1. Suppose there are two power plants that release sulfur dioxide (SO₂) into air at their current production levels. Each firm currently emits 75 tons per year, thus emitting 150 tons total. Local authorities have decided they would like to reduce annual SO₂ pollution to 100 tons per year (thus a 50 ton reduction). The power plants have different marginal abatement costs given by the following equa- tions: MAC₁ = 391 MAC₂ = 292 (a) Suppose the local authorities decide to impose a uniform reduction of pollution by both power plants. In order to achieve the 50 unit reduction under this plan, both plants must reduce their emissions (abate pollution) by 25 units each. Find the total cost of abatement under this uniform reduction policy. (b) Find the efficient abatement amount for each power plant if you wanted to achieve the 50 unit reduction at the most cost-efficient way possible (i.e. find the q₁ and 92 that achieves the 50 unit reduction in the cheapest way). What is the total cost of reducing pollution under this plan? How much must each plant pay? (c) Now suppose the local authorities wanted to achieve this 50 ton reduction in an- nual SO₂ via a pollution tax. This tax is the same for for both power plants and must be paid by each plant for every ton of SO₂ emitted annually. Find the op- timal tax per ton of SO₂. How much does each plant pay in taxes? What is the total cost for each plant from this policy (cost of tax payment and total abatement costs). Which power plant pays more?
1. Suppose there are two power plants that release sulfur dioxide (SO₂) into air at their current production levels. Each firm currently emits 75 tons per year, thus emitting 150 tons total. Local authorities have decided they would like to reduce annual SO₂ pollution to 100 tons per year (thus a 50 ton reduction). The power plants have different marginal abatement costs given by the following equa- tions: MAC₁ = 391 MAC₂ = 292 (a) Suppose the local authorities decide to impose a uniform reduction of pollution by both power plants. In order to achieve the 50 unit reduction under this plan, both plants must reduce their emissions (abate pollution) by 25 units each. Find the total cost of abatement under this uniform reduction policy. (b) Find the efficient abatement amount for each power plant if you wanted to achieve the 50 unit reduction at the most cost-efficient way possible (i.e. find the q₁ and 92 that achieves the 50 unit reduction in the cheapest way). What is the total cost of reducing pollution under this plan? How much must each plant pay? (c) Now suppose the local authorities wanted to achieve this 50 ton reduction in an- nual SO₂ via a pollution tax. This tax is the same for for both power plants and must be paid by each plant for every ton of SO₂ emitted annually. Find the op- timal tax per ton of SO₂. How much does each plant pay in taxes? What is the total cost for each plant from this policy (cost of tax payment and total abatement costs). Which power plant pays more?
Chapter1: Making Economics Decisions
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Transcribed Image Text:1. Suppose there are two power plants that release sulfur dioxide (SO₂) into air at their
current production levels. Each firm currently emits 75 tons per year, thus emitting
150 tons total. Local authorities have decided they would like to reduce annual SO2
pollution to 100 tons per year (thus a 50 ton reduction).
The power plants have different marginal abatement costs given by the following equa-
tions:
MAC₁ = 3q1
MAC₂ = 292
(a) Suppose the local authorities decide to impose a uniform reduction of pollution
by both power plants. In order to achieve the 50 unit reduction under this plan,
both plants must reduce their emissions (abate pollution) by 25 units each. Find
the total cost of abatement under this uniform reduction policy.
(b) Find the efficient abatement amount for each power plant if you wanted to achieve
the 50 unit reduction at the most cost-efficient way possible (i.e. find the 9₁ and
92 that achieves the 50 unit reduction in the cheapest way). What is the total cost
of reducing pollution under this plan? How much must each plant pay?
(c) Now suppose the local authorities wanted to achieve this 50 ton reduction in an-
nual SO₂ via a pollution tax. This tax is the same for for both power plants and
must be paid by each plant for every ton of SO₂ emitted annually. Find the op-
timal tax per ton of SO₂. How much does each plant pay in taxes? What is the
total cost for each plant from this policy (cost of tax payment and total abatement
costs). Which power plant pays more?
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