代做AEM 1500: Introduction to the Economics of Environmental and Natural Resources Problem Set #4帮做Py

 

AEM 1500: Introduction to the Economics of Environmental and Natural Resources

Problem Set #4, 100 points. 

All graphs should be clearly labeled (vertical and horizontal axis) and all other work legible.  Illegible work will receive no credit.

1. Imagine a firm that produces fertilizer with private MPC = $2/pound. Fertilizer production leads to runoff into local water supply and damages the enjoyment of nearby residents generating a MD = $2/pound. The demand (MB) of fertilizer use is given by the demand curve, P = 12 – Q.

a. Given this information, draw a diagram that depicts the private market equilibrium and solve for the values of the equilibrium price and quantity in an unregulated market? (10 points).

b. Draw a new diagram that depicts the socially optimal quantity of fertilizer and solve for the socially efficient price and quantity (10 points)

c. Show the area that represents the deadweight (welfare) loss from the private equilibrium relative to the social optimum and show that area on the diagram in (b).  Compute its value. (20 points).

d. Now suppose the government wishes to intervene to correct this externality and sets a tax rate of $2/pound that must be paid by the fertilizer company. Draw a new diagram with the firm’s new private marginal cost (the sum of the tax and the MPC) and the original demand curve. With the tax in place, how much fertilizer will be produced and sold?  (10 points).

2. Suppose two power plants emit SO2 in an airshed. A large power plant and a large smelter each pollute 10 million tons of SO2.  The total abatement cost (TAC) and marginal abatement cost (MAC) functions for the two firms are:

Power Plant : TAC1 = 20 + 8A + 1.5A²                 MAC1 = 8 + 3A

Smelter: TAC2 = 15 + 5A + 4A²                   MAC2 = 5 + 8A

Where A is the amount of SO₂ abated in millions of pounds. Remember that abated quantity + polluted quanity =total pollution before the policy.

a. In the absence of regulation, assuming these firms are strictly profit maximizing companies, how much money will each firm spend on abatement?  How much total pollution will there be at this abatement level? (20 points).

b. Suppose the EPA decides to regulate this pollution and they require that each plant will abate 50% of its SO₂ emissions. By how much does each plant cut back its emissions? What are the corresponding abatement costs for each plant and what is the total of their costs? (10 points).

c. Compute the Marginal Abatement Cost for each firm at this reduction. How much pollution will each firm generate? Is this the least cost approach to cleaning up 10 million tons of SO2? How do you know? (hint: are the MACs equal across the two firms?) (10 points).

d. Suppose the EPA requires that the Power Plant abate 7 tons and the Smelter abate 3 tons.  What will the MAC for each firm be? What will the TAC be when summer over both firms?  How does this compare to the total costs in answer b? dIs this solution technically more efficient than the 50% equal split? (10 points).