Power plants in the United States emit a variety of pollutants while producing valuable electricity.

Two power plants close to Greensboro are the Belews Creek and Dan River power plants.The Belews Creek plant has almost 2,500 MW of capacity and generated 7.1 billion kWh of electricity in 2019.To produce this electricity, it emitted 6.8 million tons of CO₂ and 5,668 tons of NO_X as well as other pollutants.

The Dan River plant has about 1000 MW of capacity and generated 4.4 billion kWh of electricity in 2019.To produce this electricity, it emitted 1.8 million tons of CO₂ and 267 tons of NO_X as well as other pollutants.

It is costly to abate emissions of CO₂ from each power plant.For CO₂, suppose the marginal abatement cost at Belews Creek is MC_b= 200X_b and at Dan River is MC_d=400X_d where marginal abatement costs are in $ per ton and X_bis abatement at Belews Creek in millions of tons and X_d is abatement at Dan River in millions of tons.

Suppose the regulator (US EPA and/or NC DEQ) wishes to reduce CO₂ from the two power plants by 0.6 million tons, so they want 0.6 million tons of total abatement.

1)Cost effectiveness

a.Suppose the regulator decides to be fair and require 0.3 million tons of CO₂ abatement from each power plant.

i.Is this cost effective?Explain your calculations.

ii.Which plant should abate more?Which plant should abate less?

b.Suppose the regulator decides to share the burden proportionally based on capacity.Because Belews Creek it bigger, it requires 0.5 million tons of abatement from Belews Creek and only 0.1 million tons of abatement from Dan River.

i.Is this cost effective?Explain your calculations.

ii.Which plant should abate more?Which plant should abate less?

c.Calculate the cost-effective abatement for each plant. Explain your calculations.

i.Hint: The equimarginal rule gives one equation.Another equation is because abatement must sum to 0.6 million. Then solve for two equations in two unknowns.Check your algebra with wolframalpha.com.

d.Illustrate your answers with a graph. Be sure to label as many points as possible.

i.Hint: The width of your diagram will be 0.6.

2)Emissions tax

a.Suppose the regulator decides to regulate CO₂ emissions with a tax of $80 per ton.

i.How much will Belews Creek abate?Explain your calculations.

ii.How much will Dan River abate? Explain your calculations.

iii.Is the emissions tax cost effective?Explain your calculations.

3)Emissions trading

a.Suppose the regulator decides to regulate CO₂ emissions with emissions trading and allocates permits so that each plant is required to abate 0.3 million tons.

i.Is this allocation cost effective?If not, explain who would like to pollute more (and buy permits) and who would like to abate more (and sell permits).

Pollution Hotspots

Suppose the regulator also wishes to reduce NOx emissions.NO_X emissions are not uniformly mixed.Because Belews Creek is not near a population center, the damages from emissions at Belews Creek are $11,000 per ton of NO_X emissions.Because Dan River is near population centers in Eden, NC and Danville, VA, the damages from emissions at Dan River are higher at $13,000 per ton of NO_X emissions.

It is costly to abate emissions of NO_X from each power plant.Suppose the marginal abatement cost of NO_X emissions at Belews Creek is MC_b=80X and at Dan River is MC_d=100X_d where marginal abatement costs are in $ per ton and X_B is abatement at Belews Creek in tons and X_dis abatement at Dan River in tons.

4)Uniform emissions tax

a.Suppose the regulator charges a uniform emissions tax of $12,000 per ton to both power plants.

i.How much does each plant abate? Explain your calculations.

ii.Is the result cost effective?

iii.Does the high damage plant (Dan River) abate more?Explain why or why not.

iv.Does the uniform emissions tax cause a pollution hotspot?Explain why or why not.

b.Suppose the regulator wishes to avoid a pollution hotspot and charges an emissions tax of $11,000 per ton at Belews Creek and $13,000 per ton at Dan River.

i.How much does each plant abate? Explain your calculations.

ii.Is the result cost effective?

iii.Does the high damage plant (Dan River) abate more?Explain why or why not.

iv.Does the differentiated emissions tax eliminate the pollution hotspot?Explain why or why not.