Question

There are two firms, A and B. Prior to any regulations, A emits 40 tons of carbon dioxide, and B emits 60 tons. A's marginal abatement costs are given by MACa = 3xa, where xa is its reduction in emissions. B's marginal abatement costs are given by MACb = 2xb, where xb is its reduction in emissions. 1. Draw a graph of the marginal abatement costs for the two firms, and the "aggregate" or social marginal abatement cost curve. Write the equation for this "aggregate" MAC curve. 2. The government decides to reduce total emissions by 50 tons. The EPA designs a command-and-control policy where each firm is allowed to pollute no more than 25 tons. What are the total abatement costs for each firm? What are the total costs of achieving this reduction? 3. The EPA changes its policy to allow tradable permits, but the initial allocation of permits remains the same as above (i.e. each rm gets 25 permits; they are freely allocated to the firms). Is there any incentive for the firms to buy or sell permits? What is the market price for permits in equilibrium? What are the total costs of the pollution reduction? 4. Instead of tradable pollution permits, suppose that now the EPA imposes a tax to reduce emissions. What tax (per ton) will achieve a 50-ton reduction in emissions? You may assume that the 25 ton limit on emissions is relaxed, and that the EPA only imposes the 50-ton reduction in emissions. 5. Give the tax in part (4), how much does each firm emit? How much does the government receive in revenue from the tax?

Answer 1

The graph of the marginal abatement costs for firms A and B can be drawn by calculating the costs for different levels of emissions reduction using their respective MAC curves. The 'aggregate' or social MAC curve can be found by adding up the reduction in emissions and corresponding costs for each level of emissions reduction across both firms.

Step-by-step explanation:

To draw the graph of the marginal abatement costs for firms A and B, we can calculate the costs for different levels of emissions reduction using their respective MAC curves. When we plot these points on a graph, we can see the shapes of the curves. To find the 'aggregate' or social MAC curve, we can add up the reduction in emissions and corresponding costs for each level of emissions reduction across both firms.

The total abatement costs for each firm can be found by multiplying their MAC by the amount of emissions reduction they are required to make. The total costs of achieving the 50-ton reduction can be calculated by summing up the abatement costs for both firms. In a system of tradable permits, there would be an incentive for firms to buy or sell permits depending on their costs of abatement. The equilibrium market price for permits would be determined by the supply and demand of permits. The total costs of pollution reduction would still be the sum of the abatement costs for both firms.

In a system of pollution tax, the tax rate per ton would need to be set such that it achieves the desired reduction in emissions. The tax rate would depend on the cost of abatement for each firm. Each firm would then determine their optimal level of emissions reduction based on the cost of abatement and the tax rate. The number of emissions for each firm can be calculated based on their optimal level of emissions reduction. The government would receive revenue from the tax equal to the tax rate multiplied by the total emissions reduction.