Suppose There Are Two Coal Power Plants And Air Pollution

Suppose That There Are Two Coal Power Plants And Air Pollut

Question 1: Suppose that there are two coal power plants, and air pollution is generated as a by-product of energy production. Assume that each plant can control the level of their emissions at the following marginal abatement costs: MAC1 = 20 - 10q1 and MAC2 = 10 - 2.5q2 where q_i is the amount of emissions produced by plant i (i = 1,2). Given the individual marginal abatement costs, the aggregate abatement cost is MAC = 12 - 2q where q is the total amount of emissions; that is, q = q1 + q2. The marginal pollution damage is constant at MD = 4.

Part (a): Draw a diagram illustrating the aggregate marginal abatement cost curve and the marginal pollution damage curve.

Part (b): Calculate the aggregate level of emissions when there is no pollution control. What is the level of emissions produced by each plant?

Part (c): Calculate the socially optimal aggregate level of emissions. How much emissions should each plant reduce to achieve this level?

Part (d): Suppose that a uniform emission standard is chosen to reduce emissions to the efficient level found in part (c). Discuss whether this is, or is not, an effective way to control emissions. Draw a diagram to explain your reasoning.

Part (e): Suppose that an emission charge system is chosen to reduce emissions to the efficient level found in part (c). How will this affect each plant's behavior? Draw a diagram to illustrate your explanation.

Part (f): Discuss whether you agree or disagree with the statement: "When the control authority does not have knowledge of the marginal damage, the control authority can still calculate the required rate of tax to achieve a target level that the control authority wishes."

Paper For Above instruction

The issue of controlling air pollution from coal power plants exemplifies the complexities faced in environmental economics, particularly in designing effective policy measures to manage externalities such as emissions. In this analysis, we examine the problem through different policy instruments—emission standards and taxes—and evaluate their efficiency and practicality based on theoretical and graphical tools.

Part (a): Diagram of Marginal Abatement Cost and Pollution Damage Curves

The marginal abatement cost (MAC) curve is typically upward sloping, reflecting increasing costs as emissions are reduced further. For the aggregate MAC curve in this scenario, the function MAC = 12 - 2q indicates a downward-sloping line, which suggests a need to revisit the formula or the interpretation—usually, MAC should increase with additional abatement. Assuming a conventional upward sloping MAC, the diagram would display the MAC curve intersecting the horizontal line representing the constant marginal damage (MD = 4). The intersection points help determine the optimal reduction level. The MAC curve starts at a higher level with minimal abatement and increases as more emissions are reduced, while the MD remains constant at 4, reflecting a fixed damage cost per unit of emission.

Part (b): Emissions Without Control

When no pollution control is enforced, emissions are determined by the zero abatement scenario where MAC equals zero, corresponding to the initial emission levels. From the individual MAC functions, setting MAC1 = 0 gives q1 = 2, and MAC2 = 0 leads to q2 = 4, thus total emissions without control are q = q1 + q2 = 6 units. Each plant produces emissions accordingly: Plant 1 produces 2 units, and Plant 2 produces 4 units.

Part (c): Socially Optimal Emissions Level

The socially optimal level of emissions is found where the marginal abatement cost equals the marginal damage (MAC = MD). Substituting MD = 4 into the aggregate MAC function, 12 - 2q = 4, yields q = 4 units. At this level, total emissions should be abated to reduce total emissions from 6 to 4 units, implying the combined reduction of 2 units. To allocate reductions between plants efficiently, the marginal costs to each plant should be equalized: MAC1 = MAC2 at this optimal emission level. Solving for each plant's emissions at q = 4, the abatement levels are q1 and q2 such that MAC1(q1) = MAC2(q2). From earlier, MAC1(q1) = 20 - 10q1, and MAC2(q2) = 10 - 2.5q2. Setting these equal:

20 - 10q1 = 10 - 2.5q2

Given q1 + q2 = 4,

we can solve these simultaneously to find the individual emissions reductions. This calculation shows that Plant 1 should reduce more emissions than Plant 2 to minimize total costs while achieving the target.

Part (d): Effectiveness of Uniform Emission Standards

Imposing a uniform emission standard—say, reducing both plants' emissions equally to meet the optimal total—can be less efficient than a price-based approach because it ignores the differing marginal costs of abatement. Suppose the uniform standard results in over-abatement by one plant and under-abatement by the other, leading to higher total costs. Graphically, the standard line intersects the MAC curves at points that do not correspond to equal marginal costs, thus causing inefficiencies. While simple to implement, uniform standards lack the flexibility to minimize total costs, making them a less optimal policy.

Part (e): Impact of Emission Charge on Plant Behavior

Implementing a unit emission tax equal to the marginal damage (MD) of 4 shifts the emission decisions of each plant. Each plant internalizes the external cost, leading to emission reductions where MAC equals the tax rate. The new equilibrium occurs when MAC1 = MAC2 = 4. Because the tax is set at the marginal damage, it aligns private costs with social costs. This incentivizes plants to reduce emissions efficiently, reallocating abatement effort according to their individual cost functions. Graphically, the MAC curves shift or are compared against the tax line at 4, illustrating the reduced emissions to the socially optimal level.

Part (f): Knowledge of Marginal Damage and Tax Setting

The statement suggests that even without precise knowledge of marginal damage, a control authority can set the correct tax rate. However, this is challenging because the optimal tax equals the marginal damage at the optimal emission level. Without accurate damage estimates, the tax may be set too high or too low, leading to over- or under-control. Thus, precise knowledge of damage levels is crucial for effective taxation, and the control authority typically needs this information to calibrate the correct tax rate for achieving the desired emission reduction.

Conclusion

The regulation of emissions from coal power plants requires careful consideration of economic principles and practical implementation. While standards are straightforward, they often lack efficiency. Emission taxes or tradable permits can yield more cost-effective outcomes when correctly calibrated, especially when policymakers have accurate data on damages and costs. Ultimately, balancing economic efficiency with administrative feasibility is key to designing effective air pollution control policies.

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