EC 435 Instructions: Your answers may be typed or handwritte

EC 435

Problem Set 1

Due September 28

F15

Papke/Loaiza

Instructions: Your answers may be typed or handwritten. Please turn in a STAPLED hardcopy of your solutions at the beginning of class on the due date. You are free to work with others, but each student must hand in his or her own work for grading.

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1. To comply with the Clean Air Act, a region must abate (reduce) pollution emissions by 300 units. Before regulation, two firms emit 600 units of pollutants. The marginal abatement cost (MAC) of firm A is given by

MAC_A = .5Q_A

where Q_A is the quantity of pollution abated by the firm. The MAC for firm B is MAC_B = Q_B

a. Suppose the EPA requires each firm to abate by 150 units. What is the MAC for each firm under this command and control regulation? Is it the least-cost allocation of abatement? What is the total cost of this policy?

b. What is the least cost (efficient) allocation of abatement between the two firms? What is the reduction in abatement cost relative to command and control regulation?

c. Suppose the EPA auctions off 300 pollution permits at a competitive auction. Each permit allows a firm to pollute by one unit. What is the market price of these permits?

2. A pulp mill has the right to discharge waste into a river. The waste reduces the number of fish, causing damage for recreational fishing. Let Q denote the quantity of waste dumped. The marginal damage (value of lost fish for an extra unit of waste) denoted MD is

MD = 2 + 5Q.

The marginal benefit (MB) of dumping waste (the cost of shipping an extra unit of waste to another dump site) is given by the equation

MB = 30 – 2Q.

a. Draw a diagram showing the efficient quantity of waste that can be dumped in the river, and the quantity dumped by a firm that ignores the damages it causes for fishing.

b. Calculate the efficient quantity of waste. What is the effluent fee in dollars per unit of waste that would cause the firm to dump only an efficient quantity of waste?

3.(Text problem11) Warrenia has two regions. In Oliviland, the marginal benefit associated with pollution cleanup is MB= 300 – 10Q, while in Linneland, the marginal benefit associated withpollution cleanup is MB= 200 – 4Q. Suppose that the marginal cost of cleanup is constant

at $12 per unit. What is the optimal level of pollution cleanup in each of the two

regions?

4. (Text problem 12) The private marginal benefit associated with a product’s consumption is PMB =360 –4Qand the private marginal cost associated with its production is PMC= 6Q. Furthermore,the marginal external damage associated with this good’s production is MD=

2Q. To correct the externality, the government decides to impose a tax of Tper unit

sold. What tax Tshould it set to achieve the social optimum?

5. (Text problem 13) Suppose that demand for a product is Q= 1,200 – 4Pand supply is Q= –200 + 2P.Furthermore, suppose that the marginal external damage of this product is $8 per

unit. How many more units of this product will the free market produce than is socially

optimal? Calculate the deadweight loss associated with the externality.

6. (Text problem 14) The marginal damage averted from pollution cleanup is MD= 200 – 5Q. The marginal cost associated with pollution cleanup is MC= 10 + Q.

a. What is the optimal level of pollution reduction?

b. Show that this level of pollution reduction could be accomplished through taxation.

What tax per unit would generate the optimal amount of pollution reduction?

7. (Text problem 17) FirmsAand Beach produce 80 units of pollution. The federal government wants toreduce pollution levels. The marginal costs associated with pollution reduction are

MC_A= 50 + 3Q_Afor firm Aand MC_B= 20 + 6Q_Bfor firm B, where Q_Aand Q_Bare the

quantities of pollution reducedby each firm. Society’s marginal benefit from pollution

reduction is given by MB =590 – 3Q_tot, where Q_totis the total reduction in pollution.

a. What is the socially optimal level of each firm’s pollution reduction?

b. How much total pollution is there in the social optimum?

c. Explain why it is inefficient to give each firm an equal number of pollution permits(if they are not allowed to trade them).

d. Explain how the social optimum can be achieved if firms are given equal numbersof pollution permits but are allowed to trade them.

e. Can the social optimum be achieved using a tax on pollution?