Question

Two firms release some pollutants into the air. Their marginal abatement cost functions are given below where emissions are in hundreds of units per week. Social efficiency requires that total emissions be reduced by 75 units per week.

MAC_A = 300 – 6E_A MAC_B = 400 – 2E_B
A. Graph the MAC functions in separate diagrams.
B. What are total emissions given no abatement by either firm?Government regulators decide to use an emission standard as the policy of choice to achieve the required reduction in pollution. The standard chosen would require equiproportionate emissions reductions by each firm.
C. How much abatement would each firm be required to undertake given this emission standard?
D. Compute each firm’s total compliance cost (emissions are in hundreds of units). Identify these areas in your graphs.
E. Does this standard satisfy the equimarginal principal? Explain why or why not. Suppose that instead of this standard government decides to tax emissions as a source of revenue to pay for environmental protection projects.
F. What uniform tax rate should be set to achieve the required abatement at the lowest possible cost to society? How many units will each firm abate per week when faced with this tax rate?
HINT: Cost-effectiveness requires MAC_A = MAC_B when abatement stops. We also know that rational firms will abate up to the point where MAC = tax.
G. Draw new graphs to illustrate your answers to (e). Compute each firm’s private cost to comply with the tax policy (emissions are in hundreds of units). Identify these areas in your graphs.
H. Based on your calculations in the previous questions which policy, the standard or emissions tax, achieves the desired reduction in emissions at the lowest cost to society. How much is this cost savings? Which policy would the two polluting firms prefer and why?

Answer 1

A firm facing a $1,000 pollution tax for every 10 pounds of particulates will abate pollution up to the point where abatement costs are lower than the tax. It will abate 30 pounds when abatement costs would otherwise exceed the tax for further reductions.

Step-by-step explanation:

When a firm is faced with a pollution tax of $1,000 for every 10 pounds of particulates emitted, it must choose between polluting and paying the tax or reducing emissions and incurring abatement costs. The marginal abatement cost (MAC) curve suggests that abatement costs increase with each additional unit of pollutant reduction. Faced with these costs and the pollution tax, a firm will reduce emissions where the abatement cost is less than the tax to minimize its expenses.

For example, if the first 10 pounds of emissions cost the firm $300 to abate, it is cheaper than the $1,000 tax, so the firm will abate. As abatement becomes more expensive ($500, $900 for the subsequent 10-pound reductions), the firm continues to abate until the abatement cost exceeds the tax. Therefore, when the cost reaches $1,500 to reduce the fourth 10 pounds, it's more economical to pay the $1,000 tax rather than incur higher abatement costs. Thus, the firm will abate 30 pounds of emissions and pay the tax on the remainder. This scenario is a practical application of the equimarginal principle in environmental economics.