Question

Assume that scientific studies provide you with the following information concerning the benefits and costs of sulfur dioxide emissions: Benefits of abating (reducing) emissions: \(M B=500-20 A\) costs of abating emissions: \(M C=200+5 A\) 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

a. The socially efficient level of emissions abatement is 12 million tons. b. The marginal benefit and cost of abatement at the socially efficient level are both $260 per ton. c. Net social benefits decrease if we abate more or less than the efficient level. d. It's more socially efficient to set marginal benefits equal to marginal costs as it provides the optimal trade-off between the costs and benefits.

Step-by-step solution

Calculating the Socially Efficient Level of Emission Abatement

First, let's set the Marginal Benefit (MB) equal to Marginal Cost (MC) as follows: \(MB=MC\), so \(500-20A=200+5A\). Solve this equation for \(A\) by adding \(20A\) and subtracting \(200\) from both sides.

Determine the Value for \(A\)

The simplified equation is \(25A = 300\). Now, let's solve for \(A\) by dividing both sides by \(25\). This will give a result \(A=12\), so the socially efficient level of abatement is 12 million tons.

Calculating the Marginal Benefit and Marginal Cost at the Socially Efficient Level of Abatement

By substituting \(A=12\) into the equations for \(MB\) and \(MC\), we get \(MB=500-20*12=260\) and \(MC=200+5*12=260\). So, at socially efficient level of abatement, both marginal benefit and cost are equal to 260.

Determine the Change in Net Social Benefits

For one million tons more abatement (\(A=13\)), calculate the new \(MB\) and \(MC\), then find the difference. Do the same for one million tons fewer abatement (\(A=11\)). This shows how net social benefits would change with the deviations from the efficient level.

Explaining the Social Efficiency of Setting MB equal to MC

Abating until total benefits equal total costs would mean continuing until the marginal benefits are zero, at which point the marginal cost of further abatement would be high. Unless there are constant marginal benefits, this is inefficient. It is more socially efficient to abate up until the point where the additional benefit of reducing pollution equals the additional cost of doing so, i.e., setting marginal benefits equal to marginal costs.

Key concepts

Marginal Benefit

When it comes to understanding emissions abatement, the concept of marginal benefit (MB) is crucial. Marginal benefit reflects the additional benefit obtained from reducing pollution by one more unit. Imagine taking small, incremental steps to clean the air by reducing sulfur dioxide emissions. Each incremental reduction brings about certain environmental and health benefits—these are your marginal benefits.

For instance, if the MB equation given is MB = 500 - 20A, we notice that as the quantity abated, denoted by 'A', increases, the marginal benefit decreases. This makes sense because the most significant improvements in environmental health tend to occur early on. After a certain point, each additional ton of emissions abated yields a smaller incremental benefit. Recognizing this diminishing return is essential for balancing costs and benefits effectively.

Marginal Cost

Opposite to the marginal benefit, we have the marginal cost (MC), which indicates the additional cost incurred for every additional unit of pollution abatement. In our given formula, MC = 200 + 5A, we can observe that the marginal cost increases with each additional unit of abatement. This rise in cost makes sense—as we implement more extensive and often more sophisticated measures to reduce emissions, the cost of each additional ton abated goes up.

• This concept tells us that easy fixes are usually less expensive, and after those are exhausted, more substantial costs are incurred for extra abatement.
• An essential element of crafting policy is to find the balance where the cost of additional abatement does not exceed its benefit, which leads us to the socially efficient level of abatement.

Socially Efficient Level of Abatement

The socially efficient level of abatement strikes a balance between the marginal benefits and marginal costs of reducing emissions. It's the 'Goldilocks' point where we neither over-abate and waste resources nor under-abate and suffer excessive environmental damage. It's derived mathematically by setting the MB equal to the MC equation: MB = MC.

In our exercise, finding this balance implied solving for 'A' where the benefits of reducing emissions perfectly match the costs of doing so. This results in an 'A' value that represents the optimum, or socially efficient, number of units to abate (in millions of tons). Decision-makers aim to operate at this level, ensuring that each dollar spent on abatement translates into a dollar's worth of environmental and health benefits.

Net Social Benefits

Net social benefits give us the complete picture of the gains from emissions abatement minus the associated costs. They show us the overall benefit to society as a whole. Calculating these—by subtracting the total cost of abatement from the total benefits—helps in understanding the efficiency of environmental policies.

The exercise demonstrates that abating beyond the socially efficient level means the marginal cost outweighs the marginal benefit, which erodes net social benefits. Conversely, abating less than the efficient level means forfeiting potential net social benefits. Policies need to hinge on this dynamic balance to ensure that society maximizes its net gains from environmental protection efforts.