum sustainable

Question

Environmental Economics Problem Set

Question 1: Suppose iron can be produced using virgin ore at a marginal cost given by MC₁ = 0.5q₁ and with recycled materials at a marginal cost given by MC₂ = 5 + 0.1q₂.

a) If the market demand is 100 units of iron, how much will be obtained from each source?

b) Suppose time passes by and iron has become more expensive to mine, MC₁ = 1.5q₁ and recycling technology has improved making it less expensive, MC₂ = 2 + 0.1q₂. Market demand is still 100. How much will be obtained from each source.

c) Comment on how the price of the different techniques changes the share of iron that is recycled.

Question 2: The table below represents the ecology of the tuna population (in millions of tuna):

Stock	10-19	20-29	30-39	40-49	50-59	60-69	70-79	80-89	90-99	100
Growth (per year)	0	1	2	2.5	3	2.5	2	1	0	-1

a) What is the natural equilibrium and the maximum sustainable yield?

b) If the population is currently 30, what will the population be in 1 year?

c) If the population starts at 30 how many years would it take for the population to grow to 50?

d) Draw a graph of this system with growth on the vertical axis and fish population on the x-axis.

Question 3: Water is an essential resource. For that reason moral considerations exert considerable pressure to assure that everyone has access to at least enough water to survive. Yet it appears that equity and efficiency considerations may conflict. Providing water at zero cost is unlikely to support efficient use (marginal cost is too low), while charging everyone the market price (especially as scarcity sets in) may result in some poor households not being able to afford the water they need.

a) Discuss how increasing block rate pricing attempts to provide some resolution to this dilemma.

b) Do you think increasing block rate pricing is a good resolution in developing countries where affordability may be a large concern?

Question 4: Two power plants are currently emitting 8,000 tons of pollution each (for a total of 16,000). Pollution reduction costs for Plant 1 are given by MCR₁ = 0.02Q₁ and for plant 2 by MCR₂ = 0.03Q₂ where Q represents the number of tons of pollution reduced.

For each policy below calculate the amount of pollution reduced by each firm, the pollution reduction costs for each firm, and the government revenue generated. Drawing a graph for each part may be helpful.

a) A regulation requiring each plant to reduce its pollution by 5,000 tons.

b) A pollution tax of $120 per ton of pollution emitted.

c) A tradable permit system where each firm is issued 3,000 permits (so the total market cap is 6,000 tons of pollution). For this part, indicate which firm sells, which firm buys, and how many permits. You should also draw the two-sided diagram.

d) Explain the intuition behind why market-based instruments (emission taxes and tradeable permits) are cost-effective, while quotas are generally not.

Question 5: Suppose you are in charge of environmental management for a firm, and the firm needs to abate 10 units. You have three possible pollution reduction methods. Assume that q₁, q₂, and q₃ are, respectively, the amount of pollution abated by each method that you choose to use so that the goal will be accomplished by any combination of methods such that q₁ + q₂ + q₃ = 10.

a) If the marginal costs of each removal method are:

MCR₁ = 10q₁, MCR₂ = 5q₂, and MCR₃ = 2.5q₃

How much of each method should you use to achieve the removal cost effectively?

b) Why isn't an exclusive use of method 3 cost-effective?

c) Suppose that the three marginal costs were constant (not increasing as in the previous case) such that MCR1 = 10, MCR2 = 5, and MCR3 = 2.5. What is the cost-effective outcome in that case?