Externalities Econ 320 Homework 5 Externalities 1 The private marginal benefit

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```					Econ 320

Homework #5

Externalities

1. The private marginal benefit for loud parties is 10 – X, where X is the decibel level of the party. The cost of cranking up the stereo another decibel is \$5. For each decibel, the neighbors must put in another pair of earplugs. Each pair of earplugs costs \$2. a. Make a graph with the private marginal benefit, the private marginal cost and the social cost. Be sure to label your axes. \$/X

7 5 2 b.

MSC MPC MD MB

X In the absence of government intervention, how loud is the party? Set Private MC = Private MB 5=10-X  X = 5 What is the socially efficient level of noise? What would be the social gain in moving to that level? Set Marginal Social Cost = MB  7=10-X  X = 3 Deadweight loss of being at the wrong level is area between MSC and MB going from the inefficient to the efficient level—Area AB above =1/2 base* height = ½ (5-3)*(7-5) =2 Suggest a tax policy that would achieve the socially efficient provision. How much revenue would the tax raise? A tax of \$2 per unit would make the MPC = MSC This tax would decrease the level down to 3 decibels and would raise 2*3 = \$6 of revenue Suppose that the neighbors have the right to peace and quiet and the cops will enforce their right if they call. What does the Coase theorem suggest will happen? Suggests the partiers will pay the \$2 for each pair of the neighbors earplugs and the noise will be 3 decibels. Suppose that the partiers have the right to be as loud as they want and the police will not enforce any noise complaints. What does the Coase theorem suggest will happen? Suggests the neighbors will pay up to \$2 for the partiers to crank it down to 3 decibels.

c.

d.

e.

f.

2. Two types of firms emit gunk, a nasty pollutant. There are ten firms of each type in the town Effluvia. “Gunk emissions” are a productive input, just like any other type of input. The price of gunk emissions is 0. Input demand by type 1 firms is P = 100 – g Input demand by type 2 firms is P = 150 – g a. Given a current price of 0, how much does each firm emit? What are total emissions? P=0 Type1: 0 = 100-g  g = 100 10 firms so G1 = 1000 Type 2: 0 = 150-g  g = 150  10 firms so G2 = 1500 Total: G = 2500 b. Suppose Effluvia wants to reduce emissions to 1000 units in total. What per unit tax would reduce emissions to that level? Find the price that reduces total to 1000 G1 = 10(100-P) G2 = 10(150-P) 1000 = 2500 – 20P  P = 75 c. Are the 1000 units allocated efficiently across the 20 firms with the tax?

Yes—each firm is equating the marginal benefit with the marginal cost. Note that type 1 firms that have a lower input demand for g use less (25 units of g each) than higher demand type 2 firms (75 units of g each), but that both have the same value of that final unit of gunk (plug their quantity into the demand functions—both have a marginal value = P = 75) d. Now suppose that each firm is given the right to emit 50 units of gunk. Firms are allowed to buy and sell these rights. What is the aggregate demand for emissions? Find aggregate demand as above G = 2500-20P (remember to add quantities and not prices) e. What is the aggregate supply of emissions? There are 50*20 =1000 permits f. What is the competitive price and quantity of emissions? Are the 1000 units allocated efficiently? Set demand = supply

g.

1000=2500-20P  P =75 Note this is the same outcome as with a tax—yes efficient Now suppose that firms are given the right to emit 50 units of gunk, but emission rights cannot be traded. Are the 1000 units of emissions allocated efficiently?

No—type 2 firms value a marginal permit more highly than type 1 firms, so there is a potential for a mutually beneficial trade. You can see their marginal values by using the demand functions: Firm 1’s marginal value is P = 100-50 = 50—That is, they would be willing to pay \$50 for the 50th unit of gunk Firm 2’s marginal value is P = 150-50=100—That is, they would be willing to pay \$100 for the 50th unit of gunk. Firm 2 has a much higher marginal value than firm 1, so these two firms could get together and make a mutually beneficial trade, where firm 2 ―buys‖ gunk from firm 1—essentially what happens with tradable permits. 3. For each of the following situations, is the Coase theorem applicable? Why or why not? For each of the following you want to think about the potential obstacles to Coase bargaining: --Are property rights insecure? --Is there a problem with information—assessing the value of the damage? --Holdouts/Free ridders—Is there a large group that must negotiate? --Transaction costs in general—what other obstacles are there to bargaining? --Credit constraints—is the party without the property right constrained from making a side payment? a. A group of college students in a dormitory share a communal kitchen. Some of the users of the kitchen never clean up the messes they make when cooking. In Brazil, it is illegal to catch and sell certain tropical fish. Nevertheless, in some remote parts of the Amazon, hundreds of divers come to capture exotic fish for sale on the international black market. The presence of so many divers is depleting the stock of exotic fish. In Utah, the government sells grazing permits to allow livestock to graze on public lands. These permits can be bought and sold by any party. Ranchers in Utah favor using public lands for livestock; environmentalists argue that grazing destroys the fragile desert ecosystem for centuries.

b.

c.

4.

Consider the following scenarios. For these, Q is the amount of emission reduction (not the amount of emissions):

Scenario A: The MB to society for reducing emissions is MB=1000. The assumed MC of reducing emissions is 10Q. Later, it is discovered that MC=20Q. Scenario B: The MB to society for reducing emissions is MB=11,000 – 100Q. The assumed MC of reducing emissions is 1000. Later, it is discovered that MC=2000. Answer the following questions for EACH scenario: a. b. c. d. e. What would be the optimal Q of emission reduction if the assumed MC were right? What tax would lead to that level of emission reductions? Now suppose that we learn later that the actual MC. In that case, what would have been the correct amount of emissions reductions? What is the deadweight loss associated with imposing the quota amount you found in part (a) given the actual MC? (A diagram will help you.) What is the deadweight loss associated with imposing the tax you found in part (b) given the actual MC? (A diagram will help you.)

What is the difference between Scenario A and B? Which do you think is more applicable to global warming? Why? Scenario A: a. If assumption were right MB = MC 1000=10Q Q = 100 The tax under the assumption is tax = MC at optimal quantity=10*100=\$1000 With Actual MC=20Q, the correct emissions would be MB=MC 1000=20Q Q = 50 To answer D and E, you need to figure out the quantity that would be produced with the tax/quota. With the quota, Q = 100. The actual MC = 100*20 =2000 DWL = ½ (100-50)(2000-1000) = \$25,000 e. The tax is \$1000 which is also the MB. The firm will cut emissions to where the tax = MC so 1000=20Q Q=50 which is the efficient quantity. Therefore there is no deadweight loss.

b. c.

d.

Scenario B:

a.

b.

If assumption were right MB = MC 11000-100Q=1000 Q = 100 The tax under the assumption is tax = MC at optimal quantity=\$1000

c.

d.

With Actual MC=2000, the correct emissions would be MB=MC 11000-100Q=2000 Q = 90 To answer D and E, you need to figure out the quantity that would be produced with the tax/quota. With the quota, Q = 100. The actual MC =2000 DWL = ½ (100-90)(2000-1000) = \$5,000

e.

The tax is \$1000 which is less than the MC of cutting emissions. This means no emissions are cut Q =0. DWL = ½ (100) (11,000-2000) = \$450,000

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