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2017 SPRING

FINAL

ENVIRONMENTAL ECONOMICS AND POLICY 101

ECONOMICS 125

TRUE / FALSE For each question, answer true or false. Then, explain. You must explain your answer regardless of whether it is true or false. Two points are awarded for getting True/False correct. Two more points are awarded for the explanation.

1. There is uncertainty about the costs and benefits of carbon dioxide abatement. A research institution finds that imposing a tax on CO2 emissions leads to a lower expected loss of societal welfare than imposing a cap and trade, because of this uncertainty.

True or false: This is consistent with the marginal cost curve being relatively steep compared to the marginal benefit curve for carbon dioxide abatement. (4 points)

True. Weitzman model tells us when there’s uncertainty about MC, a price policy (tax) is more efficient if MC is relatively steep compared to MB.

2. A coal-fired power plant produces electricity, which causes pollution. A nearby laundry suffers from a negative externality due to soot from coal production. Suppose that tax policies put in place have ensured that the quantity of electricity produced by the plant is the socially optimal amount.

True or false: Coasian bargaining between the plant and the laundry might reduce social welfare. (Assume the tax still exists, and Coasian bargaining cannot change the tax.) (4 points)

True. If there’re only tax policies, the electricity production is the socially optimal amount, then after Coasian bargaining, the electricity production will not be the socially optimal amount, therefore the social welfare might be reduced.

3. True or false: According to the rational economic model of crime that we discussed, it is always possible in theory to ensure perfect compliance, even when the audit/detection rate is low (p), so long as the penalty if caught (f) is sufficiently high. (4 points)

True. As long as p*f is sufficiently high, it’ll ensure perfect compliance.

4. In the ambient pollution model that we described in class, we said that the tax paid would be equal to t(E-E*), where E* is the social optimal emission level, E is ambient emissions, and t is set equal to marginal damages.

True or false: if the tax rate were instead t(E-E*-1), then the policy will not induce the optimal amount of emissions. (4 points)

False. The optimality condition is given by C’(E)=t. Thus, even if the tax rate were instead t(E-E*-1), then the policy will still induce the optimal amount of emissions.

5. Suppose that a coal-fired power plant emits pollution, but an optimal cap and trade system has been put in place. Now, suppose that the power plant receives an efficiency upgrade, so that it produces more electricity per unit of coal burned. Because of the rebound effect, the plant will be used more.

True or false: The rebound effect is inefficient (it lowers social welfare). (4 points)

False. Consumers’ utility are higher through more electricity usage at lower cost.

6. Demand in the market for Sprockets is Q=100 – 3P. Supply in the market for Sprockets is Q=20 + 0.3P.  Supply is perfectly competitive.

True or false: If a $1 tax is imposed on Sprockets, consumer surplus will fall by more than producer surplus. (4 points)

False. Supply is more inelastic than demand, thus producers will share more of the tax burden.

Short answer questions. Write a brief answer with explanation for each question. Points vary by question. Show your work.

7. Researchers estimate that the Value of a Statistical Life (VSL) in Country Abracadabra is $10 million using standard hedonic methods of labor markets. (Assume the data on wages and fatalities are measured accurately.)

You are a resident of Abracadabra. You are diagnosed with a terminal disease. There is a cure available, but it is not covered by insurance and you will have to pay for it.

A friend of yours describes to you the research on the VSL and says: “I guess you should be willing to pay up to $10 million for a cure for your disease.”

List three reasons why you friend’s analysis may be incorrect. Explain each in about 2 sentences. (6 points total, up to two points for each explanation.)

Reason 1:

Conceptually wrong: VSL does not say how much you are WTP for a particular life (its about risk)

Reason 2:

Convexity: VSL estimates differ at different points in risk, so estimates from low-risks may not be valid for getting a full 0 to 1 probability range

Reason 3:

Accounting for other differences: VSL is a hedonic estimate, likely biased by other differences problem.

8. Here are two brief questions about green subsidies. (4 points total)

a. Very briefly explain why green subsidies are not as efficient as a Pigouvian tax. (2 points)

Green subsidies distort market size. The price of overall negative externality generating        commodity becomes too cheap.

b. Very briefly explain a scenario in which a green subsidy is justified. (2 points)

When green subsidies have spillover effect.

9. A tech company is considering establishing an online library. It wants to find the optimal number of e-books (X) to offer as well as the total number of members (N) for the platform. The more books there are, the more value each member gets. Having more members slows down speed and jams the servers, lowering the value of a given number of books for all other users. Suppose that for each member the total benefit of the e-library is B=B(X,N). The cost of providing the public good is C(X). (4 points total)

a. State the formal optimality conditions for X and N in algebraic form. (2 points)

NMB_X=C’(X)

MB_N=-NB(X,N)

b. Explain conceptually the meaning of the optimality conditions in the context of the online library. That is, explain in English what the optimality conditions mean, using the case of the online library. (2 points)

1. The quantity of e-books is at social optimal: the marginal benefit of one additional e-book equals to the marginal cost.

2. Congestion of e-book using is at social optimal: the marginal externality cost of congestion equals to the benefit of including one additional user.

10. Jim lives by the ocean in a country called Acadia, which occasionally experiences strong storms. Strong storms may damage Jim’s house by causing flooding. Jim can prevent flooding by building a seawall near his home. The higher is Jim’s sea wall, the less damage he will experience. (8 points total)

a. Because of climate change, sea levels in Acadia rose by 0.2 meters. Before the change in sea level, Jim had spent 10,000 on his sea wall. After the sea level rise, Jim spent 40,000 on his sea wall. What can you conclude about Jim’s willingness to pay to reduce the rise in the sea level? On what does your answer depend? (Assume Jim has no insurance, and he must pay for any damages that occur.) (4 points)

WTP=30000/0.2=150000. We have to assume that sea level rise is the only factor that has been changed.

b. In order to attract more residents, the government of Acadia decides to pay the cost of repairing homes damaged by flooding. Briefly explain how this might distort Jim’s behavior. (2 points)

Jim will choose to live as close to the ocean as possible.

c. Is it possible for Jim to have flood insurance for his home without causing the distortion you described in part (b)? Explain why or why not. (2 points)

If Jim has paid actuarially fair insurance for the home, then there is no distortion.

11. The graph below depicts a public good. The upward sloping line is the marginal cost curve for the firm of providing a quantity X of the public good. There are three consumers of the public good, and they all have identical demand. The downward sloping lines represent their demand (marginal benefit) curves for quantity X of the public good. The lowest line (D1) is the demand for the first consumer. The middle line (AD2) is the aggregate demand that would exist if there were two consumers. The top line (AD3) is the aggregate demand of all three consumers.

Assume that the seller of the public good is a monopolist who wants to maximize profits. They sell the public good through an entrance fee that gives each consumer access to all X units of the public good. (5 points total)

a. Use the graph to indicate the quantity of the public good X that the monopolist will choose to build. (2 points)

b. Use the graph to indicate the entrance fee they will charge each person. (2 points)

c. Is this the socially efficient amount of the public good? Explain briefly. (1 point)

Yes. Monopoly is charging everyone’s TWTP, but social optimal amount is achieved.

12. A firm uses a chemical process that takes 10 gallons of Input and makes 8 gallons of Final Product, and 2 gallons of Toxic Waste. (Note that this is not a one-to-one ratio.) It is expensive to recycle the waste, but the firm can also dump it in the river for free. The government can observe the amount of Input that the firm buys, and it can observe recycled waste (assume recycling occurs at another facility), but the government cannot observe toxic waste dumped into the river.

The social cost per gallon of waste is $5 per gallon. The cost to the firm of recycling the waste is $2.50 per gallon. The marginal cost of producing the final output (ignoring waste) is 2X, where X is gallons of final product. Demand for the final product is 200 – 2P, where P is the price of the final product. (4 points total)

a. The government will set a tax per gallon of Input purchased, and a rebate per gallon of waste recycled. If this two-part instrument is set as we described in class, what should these two tax rates be? (2 points)

$1 tax on inputs and $5 refund on recycled waste

b. What is the socially optimal amount of toxic waste dumped into the river? (2 points)

Zero. As the marginal benefit of recycling waste is always greater than the marginal           cost.

Longer questions with several parts. Write a brief answer with explanation for each question. Points vary by question. Show your work. Label key algebra steps. This facilitates assigning partial credit if you make an algebra mistake.

Problems continue on more than one page.

13. There are five Neighborhoods and five types of households in a residential area. The price of housing in Neighborhood A is always 0. The price of living in Neighborhoods B-E is equal to the number of residents. Each household’s payoff is given by , where is a households’ marginal willingness to pay for Environmental Quality (EQ) and P is the price of housing in the neighborhood. This is the same setup as we did in class and on the problem set.

The table below shows the equilibrium. However, the price of neighborhood C and E is not shown. (7 points total)

Neighborhood	Price	EQ	Residents
A	0	0	20 Yellow, 15 Red
B	3	1	2 Red, 1 Blue
C	???	2	??? Blue
D	13	3	3 Blue, 10 Orange
E	???	4	3 Orange, ??? Green

a. For each type list in the table below, if you can infer that type’s exact value of write it in the space provided. If you cannot infer exactly, circle “not enough information”. (3 points)

Do not assume that is an integer, and do not assume that every type has a different value of . I.e., could be 0.25, or 1.75, and both yellow and red could both have =1.75. If you can infer an exact value, then fill in the answer, if you cannot infer an exact value, then say “not enough information”.

Yellow	Not enough information
Red	Not enough information	3
Blue	Not enough information	5
Orange	Not enough information
Green	Not enough information

b. What do you know about the number of Blue people living in C? (Can you say exactly how many Blue people must be living in C? Or, can you determine a range of possible values?) Explain briefly. (2 points)

Utility of Blue in B is the same as in C. Thus,

5*1-3=5*2-P_C. So, Price of C, which is the number of blue in C, is 8.

c. What do you know about the number of Green people living in E? (Can you say exactly how many Green people must be living in E? Or, can you determine a range of possible values?) Explain briefly. (2 points)

Price of E has to be greater than Price of D. So, P(E)>13. Since there are 3 oranges in E, number of green in E must be greater than 10.

14. Alice, Bob and Cliff each have total benefit from a public good equal to 2*X (Alice), 4*X (Bob) and 8*X (Cliff); where X is the quantity of the public good. The total cost of producing this good is TC=X². (9 points total)

a. State the Samuelson condition in general terms (use our standard notation, not the values from this problem). (1 point)

b. What is the optimal quantity of the public good X in this case? (2 points)

MB_A=2, MB_B=4, MB_C=8. Then the aggregate MB=14. MC=2X.

So, X*=14/2=7.

c. Suppose that the level of the public good was set through the median voter mechanism that we described in class, where each person chooses a per-capita tax rate, and the median value becomes the actual tax. (Recall that in this mechanism, each person has an incentive to honestly choose the tax level that would maximize their utility, knowing that all people will pay the tax.) How much of the public good will be provided? What tax will each person pay? (2 points)

3MB_B=3*4=MC. X*=12/2=6.

TC=36. Each pay 36/3=12 tax.

d. Bob will be the median voter. Cliff considers bribing Bob by offering him a side payment to get him to change his vote so that the socially optimal level of X that you found in part (b) is provided. Can such a bribe benefit both Cliff and Bob? Explain why or why not. (2 points)

If bribing, denoted by B, occurs, X=7, tax=7^2/3=50/3.

Before bribe, Bob’s NB=12, Cliff’s NB=36

Bob’s net benefit is 4*7-50/3+B, Cliff’s net benefit is 8*7-50/3-B.

Thus, as long as 4*7-50/3+B>12 and 8*7-50/3-B>36, bribing could occur.

This means 1/3

e. Suppose that a social planner intervenes and does provide the socially optimal amount by taxing everyone equally, instead of the amount you found in part (c). Is this a Pareto improvement? (Your answer should consider all three people.) (2 points)

No, because Alice is surely worse off, this is not a Pareto improvement.

15. The total benefit of producing a good for a firm is TB = 20Q - 0.5Q². The firm faces a constant marginal cost of 10. However the production of the good imposes a negative externality to a nearby city. The total external cost borne by the city is TEC = 0.75Q². (12 points total)

a. What is the firm’s profit maximizing level of the good? Label this Q_p. (Assume there is no policy intervention, and there is no Coasian bargaining.) (2 points)

MB=MC. 20-Q=10. Q_p=10.

b. What is the firm’s profit (producer surplus)? What is the total harm imposed on the city? (2 points)

TB-TC=20Q-0.5Q^2-10Q=100-50=50.

TEC=0.75Q^2=75.

c. What is the socially efficient level of Q? Label this Q_s. (2 points)

MB=MC+MEC, 20-Q=10+1.5Q. Q_s=4.

d. Suppose the firm and the city reach a Coasian solution where the city chooses to pay the firm a transfer equal to marginal damages per unit of emission above optimum (i.e., city pays firm the marginal damage the production of the good imposes to the city from Q_s to Q_p). Under this scenario, how much profit does the firm make? What cost is imposed on the city? (2 points)

e. Does Coasian bargaining lead to a Pareto improvement? Explain. (2 points)

Yes. After Coasian bargaining, city’s cost is the same, but the firm’s profit increased from area 1+2+3 to area 1+2+3+4 (see part d for the area labelling).

f. What is the maximum amount that the city would pay the firm to change pollution from Q_s to Q_p? (2 points)

Max=area 3+4=1/2*(1.5*4+15)*(10-4)=63.

EXTRA SHEET