Question

Assume that scientific studies provide you with the following information concerning the benefits and costs of sulfur dioxide emissions: Benefits of abating (reduc- \\[ \mathrm{MB}=500-20 A \\] ing ) emissions: costs of abating emissions: \\[ \mathrm{MC}=200+5 A \\] where \(A\) is the quantity abated in millions of tons and the benefits and costs are given in dollars per ton. a. What is the socially efficient level of emissions abatement? b. What are the marginal benefit and marginal cost of abatement at the socially efficient level of abatement? c. What happens to net social benefits (benefits minus costs) if you abate one million more tons than the efficient level? One million fewer? d. Why is it socially efficient to set marginal benefits equal to marginal costs rather than abating until total benefits equal total costs?

Short answer

Socially efficient level of emissions abatement is when Marginal Benefit equals Marginal Cost. At this level, the net social benefit is maximized. Abating more or less than this efficient level will result in a lower net social benefit. It's more efficient to set MB equal to MC because the last unit of abatement that brings equal additional benefit and cost maximizes the total net benefit.

Step-by-step solution

Calculating the Socially Efficient Level of Emission Abatement

To get the socially efficient level of emissions abatement, we have to set the Marginal Benefit (MB) equal to the Marginal Cost (MC). Hence, solve the equation \(500 - 20A = 200 + 5A\).

Find the Marginal Benefit and Marginal Cost at the Socially Efficient Level

Substitute the value of 'A' found in Step 1 into the equations for MB and MC to get the marginal benefit and cost at this level.

Effect on Net Social Benefits

To find the effect on net social benefits if you abate one million more tons than the efficient level, calculate the net benefit at 'A' + 1. Similarly, to find the effect on net social benefits if you abate one million fewer tons than the efficient level, calculate the net benefit at 'A' - 1.

The Reason for Social Efficiency in Setting Marginal Benefits Equal to Marginal Costs

Explain why it's more efficient to set MB equal to MC rather than total benefits equal to total costs using the concept of marginal utility.

Key concepts

Marginal Benefit

Marginal Benefit (MB) is a critical concept when determining the value gained from reducing or abating sulfur dioxide emissions. It represents how much benefit or worth a single additional unit of abatement provides to society. The formula used to describe this in our exercise is \( \mathrm{MB} = 500 - 20A \), where \(A\) is the amount of emissions abated in millions of tons.

This formula implies that as more emissions are reduced, the marginal benefit decreases. This decreasing trend occurs because the initial units of abatement capture the most harmful emissions, providing maximum benefits. However, as more units are abated, the advantages from reducing additional emissions gradually taper off. This concept emphasizes the importance of prioritizing initial emission reductions.

In practical terms, understanding the marginal benefit helps in identifying what actions provide the most value to society. It's not just the total benefit that matters but the benefit of each incremental unit, especially when trying to achieve socially efficient outcomes.

Marginal Cost

Marginal Cost (MC) is the expense incurred for each additional unit of emissions abatement. In our exercise, MC can be calculated using the formula \( \mathrm{MC} = 200 + 5A \).

This formula shows that marginal costs increase with each additional unit of abatement. This increase occurs because the easiest and least costly emissions are typically reduced first; to abate further requires more resources and effort. The rising cost signals the necessity for careful planning in how emissions reductions are approached and managed.

Recognizing the concept of marginal cost is vital because it helps balance the efforts to maximize benefits while minimizing costs. Businesses and policymakers can use it to decide when additional investments in emissions reductions are warranted and when they might lead to decreased financial efficiency.

• Increasing marginal costs suggest that over-abating might not be economically justifiable.
• This is why setting the marginal benefit equal to the marginal cost ensures the most efficient allocation of resources.

Net Social Benefits

Net Social Benefits measure the overall advantage to society from emission abatement, calculated as the difference between total benefits and total costs. In our discussion, this is examined by comparing the marginal benefit and marginal cost.

When the marginal benefit equals the marginal cost, net social benefits achieve their maximum since resources are being used most efficiently. If you were to abate one more million tons than the socially efficient level, the additional costs would surpass the benefits, thereby reducing net social benefits. Conversely, abating one million fewer tons would mean lost benefit potential, again decreasing net social benefits.

The principle of net social benefits emphasizes why it's prudent to equate marginal benefits with marginal costs:

• Optimizing this balance ensures societal well-being is maximized.
• It guards against unnecessary expenditures which offer little additional societal gain.

By examining net social benefits, decision-makers can align environmental goals with economic realities, ensuring sustainability and prosperity.