Economics 160
STUDY QUESTIONS
EXTERNALITIES AND PUBLIC GOODS
1. What is a negative externality (external cost)?... positive externality (external benefit)? Give examples. What are the efficiency implications of externalities? Why do externalities exist?
2. Use the table below to answer the following questions.
Quantity of steel produced TCprivate TCext TCTotal(social) MCprivate MCTotal MR
0 0 0 0 ------
1 $50 $10 .
2 $110 $20 .
3 $180 $30 .
4 $260 $40 .
5 $350 $50 .
a. Fill in the rest of the table. Assume that the price of steel is $80 per unit and that the steel firm is a price-taker.
b. How many units of steel will the steel firm produce? What is the efficient rate of output?
c. If the government was to impose a fine on the steel firm, what would be the optimal fine to
levy? That is, what fine would cause the steel firm to voluntarily produce the efficient rate of
output? Explain.
3. Use the following data to answer the next set of questions.
% of pollution eliminated MBsocial of clean air MCsocial of pollution abatement
0% ------
50% $10 million $9 million
100% $8 million $10 million.
A steel firm is emitting pollution into a residential neighborhood. The above table indicates
the value the residents place on additional units of clear air (this information is given in the MBsocial column) and the cost to the firm of reducing pollution (this information is given in the MCsocial column).
a. Assume that property rights are given to the firm and that transactions costs = 0. How many units of clean air will there be? EXPLAIN.
b. Assume that the property rights are given to the local residents, how many units of clean air will there be? Continue to assume that transactions costs = 0.
c. What is the Coase Theorem? Do your answers to parts (b) and (c) confirm this theorem?
d. If it is impossible to define or enforce property rights over the use of the air, or if transactions costs are prohibitively high, then how many units of clear air (% of pollution eliminated) will be produced in the absence of government regulation? Assume that the firm effectively has the right to pollute.
e. In the presence of high transactions costs, what can the government do to bring about the
efficient outcome?
4. What is a common pool resource? What are some examples. Why would these resources tend to be overused?
4 (continued). Use the following table to answer the questions below.
Number on Boat (L) Total Product on Boat (Q) MP AP Social Total
0 0 ------2000
1 10
2 18
3 23
4 24
5 23
6 19
7 14
8 8
Assume that there are 1000 fishermen and that each is able to catch 2 fish per unit of time on shore. Thus, it they all stayed on shore, the total catch (Social total) is 2 times 1000=2000.
a. Fill in the rest of the table.
b. What is the efficient number of fishermen to let on the boat? Explain your answer in terms of MP and MC.
c. If the boat is common property (which means what?), how many fishermen will end up on board the boat? EXPLAIN. Is this outcome efficient? What is the nature of the external cost in this case?
d. If the boat was privately owned, how many people would end up on the boat? Assume that the owner is a profit maximizer. Explain your answer by showing profit at each unit. Is this outcome efficient? Explain. Why is there no longer an externality?
5. What are the characteristics of a public good? What is the argument for the government provision of public goods and how does it tie in with your answer to the previous question?
6. Use the following table to answer the next question.
1st street light 2nd street light 3rd street light 4th street light
Voter MB Voter MB Voter MB Voter MB
A $110 A $100 A $90 A $80
B $60 B $40 B $35 B $30
C $55 C $45 C $40 C $35
It costs $150 to produce a street light. The cost (taxes) is evenly spread out over the three voters. Assume a direct democracy.
a. What is the efficient number of street lights to produce? Explain.
b. How many will actually be produced under majority-rule? How do you explain the difference in the answers to parts (a) and (b)?
ANSWERS
1. A negative externality (also called an external cost) occurs if an activity creates costs (harm or discomfort) for those not involved in the activity. Some examples include the following The pollution generated by a firm imposes costs on people located near the firm; or, reckless driving by one driver imposes costs (increased risk of accident) on other drivers. A positive externality (also called an external benefit) occurs if an activity confers benefits on those not involved in the activity. Examples: People who get vaccinations against communicable disease reduce other people’s chances of getting the disease. A farmer who drains his land happens to also drain his nearby neighbor’s land. A neighbor who hires a security guard may also (indirectly) provide protection for me. People who improve their property may create benefits for their neighbors by making the neighbor more pleasing and thereby increase property values.
Efficiency implications of negative externality: Actual production of the good exceeds the efficient level of production. This is can be seen in the graph below (Figure 1).
P P
Fig. 1 Figure 2
Social Cost Curve S
S(includes only P*
P* private costs) Pactual
Pactual
Social
D D Benefit C.
Q* Qactual Q
Qactual Q* Q
Because producers do not take into account all of the costs that their activities generate, they produce greater than the efficient amount (Qactual > Q*). (Note: The social cost curve in Figure 1 includes all costs—both private costs and external costs.)
Efficiency implications of positive externality: Actual production of the good is less than the efficient level of production. This is can be seen in the graph above (Figure 2). Because consumers do not take into account all of the benefits that their activities generate, they produce less than the efficient amount (Qactual < Q*).
Externalities tend to exist either because it is too difficult to define, or enforce, or to trade property rights. Take the example of pollution. Firms will dump too much pollution into the air if they do not have to pay for the right to do so. Why is there no price charged for this right? Answer: Because there are no property rights for the resource “use of air ”. Why are there no property rights? Answer: It is either too difficult to define or enforce property rights over this resource. (Note: By property rights, I mean the right to use the resource, the right to exclude others from using the resource, the right to rent or to sell the resource, etc.)
2a.
Quantity of steel produced TCp TCext TCT MCprivate MCTotal MR
0 0 0 0 ------
1 $50 $10 $60 $50 $60 $80
2 $110 $20 $130 $60 $70 $80
3 $180 $30 $210 $70 $80 $80
4 $260 $40 $300 $80 $90 $80
5 $350 $50 $400 $90 $100 $80
2b. If P=$80, then a profit-maximizing firm will produce where MR (or P for a price taker) equals MCprivate. This occurs at 4 units of output. Notice that since the firm does not bear the external costs, it does not take this cost into account in deciding how many units of output to produce. The efficient rate of output occurs at a quantity of three where P = MCtotal .
To find the optimal tax, we need to first find the gap between MCprivate and MCtotal at the efficient quantity. At an output quantity of 3, the gap is $10 ($80 minus $70). Therefore, the tax should be set at $10 per unit. The firm will now not produce the 4th unit since MR is $80 but marginal cost to the firm would be the private $80 + tax of $10, or $90.
3a. If the property rights are given to the firm, and thus the firm has the right to emit pollutants, then the local residents would have to pay the firm to reduce pollution. Suppose we start at 0% reduction. How much are local residents willing to pay to the firm to induce it to reduce pollution from 0% cleanup to 50% cleanup? Answer: $10 million. Would the firm be willing to accept this offer? Yes, since the cost to the firm of reducing pollution by this amount (that is, from 0% to50%) is $9 million, so the firm will accept any offer above $9 million. Therefore, any offer between $10million and $9 million will make BOTH parties better off. Now that we are at 50% reduction, is another mutually beneficial trade between the firm and the local residents possible? Locals will pay up to $8 million to get the firm to reduce pollution from 50% to 100%. But the cost to firm of doing so is $10million, so this offer from the locals is not high enough to get the firm to do this. So trade will stop at 50% reduction.
3b. If the property rights are given to the locals, and so they have the right to stop the firm from emitting any pollutants, then the firm would have to pay the locals for the right to emit pollutants.
Suppose that the locals initially force the firm to eliminate all pollution (that is, we start at 100%).
The firm would be willing to pay up to $10 million to escape the cleanup cost associated with reducing pollution from 50 to 100%. The locals value this last unit of clear air at $8 million. So the locals will accept any offer above $8 million from the firm for the right to move from 100% cleanup to 50% cleanup. Therefore, any offer between $8 million and $10 million will make both parties better off. So we move from 100% to 50%. But trade stops at this point since the firm would only be willing to pay $9 million to move from 50% to 0%, but the locals would require at least $10 million to allow this.
3c. Coase Theorem: If property rights are defined and enforced, and if transactions costs are zero or low, then the outcome will be the same regardless of who has the property rights and that outcome is efficient. Yes, the answers to parts (a) and (b) confirm the Coase Theorem. No matter which party had the property rights, the outcome ended up at 50% reduction. This outcome is efficient because the marginal social benefits of moving from 0% to 50% exceed the marginal social costs of doing so. But the marginal social benefits of moving from 50% to 100% are less than the marginal social costs of doing so. Thus, the efficient outcome is 50%.
3d. If the firm has the right to pollute, and if trade is not possible because of high transactions costs, then the outcome will be at 0% reduction. This is because the firm would have no incentive to incur the costs of cleanup if they were not compensated for doing so. This outcome is not efficient.
3e. The government could possibly impose a fine on the polluting firm. The optimal fine would have to be set so as to bring about 50% reduction.
4. Common pool resource is a resource that is owned in common by many people.
Examples: A reservoir of oil that lies under a large area of land owned by many different people. Any one of the owners could drill down and extract oil under his or her land. A problem is that all of the landowners have an incentive to pump as much of the oil as fast as they can, because the oil you do not pump and sell can be pumped and sold by someone else. This reduces the incentive to conserve oil. A reservoir of water that lies under a large area of land owned by many different people would create similar problems. The more water I pump, the lower the water table and thus the more difficult it becomes for someone else to pump. Thus, pumping water imposes external costs on others in the form of higher pumping costs. Commonly held pasture land will tend to be overgrazed. Freeways, sidewalks, national forests and parks, or certain animal species are additional examples.
4a.
Number on Boat (L) Total Product on Boat (Q) MP=(Q/L) AP=(Q/L) Social Total
0 0 ------2000 .
1 10 10 10 1998+10=2008 .
2 18 8 9 1996+18=2014.
3 23 5 7.67 1994+23=2017.
4 24 1 6 1992+24=2016
5 23 -1 4.6 1990+23=2013
6 19 -4 3 1/6 1988+19=2007
7 14 -5 2 1986+14=2000
8 8 -6 1 1984+ 8=1992
4b. It is efficient to let another person on the boat as long as MP MC, where MC is the number of fish a person could have caught if he or she had stayed on the shore. MC is 2 in this example.
So the efficient number to let on the boat is 3 since MP > MC for the third person, but not for the fourth person. Notice that the social total is maximized at this number (social total is 2017 at L=3).
4c. If the boat is common property, then everyone has the right to get on the boat and no one has the right to prevent someone else from getting on board. It would be in the interest of any given person to get on the boat as long as the catch they get on the boat is greater than or equal to the catch they would get if they stayed on the shore (which is 2). Therefore, under common property a person will get on the boat as long as AP MC. Thus, under common property seven people get on the boat. Notice that the social total is 2000 in this case—the same total before the boat was discovered!! This resource—the boat—is overused.
The nature of the negative externality is that as one more person gets on the boat it makes it more difficult for those already on the boat to catch fish (that is, AP falls). But since anyone can get on boat without paying, they will not take this externality into account.
4d. Under private property:
L rental price per person on boat = AP – MC Profit = (L)(AP-MC)
1 10-2 = 8 (1)(8)=8
2 9-2= 7 (2)(7)=14
3 7.67-2=5.67 (3)(5.67)=17
4 6-2= 4 (4)(4)=16
5 4.6-2=2.6 (5)(2.6)=13
It can be seen from this table that the profit-maximizing number of people to let on the boat is three. This is also the efficient amount. There is no longer a negative externality because the owner of boat takes into account the fact that letting one more person on the boat makes it harder for those already on the boat to catch fish. In what way does the owner take this fact into account? Answer: the owner’s rental price would fall—people would not be willing to pay as much to get on the boat if it is harder to catch fish. So owner will weigh this reduction in rental price with the benefit of receiving rent from one more person.
5. Characteristics of public good are:
a. Non-excludability-- Once the good has been produced, it is difficult to exclude non-payers from using and benefiting from the good.
b. Non-rivalry--The use or consumption of the good by one more person does not reduce the ability of other people to use or consume the same unit of the good. (Effectively, this means that once the good is produced the MARGINAL cost of letting one more person use it is zero.)
Examples: A lighthouse, ideas, weather reports, radio shows, national defense, mosquito abatement. Once a lighthouse is built and in operation, it is difficult to exclude non-paying ships from benefiting from the lighthouse (non-excludability) and the use of that lighthouse by one more ship does not stop other ships from benefiting from the same lighthouse (non-rivalry).
The fact that public goods are non-excludable makes it very difficult to provide the efficient amount of those goods through private transactions. People would have an incentive to not pay for the good once it is produced since they know they can use it whether they paid for it or not.
This is known as the free-riderproblem. Thus, a private firm would have little incentive to incur the cost to produce the good if it finds it difficult to get people to pay for it. Thus governments tend to provide public goods and finance the production of these goods with taxes.
6.
1st street light 2nd street light 3rd street light 4th street light
Voter MB Voter MB Voter MB Voter MB
A $110>50 Yes A $100>50 Yes A $90>50 Yes A $80>50 Yes
B $60>50 Yes B $40 <50 No B $35<50 No B $30<50 No
C $55>50 Yes C $45 <50 No C $40<50 No C $35<50 No
TOTAL 225>150 185> 150 165>150 145<150
a. It is efficient to produce three streetlights since the MBsocial > MCsocial for the first three streetlights.
b. Under majority-rule, only one streetlight is produced.
First, because the benefits are not spread evenly, and secondly because “Yes-No” voting does not take into account the intensity of preferences we get this outcome. For example, the second light is not produced because B and C vote against it. Yet, there net losses would be small and A’s net gain would be large—but A still gets just one vote. (Footnote: If transactions costs were low, A could bribe one of the other two voters to change their vote from “No” to “Yes” and would we would arrive at the efficient outcome. However, with a large number of voters this would be difficult to do and so the inefficient outcome remains.)