Problems

1.What type of externality (positive or negative) is present in each of the following examples? Is the marginal social benefit of the activity greater than or equal to the marginal benefit to the individual? Is the marginal social cost of the activity greater than or equal to the marginal cost to the individual? Without intervention, will there be too little or too much (relative to what would be socially optimal) of this activity?

  • a. Mr. Chau plants lots of colorful flowers in his front yard.
  • b. Your next-door neighbor likes to build bonfires in his backyard, and sparks often drift onto your house.
  • c. Maija, who lives next to an apple orchard, decides to keep bees to produce honey.
  • d. Justine buys a large SUV that consumes a lot of gasoline.

2.The loud music coming from the sorority next to your dorm is a negative externality that can be directly quantified. The accompanying table shows the marginal social benefit and the marginal social cost per decibel (dB, a measure of volume) of music.

  • a. Draw the marginal social benefit curve and the marginal social cost curve. Use your diagram to determine the socially optimal volume of music.
  • b. Only the members of the sorority benefit from the music and they bear none of the cost. Which volume of music will they choose?
  • c. The college imposes a Pigouvian tax of $3 per decibel of music played. From your diagram, determine the volume of music the sorority will now choose.

3.Many dairy farmers in California are adopting a new technology that allows them to produce their own electricity from methane gas captured from animal wastes. (One cow can produce up to 2 kilowatts a day.) This practice reduces the amount of methane gas released into the atmosphere. In addition to reducing their own utility bills, the farmers are allowed to sell any electricity they produce at favorable rates.

  • a. Explain how the ability to earn money from capturing and transforming methane gas behaves like a Pigouvian tax on methane gas pollution and can lead dairy farmers to emit the efficient amount of methane gas pollution.
  • b. Suppose some dairy farmers have lower costs of transforming methane into electricity than others. Explain how this system leads to an efficient allocation of emissions reduction among farmers.

4.According to a report from the U.S. Census Bureau, “the average [lifetime] earnings of a full-time, year round worker with a high school education are about $1.2 million compared with $2.1 million for a college graduate.” This indicates that there is a considerable benefit to a graduate from investing in his or her own education. Tuition at most state universities covers only about two-thirds to three-quarters of the cost, so the state applies a Pigouvian subsidy to college education.

If a Pigouvian subsidy is appropriate, is the externality created by a college education a positive or a negative externality? What does this imply about the differences between the costs and benefits to students compared to social costs and benefits? What are some reasons for the differences?

5.The city of Falls Church, Virginia, subsidizes trees planted in homeowners’ front yards when they are within 15 feet of the street.

  • a. Using concepts from this section, explain why a municipality would subsidize trees planted on private property, but near the street.
  • b. Draw a diagram similar to Figure 37-3 that shows the marginal social benefit, the marginal social cost, and the optimal Pigouvian subsidy on trees.

6.Smoking produces a negative externality because it imposes a health risk on others who inhale second-hand smoke. Cigarette smoking also causes productivity losses to the economy due to the shorter expected life span of a smoker. The U.S. Centers for Disease Control and Prevention (CDC) has estimated the average social cost of smoking a single pack of cigarettes for different states by taking these negative externalities into account. Assume that the accompanying table provides the price of cigarettes and the estimated average social cost of smoking in five states.

State Cigarette retail price with taxes (per pack) CDC estimate of smoking cost in 2013 (per pack)
California $4.40 $15.10
New York   5.82   21.91
Florida   3.80   10.14
Texas   4.76     9.94
Ohio   4.60     9.19
  • a. At the current level of consumption, what is the optimal retail price of a pack of cigarettes in the different states? Is the current price below or above this optimal price? Does this suggest that the current level of consumption is too high or too low? Explain your answer.
  • b. In order to deal with negative externalities, state governments currently impose excise taxes on cigarettes. Are current taxes set at the optimal level? Justify your answer.
  • c. What is the correct size of an additional Pigouvian tax on cigarette sales in the different states if the CDC’s estimate for smoking cost does not change with an increase in the retail price of cigarettes?

7.Fishing for sablefish has been so intensive that sablefish were threatened with extinction. After several years of banning such fishing, the government is now proposing to introduce tradable vouchers, each of which entitles its holder to a catch of a certain size. Explain how fishing generates a negative externality and how the voucher scheme may overcome the inefficiency created by this externality.

8.Which of the following are characterized by network externalities? Which are not? Explain.

  • a. the choice between installing 110-volt electrical current in structures rather than 220-volt
  • b. the choice between purchasing a Toyota versus a Ford
  • c. the choice of a printer, where each printer requires its own specific type of ink cartridge
  • d. the choice of whether to purchase an iPod Touch or an iPod Nano.

9.The government is involved in providing many goods and services. For each of the goods or services listed, determine whether it is rival or nonrival in consumption and whether it is excludable or nonexcludable. What type of good is it? Without government involvement, would the quantity provided be efficient, inefficiently low, or inefficiently high?

  • a. street signs
  • b. Amtrak rail service
  • c. regulations limiting pollution
  • d. an interstate highway without tolls
  • e. a lighthouse on the coast

10.A residential community has 100 residents who are concerned about security. The accompanying table gives the total cost of hiring a 24-hour security service as well as each individual resident’s total benefit.

Quantity of security guards Total cost Total individual benefit to each resident
0 $    0 $  0
1   150   10
2   300   16
3   450   18
4   600   19
  • a. Explain why the security service is a public good for the residents of the community.
  • b. Calculate the marginal cost, the individual marginal benefit for each resident, and the marginal social benefit.
  • c. If an individual resident were to decide about hiring and paying for security guards on his or her own, how many guards would that resident hire?
  • d. If the residents act together, how many security guards will they hire?

11.The accompanying table shows Tanisha’s and Ari’s individual marginal benefit of different numbers of street cleanings per month. Suppose that the marginal cost of street cleanings is constant at $9 each.

  • a. If Tanisha had to pay for street cleaning on her own, how many street cleanings would there be?
  • b. Calculate the marginal social benefit of street cleaning. What is the optimal number of street cleanings?
  • c. Consider the optimal number of street cleanings. The last street cleaning of that number costs $9. Is Tanisha willing to pay for that last cleaning on her own? Is Ari willing to pay for that last cleaning on his own?

12.Anyone with a radio receiver can listen to public radio, which is funded largely by donations.

  • a. Is public radio excludable or nonexcludable? Is it rival in consumption or nonrival? What type of good is it?
  • b. Should the government support public radio? Explain your reasoning.
  • c. In order to finance itself, public radio decides to transmit only to satellite radios, for which users have to pay a fee. What type of good is public radio then? Will the quantity of radio listening be efficient? Why or why not?

13.Your economics teacher assigns a group project for the course. Describe the free-rider problem that can lead to a suboptimal outcome for your group. To combat this problem, the instructor asks you to evaluate the contribution of your peers in a confidential report. Will this evaluation have the desired effects?

14.The accompanying table shows six consumers’ willingness to pay (his or her individual marginal benefit) for one MP3 file copy of a Jay-Z album. The marginal cost of making the file accessible to one additional consumer is constant, at zero.

Consumer Individual marginal benefit
Adriana $  2
Bhagesh   15
Chizuko     1
Denzel   10
Emma     5
Frank     4
  • a. What would be the efficient price to charge for a download of the file?
  • b. All six consumers are able to download the file for free from a file-sharing service, Pantster. Which consumers will download the file? What will be the total consumer surplus to those consumers?
  • c. Pantster is shut down for copyright law infringement. In order to download the file, consumers now have to pay $4.99 at a commercial music site. Which consumers will download the file? What will be the total consumer surplus to those consumers? How much producer surplus accrues to the commercial music site? What is the total surplus? What is the deadweight loss from the new pricing policy?

15.Software has historically been an artificially scarce good—it is nonrival because the cost of replication is negligible once the investment to write the code is made, but software companies make it excludable by charging for user licenses. Recently, however, open-source software has emerged, most of which is free to download and can be modified and maintained by anyone.

  • a. Discuss the free-rider problem that might exist in the development of open-source software. What effect might this have on quality? Why does this problem not exist for proprietary software, such as the products of a company like Microsoft or Adobe?
  • b. Some argue that open-source software serves an unsatisfied market demand that proprietary software ignores. Draw a typical diagram that illustrates how proprietary software may be underproduced. Put the price and marginal cost of software on the vertical axis and the quantity of software on the horizontal axis. Draw a typical demand curve and a marginal cost curve (MC) that is always equal to zero. Assume that the software company charges a positive price, P, for the software. Label the equilibrium point and the efficient point.

16.The two dry-cleaning companies in Collegetown, College Cleaners and Big Green Cleaners, are a major source of air pollution. Together they currently produce 350 units of air pollution, which the town wants to reduce to 200 units. The accompanying table shows the current pollution level produced by each company and each company’s marginal cost of reducing its pollution. The marginal cost is constant.

Company Initial pollution level (units) Marginal cost of reducing pollution (per unit)
College Cleaners 230 $5
Big Green Cleaners 120   2
  • a. Suppose that Collegetown passes an environmental standards law that limits each company to 100 units of pollution. What would be the total cost to the two companies of each reducing its pollution emissions to 100 units?

Suppose instead that Collegetown issues 100 pollution vouchers to each company, each entitling the company to one unit of pollution, and that these vouchers can be traded.

  • b. How much is each pollution voucher worth to College Cleaners? to Big Green Cleaners? (That is, how much would each company, at most, be willing to pay for one more voucher?)
  • c. Who will sell vouchers and who will buy them? How many vouchers will be traded?
  • d. What is the total cost to the two companies of the pollution controls under this voucher system?

17.Ronald owns a cattle farm at the source of a long river. His cattle’s waste flows into the river and down many miles to where Carla lives. Carla gets her drinking water from the river. By allowing his cattle’s waste to flow into the river, Ronald imposes a negative externality on Carla. In each of the two following cases, do you think that through negotiation, Ronald and Carla can find an efficient solution? What might this solution look like?

  • a. There are no telephones, and for Carla to talk to Ronald, she has to travel for two days on a rocky road.
  • b. Carla and Ronald both have e-mail access, making it costless for them to communicate.

18.In the city of Metropolis, there are 100 residents, each of whom lives until age 75. Residents of Metropolis have the following incomes over their lifetime: Through age 14, they earn nothing. From age 15 until age 29, they earn 200 metros (the currency of Metropolis) per year. From age 30 to age 49, they earn 400 metros. From age 50 to age 64, they earn 300 metros. Finally, at age 65 they retire and are paid a pension of 100 metros per year until they die at age 75. Each year, everyone consumes whatever their income is that year (that is, there is no saving and no borrowing). Currently, 20 residents are 10 years old, 20 residents are 20 years old, 20 residents are 40 years old, 20 residents are 60 years old, and 20 residents are 70 years old.

  • a. Study the income distribution among all residents of Metropolis. Split the population into quintiles according to their income. How much income does a resident in the lowest quintile have? In the second, third, fourth, and top quintiles? What share of total income of all residents goes to the residents in each quintile? Construct a table showing the share of total income that goes to each quintile. Does this income distribution show inequality?
  • b. Now look only at the 20 residents of Metropolis who are currently 40 years old, and study the income distribution among only those residents. Split those 20 residents into quintiles according to their income. How much income does a resident in the lowest quintile have? In the second, third, fourth, and top quintiles? What share of total income of all 40-year-olds goes to the residents in each quintile? Does this income distribution show inequality?
  • c. What is the relevance of these examples for assessing data on the distribution of income in any country?

19.The accompanying table presents data from the U.S. Census Bureau on median and mean income of male workers for the years 1972 and 2009. The income figures are adjusted to eliminate the effect of inflation.

Year Median income Mean income
(in 2009 dollars)
1972 $34,159 $39,593
2009   32,184   46,800
Source: U.S. Census Bureau.
  • a. By what percentage has median income changed over this period? By what percentage has mean income changed over this period?
  • b. Between 1972 and 2009, has the income distribution become less or more unequal? Explain.

20.There are 100 households in the economy of Equalor. Initially, 99 of them have an income of $10,000 each, and one household has an income of $1,010,000.

  • a. What is the median income in this economy? What is the mean income?

Through its poverty programs, the government of Equalor now redistributes income: it takes $990,000 away from the richest household and distributes it equally among the remaining 99 households.

  • b. What is the median income in this economy now? What is the mean income? Has the median income changed? Has the mean income changed? Which indicator (mean or median household income) is a better indicator of the typical Equalorian household’s income? Explain.

21.The tax system in Taxilvania includes a negative income tax. For all incomes below $10,000, individuals pay an income tax of –40% (that is, they receive a payment of 40% of their income). For any income above the $10,000 threshold, the tax rate on that additional income is 10%. For the first three scenarios below, calculate the amount of income tax to be paid and after-tax income.

  • a. Lowani earns income of $8,000.
  • b. Midram earns income of $40,000.
  • c. Hi-Wan earns income of $100,000.
  • d. Can you find a notch in this tax system? That is, can you find a situation where earning more pre-tax income actually results in less after-tax income?

22.In the city of Notchingham, each worker is paid a wage rate of $10 per hour. Notchingham administers its own unemployment benefit, which is structured as follows: If you are unemployed (that is, if you do not work at all), you get unemployment benefits (a transfer from the government) of $50 per day. As soon as you work for only one hour, the unemployment benefit is completely withdrawn. That is, there is a notch in the benefit system.

  • a. How much income does an unemployed person have per day? How much daily income does an individual who works four hours per day have? How many hours do you need to work to earn just the same as if you were unemployed?
  • b. Will anyone ever accept a part-time job that requires working four hours per day, rather than being unemployed?
  • c. Suppose that Notchingham now changes the way in which the unemployment benefit is withdrawn. For each additional dollar an individual earns, $0.50 of the unemployment benefit is withdrawn. How much daily income does an individual who works four hours per day now have? Is there an incentive now to work four hours per day rather than being unemployed?

23.The accompanying table shows data on the total number of people in the United States and the number of all people who were uninsured, for selected years from 1999 to 2009. It also shows data on the total number of poor children in the United States—those under 18 and below the poverty threshold—and the number of poor children who were uninsured.

Year Total people Uninsured people Total poor children Uninsured poor children
(millions)
1999 276.8 38.8 12.3 2.8
2001 282.1 39.8 11.7 2.4
2003 288.3 43.4 12.9 2.4
2005 293.8 44.8 12.9 2.4
2007 299.1 45.7 13.3 2.3
2009 304.3 50.7 15.5 2.3
Source: U.S. Census Bureau.

For each year, calculate the percentage of all people who were uninsured and the percentage of poor children who were uninsured. How have these percentages changed over time? What is a possible explanation for the change in the percentage of uninsured poor children?

24.The American National Election Studies conducts periodic research on the opinions of U.S. voters. The accompanying table shows the percentage of people, in selected years from 1952 to 2008, who agreed with the statement “There are important differences in what the Republicans and Democrats stand for.”

Year Agree with statement
1952 50%
1972 46
1992 60
2004 76
2008 78
Source: American National Election Studies.

What do these data say about the degree of partisanship in U.S. politics over time?

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