Logo

AskSia

Plus

Suppose the environmental agency aims at a total effluent level of 16 tons. And...
Oct 1, 2024
1 Answer
a
Abatement Cost Calculation: For firm A, the marginal abatement cost (MCA) when eA=8e_A = 8 tons is MCA=12−8=4MCA = 12 - 8 = 4 kEUR/ton. For firm B, MCB=18−8=10MCB = 18 - 8 = 10 kEUR/ton. Total abatement cost is the sum of individual costs: Total Abatement Cost=MCA+MCB=4+10=14Total\ Abatement\ Cost = MCA + MCB = 4 + 10 = 14 kEUR
Answer
Each firm's abatement costs are 4 kEUR for firm A and 10 kEUR for firm B, with a total abatement cost of 14 kEUR.
Key Concept
Marginal Abatement Cost (MAC) is the cost of reducing one additional unit of pollution.
Explanation
The abatement costs reflect the costs incurred by firms to reduce emissions to meet regulatory requirements.
---
2 Answer
a
Tax Rate Calculation: To achieve a total effluent level of 16 tons, the government should set a tax rate equal to the marginal abatement cost at the target emissions. The tax rate TT can be derived from the equations: T=MCA+MCB=(12−eA)+(18−eB)T = MCA + MCB = (12 - e_A) + (18 - e_B). Setting eA+eB=16e_A + e_B = 16, we find T=12−(16−eB)+18−eBT = 12 - (16 - e_B) + 18 - e_B. Solving gives T=14T = 14 kEUR/ton
b
Abatement Costs and Taxes: Each firm will abate to the point where MCA=TMCA = T and MCB=TMCB = T. For firm A, 12−eA=14⇒eA=−212 - e_A = 14 \Rightarrow e_A = -2 (not feasible, so eA=0e_A = 0). For firm B, 18−eB=14⇒eB=418 - e_B = 14 \Rightarrow e_B = 4. Total abatement costs are MCA=12−0=12MCA = 12 - 0 = 12 and MCB=18−4=14MCB = 18 - 4 = 14. Total tax paid is T×(eA+eB)=14×16=224T \times (e_A + e_B) = 14 \times 16 = 224 kEUR
Answer
The tax rate should be set at 14 kEUR/ton, with firm A abating 0 tons and firm B abating 4 tons, leading to total taxes of 224 kEUR.
Key Concept
Environmental taxes are designed to internalize the external costs of pollution.
Explanation
The tax incentivizes firms to reduce emissions by making it costly to pollute, thus aligning private costs with social costs.
---
3 Answer
a
Tradable Quotas Price: In a competitive market for quotas, the price of a quota will equal the marginal abatement cost at the equilibrium emissions level. Given that each firm has an initial allocation of 8 tons, the total emissions are 16 tons. The price of a quota PP can be found where MCA=MCBMCA = MCB. Setting 12−eA=18−eB12 - e_A = 18 - e_B and solving gives P=6P = 6 kEUR/ton
b
Quota Transactions: Firm A will buy quotas to cover its emissions, while firm B will sell excess quotas. If firm A needs to emit 8 tons, it will buy 4 quotas from firm B. Total abatement costs for firm A are MCA=12−4=8MCA = 12 - 4 = 8 kEUR, and for firm B, MCB=18−4=14MCB = 18 - 4 = 14 kEUR. Total costs include the cost of quotas: Total CostA=8+(4×6)=32Total\ Cost_A = 8 + (4 \times 6) = 32 kEUR and Total CostB=14+(4×6)=38Total\ Cost_B = 14 + (4 \times 6) = 38 kEUR
Answer
The price of a quota is 6 kEUR, with firm A buying 4 quotas and total abatement costs of 32 kEUR for firm A and 38 kEUR for firm B.
Key Concept
Tradable quotas create a market for pollution rights, allowing firms to trade emissions allowances.
Explanation
This system encourages firms to reduce emissions where it is cheapest to do so, leading to overall cost-effective pollution control.
---
4 Answer
a
Auction Price Calculation: In a competitive auction for 16 tons, the price will be determined by the marginal abatement costs of both firms. The auction price PP will be set where MCA=MCBMCA = MCB. Solving 12−eA=18−eB12 - e_A = 18 - e_B gives P=6P = 6 kEUR/ton
b
Total Costs and Government Revenue: Each firm will incur costs based on their abatement and the price of quotas. Firm A will abate to 8 tons, costing MCA=12−8=4MCA = 12 - 8 = 4 kEUR, and firm B will abate to 8 tons, costing MCB=18−8=10MCB = 18 - 8 = 10 kEUR. Total costs for each firm are Total CostA=4+(8×6)=52Total\ Cost_A = 4 + (8 \times 6) = 52 kEUR and Total CostB=10+(8×6)=58Total\ Cost_B = 10 + (8 \times 6) = 58 kEUR. Government revenue from the auction is 16×6=9616 \times 6 = 96 kEUR
Answer
The competitive auction price is 6 kEUR, with total costs of 52 kEUR for firm A and 58 kEUR for firm B, generating government revenues of 96 kEUR.
Key Concept
Auctions for emissions allow for efficient allocation of pollution rights.
Explanation
This method ensures that the price reflects the true cost of emissions, promoting efficient resource allocation.
---
5 Answer
a
Subsidy Calculation: To achieve a total effluent level of 16 tons, the government needs to set a subsidy SS that incentivizes firms to reduce emissions. The subsidy should equal the marginal abatement cost at the target emissions level. Setting S=MCA+MCBS = MCA + MCB gives S=12−eA+18−eBS = 12 - e_A + 18 - e_B. To achieve 16 tons, we can set a baseline emission level of 8 tons for each firm
b
Total Costs and Government Expenditure: Each firm will receive a subsidy for emissions below 8 tons. If both firms reduce emissions to 8 tons, the total cost for firm A is MCA=12−8=4MCA = 12 - 8 = 4 kEUR, and for firm B is MCB=18−8=10MCB = 18 - 8 = 10 kEUR. The government expenditure on subsidies is S×16=16×6=96S \times 16 = 16 \times 6 = 96 kEUR
Answer
The per unit subsidy needed is 6 kEUR, with a baseline emission level of 8 tons, leading to total government expenditure of 96 kEUR.
Key Concept
Subsidies can encourage firms to reduce emissions by offsetting their costs.
Explanation
By providing financial incentives, subsidies can effectively lower the cost of abatement for firms, promoting environmental goals.
---
6 Answer
a
Summary Table: The results for each policy option can be summarized as follows: - Regulation: Total Abatement Cost = 14 kEUR, Total Industry Cost = 14 kEUR, Government Revenue = 0 kEUR. - Tax: Total Abatement Cost = 14 kEUR, Total Industry Cost = 224 kEUR, Government Revenue = 224 kEUR. - Tradable Quotas: Total Abatement Cost = 70 kEUR, Total Industry Cost = 70 kEUR, Government Revenue = 96 kEUR. - Auctioned Quotas: Total Abatement Cost = 52 kEUR, Total Industry Cost = 110 kEUR, Government Revenue = 96 kEUR. - Subsidy: Total Abatement Cost = 14 kEUR, Total Industry Cost = 96 kEUR, Government Revenue = -96 kEUR
b
Recommendation: Based on the analysis, I would recommend the auctioned quotas policy as it balances abatement costs and government revenue effectively while providing flexibility for firms
Answer
The auctioned quotas policy is recommended due to its balance of costs and revenues, promoting efficient emissions reduction.
Key Concept
Policy evaluation involves comparing costs and benefits of different environmental regulations.
Explanation
Analyzing various policies helps identify the most effective approach to achieve environmental goals while minimizing economic impact.
Solution
a
Marginal Abatement Cost for Firm A: The marginal abatement cost (MAC) for firm A can be derived from its abatement cost function CAC_A. The function is given by CA=(10−eA)22C_A = \frac{(10 - e_A)^2}{2} for eA≤10e_A \leq 10. Thus, the marginal abatement cost is the derivative of CAC_A with respect to eAe_A: MACA=dCAdeA=10−eA. MAC_A = \frac{dC_A}{de_A} = 10 - e_A. For Firm B, the abatement cost function is CB=(12−0.5eB)2C_B = (12 - 0.5 e_B)^2 for eB≤24e_B \leq 24. The marginal abatement cost is: MACB=dCBdeB=12−eB. MAC_B = \frac{dC_B}{de_B} = 12 - e_B.
b
Socially Optimal Level of Pollution: To find the socially optimal level of pollution, we need to equate the marginal abatement costs of both firms to the marginal damage from pollution. The damage function is given by D(E)=12E2D(E) = \frac{1}{2}E^2. The marginal damage (MD) is the derivative of the damage function: MD=dDdE=E. MD = \frac{dD}{dE} = E. Setting MACA+MACB=MDMAC_A + MAC_B = MD: (10−eA)+(12−eB)=E. (10 - e_A) + (12 - e_B) = E. We also have the constraint E=eA+eBE = e_A + e_B. Solving these equations will yield the socially optimal level of aggregate emissions
c
Unregulated Market Effluent Levels: In an unregulated market, firms will emit until their marginal abatement cost equals zero. For Firm A, setting MACA=0MAC_A = 0 gives eA=10e_A = 10. For Firm B, setting MACB=0MAC_B = 0 gives eB=12e_B = 12. Thus, the total effluent level in an unregulated market is: E=eA+eB=10+12=22. E = e_A + e_B = 10 + 12 = 22.
Answer
a) MACA=10−eAMAC_A = 10 - e_A, MACB=12−eBMAC_B = 12 - e_B
b) Socially optimal level of pollution requires solving MACA+MACB=EMAC_A + MAC_B = E
c) Unregulated effluent levels: eA=10e_A = 10, eB=12e_B = 12, total E=22E = 22
Key Concept
Marginal abatement costs and socially optimal pollution levels are crucial for understanding efficient pollution reduction.
Explanation
The marginal abatement cost curves help determine how much each firm should reduce emissions to minimize total costs, while the socially optimal level balances abatement costs with damage costs.
Solution
a
Change in Consumer Surplus: The consumer surplus decreases due to the tax, as the price consumers pay increases from P∗P^* to P∗−tP^*-t. The area representing consumer surplus before the tax is the triangle formed by the demand curve and the price line P∗P^*, while after the tax, it is the triangle formed by the demand curve and the price line P∗−tP^*-t. The reduction in consumer surplus can be calculated as the area of the triangle that is lost due to the tax
b
Change in Producer Surplus: The producer surplus also decreases as the price received by producers falls from P∗P^* to P∗−tP^*-t. The area representing producer surplus before the tax is the area between the price line P∗P^* and the marginal private cost (MPC) curve, while after the tax, it is the area between the price line P∗−tP^*-t and the MPC curve. The reduction in producer surplus can be calculated similarly as the area lost due to the tax
c
Change in Environmental Damage: The environmental damage decreases as the quantity produced falls from q∗q^* to qcq^c. The area between the marginal external cost (MEC) and the marginal private cost (MPC) curves represents the environmental damage. The reduction in this area indicates a decrease in environmental damage due to the tax, as it incentivizes lower emissions
d
Tax Revenues: The tax revenue generated by the government is represented by the rectangle formed by the tax amount tt and the quantity sold qcq^c. This can be calculated as Tax Revenue=t×qcTax\ Revenue = t \times q^c
e
Incidence of the Tax: The incidence of the tax refers to how the burden of the tax is shared between consumers and producers. Consumers pay a higher price, while producers receive a lower price. The change in consumer surplus and producer surplus indicates that consumers lose more than producers gain, suggesting that consumers bear a larger share of the tax burden compared to producers
Answer
The consumer surplus decreases, the producer surplus decreases, environmental damage decreases, tax revenues are generated, and consumers bear a larger share of the tax burden compared to producers.
Key Concept
The impact of a per unit tax on consumer and producer surplus, environmental damage, and tax revenue.
Explanation
The tax leads to a decrease in both consumer and producer surplus, a reduction in environmental damage, and generates tax revenue, with consumers bearing a larger burden of the tax.
© 2023 AskSia.AI all rights reserved