CH-17-20 Public Goods and Common Resources – Microeconomics : Book Guide

This Document Contains Chapters 17 to 20 Public Goods and Common Resources Chapter 17 1. 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. A congested interstate highway without tolls e. A lighthouse on the coast 1. a. Street signs are nonrival in consumption (if I make use of a street sign, that does not reduce your opportunity to use it) and nonexcludable (no one can prevent another person from making use of a street sign). So street signs are a public good. Because of the free-rider problem, the quantity provided privately would be inefficiently low. b. Amtrak rail service is rival in consumption (if I consume a seat, you cannot) and excludable (you cannot consume the service if you do not have a ticket). Although Amtrak rail service is a private good, it creates a positive externality in the form of reduced road and air traffic congestion. The market would provide an inefficiently low level of passenger rail service, so there is a justification for government intervention to support Amtrak. c. Regulations limiting pollution are nonrival in consumption (my benefit from these regulations is not diminished by your benefit) and nonexcludable (people cannot be selectively excluded from benefiting from these regulations—that is, excluded from breathing clean air or drinking clean water). So these regulations are a public good. Because of the free-rider problem, the privately ­provided quantity of these regulations would be inefficiently low. d. A congested interstate highway without tolls is rival in consumption (if I use the highway, I create a negative externality for you—more congestion; that is, I reduce your benefit from the highway) but nonexcludable (drivers can use the highway without paying for access). So the highway is a common resource. Because of nonexcludability, a free-rider problem exists, and the privately ­provided quantity of highways would be inefficiently low. e. A lighthouse is nonrival in consumption (if I use the lighthouse to steer my boat away from rocks, you can still use the same lighthouse) and nonexcludable (boats cannot selectively be made to pay for the services provided by the lighthouse). So the lighthouse is a public good. Because of the free-rider ­problem, the privately provided quantity would be inefficiently low. Chapter 17 2. An economist gives the following advice to a museum director: “You should introduce ‘peak pricing.’ At times when the museum has few visitors, you should admit visitors for free. And at times when the museum has many visitors, you should charge a higher admission fee.” a. When the museum is quiet, is it rival or nonrival in consumption? Is it excludable or nonexcludable? What type of good is the museum at those times? What would be the efficient price to charge visitors during that time, and why? b. When the museum is busy, is it rival or nonrival in consumption? Is it excludable or nonexcludable? What type of good is the museum at those times? What would be the efficient price to charge visitors during that time, and why? 2. a. When the museum is quiet, it is nonrival in consumption: one additional visitor does not diminish any other visitor’s ability to enjoy the museum. Furthermore, the museum is excludable (if you don’t pay the entrance fee, you are not admitted). So the museum is an artificially scarce good. The marginal cost of admitting one more visitor is zero (the museum is already staffed, lighted, and heated or air-conditioned), and so the efficient admission fee would be zero. b. When the museum is busy, it is rival in consumption: one additional visitor in the museum diminishes any other visitor’s ability to enjoy the museum because of overcrowding. The museum is still excludable (if you don’t pay the entrance fee, you are not admitted). So the museum is a private good. There is now a marginal external cost to admitting one more visitor (the cost imposed on other visitors from a more crowded museum). So the efficient admission fee would be equal to the marginal external cost at the efficient number of visitors. 3. In many planned communities, various aspects of community living are ­subject to regulation by a homeowners’ association. These rules can regulate house architecture; require snow removal from sidewalks; exclude outdoor equipment, such as backyard swimming pools; require appropriate conduct in shared spaces such as the community clubhouse; and so on. Suppose there has been some conflict in one such community because some homeowners feel that some of the regulations mentioned above are overly intrusive. You have been called in to mediate. Using what you have learned about public goods and common resources, how would you decide what types of regulations are warranted and what types are not? 3. Using efficiency as the goal, a regulation is warranted if it provides a public good or if it conserves a common resource. The enjoyment of pleasing and ­harmonious architecture and snow removal from sidewalks are examples of ­public goods: they are nonexcludable and nonrival in consumption. A clubhouse is a common resource: it is nonexcludable but rival in consumption. So it promotes efficiency if these aspects of the community are regulated for the benefit for all. But it is questionable whether or not aspects such as backyard swimming pools should be regulated: their presence in someone’s yard does not benefit or hurt neighbors (so they are rival in consumption) and they are solely for the benefit of the homeowner who owns them (they are excludable). So they are private goods and should not be subject to regulation by the homeowners’ association. The regulation of private goods in the community is unwarranted. 4. The accompanying table shows Tanisha’s and Ari’s individual marginal benefit of different amounts of street cleanings per month. Suppose that the marginal cost of street cleanings is constant at $9 each. Quantity of street cleanings per month Tanisha’s individual marginal benefit Ari’s individual marginal benefit $10 $8 6 4 2 1 0 1 2 3 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 the optimal number of street cleanings 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? 4. a. If Tanisha had to pay for street cleaning on her own, she would pay for the street to be cleaned once: her individual marginal benefit of the first cleaning, $10, exceeds the marginal cost of $9. However, she would not pay for more than one: her marginal benefit of the second cleaning is $6, less than the ­marginal cost of $9. b. The accompanying table shows the marginal social benefit of street cleaning. The optimal number of street cleanings is 2: the marginal social benefit of the second cleaning is $10, which exceeds the marginal cost of $9. A third cleaning would be inefficient because its marginal social benefit is $3, less than the marginal cost of $9. Quantity of street cleanings per month Tanisha’s individual marginal benefit Ari’s individual marginal benefit Marginal social benefit $10 $8 $18 6 4 10 2 1 3 0 1 2 3 c. Tanisha on her own would be willing to pay only $6 (her individual marginal benefit) for the second cleaning. Ari on his own would be willing to pay only $4 (his individual marginal benefit) for the second cleaning. So neither would be individually willing to pay for the second cleaning. 5. 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? 5. a. Public radio is nonexcludable: anyone with a radio receiver can pick up the radio waves. It is nonrival: if I listen to public radio, that does not diminish your opportunity to listen to it also. So public radio is a public good. b. As with all public goods, private markets lead to an inefficient quantity of the good being supplied. The individual marginal benefit from a certain amount of public radio programming is less than the marginal social benefit from that amount of public radio programming. So individuals are not willing to pay for the efficient level of public radio programming, and as a result the privately provided quantity of programming would be inefficiently low. There is a case for government support of public radio. c. Transmitting only to satellite radios, where a fee is charged for the service, makes public radio excludable. So public radio is now an artificially scarce good. The efficient price for receiving the satellite radio signal would be zero, since the marginal cost is zero. But since a positive price is charged, only ­consumers with a marginal benefit greater than or equal to that price will choose to purchase the good. As a result, there are many consumers with individual marginal benefits that exceed the marginal cost but who do not get access to public radio because the price exceeds their individual marginal benefit. The quantity of radio listening is therefore inefficiently low. 6. Your economics professor 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? 6. Without the confidential evaluation, the grade a member of a group receives on the assignment depends only on the project as a whole, not on the contributions of individual members. Since each member of the group is aware of this, they realize that it is possible to shirk undetected and free-ride on the efforts of others. Consequently, everyone in the group is likely to underperform. The ­confidential peer evaluation provides an incentive to a potential free-rider to work harder. Since shirkers may be discovered through this evaluation and receive a lower grade as a result, the free-rider problem is mitigated. 7. The village of Upper Bigglesworth has a village “commons,” a piece of land on which each villager, by law, is free to graze his or her cows. Use of the commons is measured in units of the number of cows grazing on it. Assume that the marginal private cost curve of cow-grazing on the commons is upward sloping (say due to more time spent herding). There is also a marginal social cost curve of cow-grazing on the commons: each additional cow grazed means less grass available for others, and the damage done by overgrazing of the commons increases as the number of cows grazing increases. Finally, assume that the private benefit to the villagers of each additional cow grazing on the commons declines as more cows graze, since each additional cow has less grass to eat than the previous one. a. Is the commons excludable or nonexcludable? Is it rival in consumption or nonrival? What kind of good is the commons? b. Draw a diagram showing the marginal social cost, marginal private cost, and the marginal private benefit of cow-grazing on the commons, with the quantity of cows that graze on the commons on the horizontal axis. How does the quantity of cows grazing in the absence of government intervention compare to the efficient quantity? Show both in your diagram. c. The villagers hire you to tell them how to achieve an efficient use of the commons. You tell them that there are three possibilities: a Pigouvian tax, the assignment of property rights over the commons, and a system of tradable licenses for the right to graze a cow. Explain how each one of these options would lead to an efficient use of the commons. In the assignment of property rights, assume that one person is assigned the rights to the commons and the rights to all the cows. Draw a diagram that shows the Pigouvian tax. 7. a. The commons is nonexcludable since, by law, each villager is free to send his or her cows there. It is also rival in consumption, since the grass that one villager’s cow eats is no longer available for another villager’s cow. So the commons is a common resource. b. The accompanying diagram shows the marginal private cost to villagers of cow-grazing on the commons, MPC. It is also the supply curve of cows for grazing. It lies below the marginal social cost curve, MSC. MSC is higher than MPC because each villager who sends his or her cow to graze inflicts a cost on every other villager, a cost that increases as the number of cows grazing increases. The marginal private benefit curve, MPB, shows the marginal benefit that accrues to villagers according to the number of cows grazing. Price of cowgrazing MSC O MPC EMKT MPB QOPT QMKT Quantity of cows grazing The outcome without government intervention is indicated by QMKT, the ­ uantity at which the marginal private benefit equals marginal private cost. q It is greater than the optimal, or efficient, equilibrium quantity, QOPT. That is, the villagers will send too many cows to the commons to graze. This problem is known as the “tragedy of the commons” [G. Hardin, “The Tragedy of the Commons,” Science, pp. 1243–1248, 1968]. c. A Pigouvian tax on grazing would increase the villagers’ marginal cost and shift the MPC upward until it intersects MPB at the efficient quantity, QOPT. This is shown in the diagram as the movement of MPC to its new position at MPC1. Each individual villager would now make the socially optimal, or efficient, decision. Alternatively, ownership of the commons and the cows could be assigned to one person. He or she would set the amount of grazing to the efficient quantity. Last, villagers could create a system of tradable licenses for grazing one cow, where the number of licenses issued is equal to the efficient quantity of grazing. Price of cowgrazing MSC MPC1 O Pigouvian tax EMKT MPC MPB QOPT QMKT Quantity of cows grazing 8. Prior to 2003, the city of London was often one big parking lot. Traffic jams were common, and it could take hours to travel a couple of miles. Each additional commuter contributed to the congestion, which can be measured by the total number of cars on London roads. Although each commuter suffered by spending valuable time in traffic, none of them paid for the inconvenience they caused others. The total cost of travel includes the opportunity cost of time spent in traffic and any fees levied by London authorities. a. Draw a graph illustrating the overuse of London roads, assuming that there is no fee to enter London in a vehicle and that roads are a common resource. Put the cost of travel on the vertical axis and the quantity of cars on the horizontal axis. Draw typical demand, individual marginal cost (MC), and marginal social cost (MSC) curves and label the equilibrium point. (Hint: The marginal cost takes into account the opportunity cost of spending time on the road for individual drivers but not the inconvenience they cause to others.) b. In February 2003, the city of London began charging a £5 congestion fee on all vehicles traveling in central London. Illustrate the effects of this congestion charge on your graph and label the new equilibrium point. Assume the new equilibrium point is not optimally set (that is, assume that the £5 charge is too low relative to what would be efficient). c. The congestion fee was raised to £9 in January 2011. Illustrate the new equilibrium point on your graph, assuming the new charge is now optimally set. 8. a. The accompanying diagram depicts the demand and individual marginal cost (MC1) for using London roads. When no fees are levied for using the roads, the equilibrium point is EMKT1. This is the usual market equilibrium when market externalities are not corrected. Cost of travel MSC O MC1 EMKT1 D QOPT QMKT1 Quantity of cars b. After the £5 fee is imposed, the market equilibrium moves as shown in the accompanying diagram. The congestion charge effectively increases the cost of traveling by car in central London, and the marginal cost curve shifts upward, from MC1 to MC2. The commuters who are easily able to switch to public transport stop driving, causing the quantity of cars to fall. However, the charge is too low: although the quantity of cars falls relative to the situation in part a, it is still greater than the efficient quantity, QOPT. Cost of travel MSC Upward shift by £5 MC2 O EMKT2 MC1 EMKT1 D QOPT QMKT2 QMKT1 Quantity of cars c. When the fee is raised to £9, the marginal cost curve moves farther up, to MC3, and more people refrain from using central London roads as the equilibrium quantity falls to the efficient quantity, QOPT. The charge of £9 is the optimal Pigouvian tax in this case: it moves the equilibrium to the efficient outcome, O. Cost of travel MSC MC3 O = EMKT3 Upward shift by £9 MC1 D QOPT = QMKT3 Quantity of cars 9. The accompanying table shows six consumers’ willingness to pay (his or her individual marginal benefit) to download 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? 9. a. Since the marginal cost of delivering the good to one additional consumer is zero, the efficient price would be zero. b. Since each of the six consumers has a marginal benefit greater than zero, all six will download the file. Adriana’s individual consumer surplus will be $2, Bhagesh’s $15, Chizuko’s $1, Denzel’s $10, Emma’s $5, and Frank’s $4. The total consumer surplus is therefore $2 + $15 + $1 + $10 + $5 + $4 = $37. c. At a price of $4.99, Bhagesh, Denzel, and Emma will download the file. Bhagesh’s individual consumer surplus will be $10.01, Denzel’s $5.01, and Emma’s $0.01. So total consumer surplus is $10.01 + $5.01 + $0.01 = $15.03. Producer surplus is 3 × $4.99 = $14.97. So total surplus is $15.03 + $14.97 = $30. This is $7 less than in part b. So the deadweight loss from making the good artificially scarce is $7. 10. Butchart Gardens is a very large garden in Victoria, British Columbia, renowned for its beautiful plants. It is so large that it could hold many times more visitors than currently visit it. The garden charges an admission fee of $30. At this price, 1,000 people visit the garden each day. If admission were free, 2,000 people would visit each day. a. Are visits to Butchart Gardens excludable or nonexcludable? Are they rival in consumption or nonrival? What type of good is it? b. In a diagram, illustrate the demand curve for visits to Butchart Gardens. Indicate the situation when Butchart Gardens charges an admission fee of $30. Also indicate the situation when Butchart Gardens charges no admission fee. c. Illustrate the deadweight loss from charging a $30 admission fee. Explain why charging this admission fee is inefficient. 10. a. Visits to Butchart Gardens are excludable (there is an entrance fee) and ­nonrival (the garden could hold many more visitors than it currently hosts, so one visitor’s enjoyment of the park does not diminish another visitor’s enjoyment). So visits to Butchart Gardens are an artificially scarce good. b. The demand curve is illustrated in the accompanying diagram. The situation when Butchart Gardens charges a $30 admission fee is indicated by point A on the demand curve. The situation when Butchart Gardens charges no admission fee is indicated by point B on the demand curve. Price of visit $30 D A Deadweight loss B 0 1,000 2,000 Quantity of visits c. The deadweight loss from charging a $30 admission fee rather than no fee is indicated by the shaded area in the diagram. Since the marginal cost of admitting one more visitor is zero, it would be efficient to charge no admission. However, since the good is artificially scarce and an admission fee of $30 is charged, only those consumers with a marginal benefit greater than $30 will visit the gardens. There are 1,000 consumers who have marginal benefits that exceed the marginal cost of allowing them access, but they are prevented from visiting the gardens by the $30 admission fee. 11. 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. But then open-source software 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 opensource 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. 11. a. In principle, the developers of open-source software are not strictly monitored. Some developers may shirk and write poor code in the hope that others in the development community will correct their mistakes. A free-rider problem is created because individual developers are not held responsible for their code, potentially resulting in poor quality. Microsoft and Adobe, however, are responsible for the quality of their software; they risk losing business and profits if their product is substandard. So company management enforces quality-control measures that mitigate the free-rider problem. b. The accompanying diagram shows a demand curve, D, and a marginal cost curve that is constant and always equal to zero, MC. The equilibrium is at point EMKT, with a quantity, QMKT, that is lower than the efficient quantity, QOPT. Price, marginal D cost of software P EMKT MC = O O QMKT QOPT Quantity of software 12. In developing a vaccine for the SARS virus, a pharmaceutical company incurs a very high fixed cost. The marginal cost of delivering the vaccine to patients, however, is negligible (consider it to be equal to zero). The pharmaceutical company holds the exclusive patent to the vaccine. You are a regulator who must decide what price the pharmaceutical company is allowed to charge. a. Draw a diagram that shows the price for the vaccine that would arise if the company is unregulated, and label it PM. What is the efficient price for the ­vaccine? Show the deadweight loss that arises from the price PM. b. On another diagram, show the lowest price that the regulator can enforce that would still induce the pharmaceutical company to develop the vaccine. Label it P*. Show the deadweight loss that arises from this price. How does it compare to the deadweight loss that arises from the price PM? c. Suppose you have accurate information about the pharmaceutical company’s fixed cost. How could you use price regulation of the pharmaceutical company, combined with a subsidy to the company, to have the efficient quantity of the vaccine provided at the lowest cost to the government? 12. a. If the company is unregulated, it will behave like a monopolist and choose a quantity, QM, at which marginal revenue is equal to marginal cost, which is equal to zero. This leads to the price PM. The efficient price, however, is zero. There is a deadweight loss equal to the shaded area in the accompanying diagram. Price, cost, marginal revenue Deadweight loss at PM PM ATC 0 D QM MR Quantity of vaccine b. The lowest price that still induces the company to develop the vaccine is the price at which the demand curve crosses the average total cost curve. At this price, the company just breaks even. There is a smaller deadweight loss than under the price PM. The deadweight loss is indicated by the shaded area in the accompanying diagram. Price, cost, marginal revenue PM Deadweight loss at P* P* 0 ATC D QM Q* MR Quantity of vaccine c. You could regulate the company’s price to be equal to zero. That way, all ­consumers with a positive willingness to pay will get the vaccine. To guarantee that the company will develop the vaccine, the government will pay the ­company a subsidy equal to its fixed cost. WORK IT OUT Interactive step-by-step help with solving this problem can be found online. 13. 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? 13. a. Security services are nonexcludable: as soon as security is provided to the community, every resident benefits from it. Security services are nonrival: if one resident enjoys protection, this does not diminish any other resident’s ability to enjoy the service. b. The accompanying table calculates the marginal cost, the individual marginal benefit, and the marginal social benefit. The marginal social benefit is just the individual marginal benefit times 100, since there are 100 residents. Quantity of security guards Total cost 0 $0 Marginal cost Total individual benefit to each resident 150 2 300 3 450 4 600 Marginal social benefit $10 $1,000 6 600 2 200 1 100 $0 $150 1 Individual marginal benefit 10 150 16 150 18 150 19 c. An individual resident would compare the marginal cost of hiring an additional security guard against his or her individual marginal benefit. Since the marginal cost of hiring even the first security guard exceeds the individual marginal benefit to the resident, the resident would decide to hire no security guards on his or her own. d. If the residents act together, they will compare the marginal cost of hiring an additional security guard against the marginal social benefit. They will therefore decide to hire 3 security guards. For the third security guard, the marginal social benefit of $200 exceeds the marginal cost of $150. But for the fourth security guard, the marginal cost of $150 would exceed the marginal social benefit of $100. The Economics of the Welfare State 1. The accompanying table contains data on the U.S. economy for the years 1983 and 2015. The second column shows the poverty threshold. The third column shows the consumer price index (CPI), a measure of the overall level of prices. And the fourth column shows U.S. gross domestic product (GDP) per capita, a measure of the standard of living. Year Poverty threshold 1983 2015 CPI (1982-1984 = 100) GDP per capita $5,180 99.6 $15,525 12,331 237.8 56,066 Data from: U.S. Census Bureau; Bureau of Labor Statistics; Bureau of Economic Analysis. a. By what factor has the poverty threshold increased from 1983 to 2015? That is, has it doubled, tripled, and so on? b. By what factor has the CPI (a measure of the overall price level) increased from 1983 to 2015? That is, has it doubled, tripled, and so on? c. By what factor has GDP per capita (a measure of the standard of living) increased from 1983 to 2015? That is, has it doubled, tripled, and so on? d. What do your results tell you about how those people officially classified as “poor” have done economically relative to other U.S. citizens? 1. a. The poverty threshold has increased by a factor of $12,331/$5,180 = 2.4 from 1983 to 2015. That is, it has roughly doubled. b. The CPI has increased by a factor of 237.8/99.6 = 2.4 from 1983 to 2015. That is, it also has roughly doubled. This, of course, is unsurprising: the poverty threshold each year is adjusted upward nearly by the increase in the overall price level. c. GDP per capita has increased by a factor of $56,066/$15,525 = 3.6 from 1983 to 2015. That is, it has roughly qaudrupled. d. Since the standard of living has grown more rapidly than the poverty threshold, those officially classified as “poor” have done increasingly worse relative to other U.S. citizens: if you are classified as “poor” (that is, below the poverty threshold) today, you are doing dramatically worse relative to the rest of the population than someone who was classified as “poor” in 1983. 2. 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. Chapter 18 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? 2. a. Each quintile will contain 100/5 = 20 citizens. Total income in Metropolis among all citizens is (20 × 0) + (20 × 200) + (20 × 400) + (20 × 300) + (20 × 100) = 20,000. The citizens in the lowest quintile are the 10-year-olds, with income of 0 metros each, for a total income in that quintile of 0 metros, which is 0% of the total income. The citizens in the second quintile are the 70-year-olds, with income of 100 metros each, for a total income in that quintile of 20 × 100 = 2,000 metros, which is 2,000/20,000 = 10% of the total income. The citizens in the third quintile are the 20-year-olds, with income of 200 metros each, for a total income in that quintile of 20 × 200 = 4,000 metros, which is 4,000/20,000 = 20% of the total income. The citizens in the fourth quintile are the 60-yearolds, with income of 300 metros each, for a total income in that quintile of 20 × 300 = 6,000 metros, which is 6,000/20,000 = 30% of the total income. The citizens in the top quintile are the 40-year-olds, with income of 400 metros each, for a total income in that quintile of 20 × 400 = 8,000 metros, which is 8,000/20,000 = 40% of the total income. The accompanying table shows the income distribution. This income distribution exhibits considerable inequality. Quintile Lowest Share of total income 0% Second 10 Third 20 Fourth 30 Top 40 b. All 40-year-olds have the same income: 400 metros. Each quintile will contain 20/5 = 4 citizens. That is, the citizens in the lowest quintile (the lowest four earners) have income of 400 metros. The citizens in the second quintile (the next higher four earners) also have income of 400 metros, and so on. Since total income of all 40-year-olds is 20 × 400 = 8,000 metros, the share of total income earned by citizens in the lowest quintile is (4 × 400)/8,000 = 20%. This is the same for all quintiles. The income distribution exhibits complete ­equality: the share of total income earned by citizens in each quintile is exactly equal. c. These examples show how looking at the overall income distribution can overstate the true degree of inequality. Since incomes tend to vary over the life cycle, studying the income distribution across all citizens shows greater inequality than when studying the income distribution across citizens of the same age. 3. The accompanying table presents data from the U.S. Census Bureau on median and mean income of male workers for the years 1972 and 2015. The income ­f igures are adjusted to eliminate the effect of inflation. Median income Year Mean income (in 2015 dollars) 1972 $37,760 $43,766 2015 37,138 54,757 Data from: 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 2015, has the income distribution become less or more unequal? Explain. 3. a. Median income, the income of the typical worker, has actually fallen, by $622. In percentage terms this is a fall of $622/$37,760 = 1.6%. However, mean (or average) income has increased by $10,991; in percentage terms this is an increase of $10,991/$43,766 × 100 = 25.1%. b. Since median income has fallen slightly, but mean income has grown significantly, this means that most of the growth in incomes has been at the top of the income distribution. If the incomes of the highest earners increase, this will raise the average income but leave the median income unchanged. So the income distribution has become more unequal from 1972 to 2015. 4. 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. 4. a. The median income is the income of the household in the exact middle of the income distribution. The exact middle of 100 households is in between the 49th and the 50th household; but since both of those households have income of $10,000, we can say that the median household income is exactly $10,000. The mean (or average) household income is the total income of all households, divided by the number of households. In Equalor, the mean household income is therefore (99 × $10,000 + $1,010,000)/100 = $20,000. b. After this redistribution, all households now have income of $20,000. So the median household income is $20,000. The mean (or average) household income is (100 × $20,000)/100 = $20,000. Note that although the median household income has increased, the mean household income has remained the same. This is one reason why economists generally think of median household income as a better indicator of the typical household’s income than mean income: it is obvious that as a result of the redistribution, the typical Equalorian household has been made better off. This is reflected by the increased median household income. However, this increase in the typical household’s income is not captured by mean (or average) household income at all. 5. The country of Marxland has the following income tax and social insurance system. Each citizen’s income is taxed at an average tax rate of 100%. A social insurance system then provides transfers to each citizen such that each citizen’s after-tax income is exactly equal. That is, each citizen gets (through a ­government transfer payment) an equal share of the income tax revenue. What is the incentive for one individual citizen to work and earn income? What will the total tax revenue in Marxland be? What will be the after-tax income (including the transfer payment) for each citizen? Do you think such a tax system that creates perfect equality will work? 5. If each citizen is taxed at an average tax rate of 100%, his or her income is entirely taxed away. Each citizen then receives an equal share of the total tax revenue. So the incentive for an individual citizen is not to work at all, to pay no taxes, but still to receive an equal share of the income (the tax revenue) generated by everyone else. As a result, no one will work, there will be no pre-tax income or tax revenue, and each citizen’s after-tax income will also be zero. A tax system that creates perfect equality in this way will destroy any incentive to earn income and so be impossible to implement. 6. 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%. a. For each scenario in the table, calculate the amount of income tax to be paid and after-tax income. b. Can you find a situation in this tax system where earning more pre-tax income actually results in less after-tax income? Explain. Scenarios 1 Lowani earns income of $8,000 2 Midram earns income of $40,000 3 Hi-Wan earns income of $100,000 6. a. 1. The income tax on the first $10,000 is −40%, and since Lowani does not earn more than $10,000, this determines her income tax: she pays income tax of −0.4 × $8,000 = −$3,200. That is, she receives a payment of $3,200 from the government. So her total after-tax income is $8,000 + $3,200 = $11,200. 2. T he income tax on the first $10,000 is −40%, so on that income Midram pays −0.4 × $10,000 = −$4,000. On the next $30,000 of his income, Midram pays 10% taxes, so his tax payment on that portion of his income is 0.10 × $30,000 = $3,000. Overall, Midram pays income tax of −$4,000 + $3,000 = −$1,000. That is, he still receives a payment of $1,000 from the government. So his total after-tax income is $40,000 + $1,000 = $41,000. 3. T he income tax on the first $10,000 is −40%, so on that income Hi-Wan pays −0.4 × $10,000 = −$4,000. On the next $90,000 of his income, Hi-Wan pays 10% taxes, so his tax payment on that portion of his income is 0.10 × $90,000 = $9,000. Overall, Hi-Wan pays income tax of −$4,000 + $9,000 = $5,000. So his total after-tax income is $100,000 − $5,000 = $95,000. b. There is no situation where earning more pre-tax income actually results in less after-tax income in this tax system. Whenever you earn more pre-tax income, your after-tax income increases as well. This is certainly true for the first $10,000 earned: for each additional dollar earned below $10,000, your after-tax income actually increases by $1.40. And it is still true for any amount earned above $10,000: for each additional dollar earned above $10,000, your after-tax income increases by $0.90. So there is no situation where earning more pre-tax income actually reduces your after-tax income. 7. 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? 7. a. An unemployed person has $50 income per day. An individual who works four hours per day has daily income of $40. If you worked five hours per day, you would earn equally as much as if you were unemployed. b. Since leisure is presumably preferable to work, no one would want to take a job that requires less than five hours work per day, since such a job would generate less income than the unemployment benefit and would require giving up leisure time. c. If $0.50 of the unemployment benefit is withdrawn for every earned dollar of income, for an individual who works four hours per day and so has earned income of $40, the unemployment benefit is cut by $40 × $0.50 = $20. That is, an individual who works for four hours per day has total income of $40 + $50 − $20 = $70 (income from work plus unemployment benefit minus cut in unemployment benefit). Now there is a financial incentive to working four hours per day: the individual makes $20 more than by being unemployed. 8. 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 2003 to 2015. 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. Total people Uninsured people Year Total poor children Uninsured poor children (millions) 2003 288.3 43.4 12.9 8.3 2005 293.8 44.8 12.9 8.0 2007 299.1 45.7 13.3 8.1 2009 304.3 50.7 15.5 7.5 2011 308.8 48.6 16.1 7.0 2013 313.1 41.8 15.8 5.4 2015 318.4 29.0 14.5 4.5 Data from: 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? 8. The accompanying table calculates the percentages of all uninsured people in the United States and the percentages of uninsured poor children. Year Uninsured people 2003 2005 2007 2009 2011 2013 2015 15% 15 15 17 16 13 9 Uninsured poor children 64% 62 61 48 43 34 31 The percentage of all uninsured people in the United States had been relatively steady through 2011. However, with the implementation of the Affordable Care Act in 2014, the number of uninsured Americans has been reduced by over 20 million people. The total percentage of uninsured has dropped from a high of 17% in 2009 to under 9% by 2015. Even prior to the arrival of the ACA, the percentage of uninsured poor children had fallen dramatically—even in 2009, when the percentage of uninsured people overall increased. As the chapter explained, SCHIP, created in 1997, gives health insurance benefits to certain children. This has almost certainly helped to lower the percentage of uninsured children, especially those in poverty. The ACA further lowered the percentage of uninsured children—three million more children now have insurance because of the ACA. 9. 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 2012, who agreed with the statement “There are important differences in what the Republicans and Democrats stand for.” What do these data say about the degree of partisanship in U.S. politics over time? Year Agree with statement 1952 1972 1992 2004 2008 2012 50% 46 60 76 78 81 Data from: American National Election Studies. 9. Clearly, voters increasingly feel that the degree of partisanship in U.S. politics has increased over time, as political parties are perceived to be increasingly ­different in their platforms. 10. For this Discovering Data exercise, go to FRED (fred.stlouisfed.org) to create a line graph that compares poverty rates for different counties across the United States. In the search bar enter “Estimated Percent of People of All Ages in Poverty for United States” and select the subsequent series. Follow the steps below to add the series for additional counties. Then answer the ­questions that follow. i. Select “Edit Graph” and under “Add Line” enter “Estimated Percent of People in Poverty for Wayne County, MI,” which includes Detroit, Michigan. ii. Repeat step i to add the following counties: i. King County, WA (for Seattle, Washington) ii. Miami-Dade County, FL (for Miami, Florida) iii. San Francisco County/City, CA (for San Francisco, California) iv. Cuyahoga County, OH (for Cleveland, OH) iii. In the graph frame change the start date to 1997-01-01 and the end date to 2014-01-01. a. Which counties have the lowest poverty rates? Highest? How do poverty rates compare to the national average? b. How has the difference in poverty rates changed from 2004 (prior to the Great Recession) to 2012 (after the Great Recession)? c. Create a second line graph including “Estimated Percent of People of All Ages in Poverty for United States” and a second line with your home county. How does the poverty rate in your home county compare with that of the national average? 10. Answers to this Discovering Data exercise can be found online. 11. In a private insurance market, there are two different kinds of people: some who are more likely to require expensive medical treatment and some who are less likely to require medical treatment and who, if they do, require less expensive treatment. One health insurance policy is offered, tailored to the average person’s health care needs: the premium is equal to the average ­person’s medical expenses (plus the insurer’s expenses and normal profit). a. Explain why such an insurance policy is unlikely to be feasible. In an effort to avoid the adverse selection death spiral, a private health insurer offers two health insurance policies: one that is intended for those who are more likely to require expensive treatment (and therefore charges a higher premium) and one that is intended for those who are less likely to require treatment (and therefore charges a lower premium). b. Could this system overcome the problem created by adverse selection? c. How does the British National Health Service avoid these problems? 11. a. This insurance policy is unlikely to be feasible because those people who are less likely to require expensive treatment generally know that they are less likely to need health insurance. And since the insurance premium is based on the average person’s medical expenses, those who are less likely to require treatment will find this policy too expensive. So many of these individuals will not purchase this one-size-fits-all policy. However, the policy is generally a good deal for those who know they are likely to require a lot of—and very expensive—medical treatment, and those individuals will want to buy the policy. So the insurer will be left with an adverse selection of mostly high-risk individuals and, in order to avoid losing money on selling the policy, will have to increase the premium. These are the first steps in what is known as the adverse selection death spiral. b. Even offering two different insurance policies will likely not work, because the insurer generally knows less well than the individual whether any given individual has a high or low risk of requiring treatment. As a result, everyone would want to buy the cheaper (lower-premium) policy. If the insurer is unable to tell whether some high-risk individuals are purchasing the insurance policy not intended for them, it will lose money on this policy and will have to increase the premium. This, again, is the first step in the adverse ­selection death spiral. c. As you learned in the chapter, the British National Health Service is a government agency that extends health care to everyone in Britain (this includes you as an American if you are in Britain on vacation!). And it pays for the cost out of general taxation. That is, no one has the option to opt out of paying for this government-provided health insurance policy. Chapter 19 Factor Markets and the Distribution of Income 1. In 2015, national income in the United States was $15,665.3 billion. In the same year, 148.8 million workers were employed, at an average wage, including ­benefits, of $62,187 per worker per year. a. How much compensation of employees was paid in the United States in 2015? b. Analyze the factor distribution of income. What percentage of national income was received in the form of compensation to employees in 2015? c. Suppose that a huge wave of corporate downsizing leads many terminated employees to open their own businesses. What is the effect on the factor distribution of income? d. Suppose the supply of labor rises due to an increase in the retirement age. What happens to the percentage of national income received in the form of compensation of employees? 1. a. Since 148.8 million workers were employed at an average yearly wage of $62,187, the total amount of compensation of employees was 148.8 million × $62,187 = $9,253.4 billion. b. Of a total of $15,665.3 billion, the amount received by workers was $9,253.4 billion. In percentage terms, this is ($9,253.4 billion/$15,665.3 billion) × 100 = 59.1%. c. The effect of this change is to diminish the share of income going to compensate employees and increase the share going to proprietors’ income. d. As the supply of labor increases, the equilibrium wage rate falls, but the equilibrium number of workers employed rises. So it is not clear whether more or less of national income is paid to workers in the form of compensation. 2. Marty’s Frozen Yogurt has the production function per day shown in the accompanying table. The equilibrium wage rate for a worker is $80 per day. Each cup of frozen yogurt sells for $2. Quantity of labor (workers) Quantity of frozen yogurt (cups) 0 0 1 110 2 200 3 270 4 300 5 320 6 330 a. Calculate the marginal product of labor for each worker and the value of the marginal product of labor per worker. b. How many workers should Marty employ? 2. a. The accompanying table shows the marginal product of labor (MPL) and the value of the marginal product of labor (VMPL) of each worker. Remember that VMPL = P × MPL. Here that means that VMPL = $2 × MPL. Quantity of labor (workers) Quantity of frozen yogurt (cups) 0 0 1 110 2 200 3 270 4 300 5 320 6 330 MPL (cups per worker) VMPL (per worker) 110 $220 90 180 70 140 30 60 20 40 10 20 b. Marty should employ 3 workers. The value of the marginal product of the third worker ($140) is above the wage rate of $80: Marty should hire the third worker. But the fourth worker’s value of the marginal product is only $60. This is less than Marty would have to pay this worker, so Marty should not hire a fourth worker. 3. The production function for Patty’s Pizza Parlor is given in the table in Problem 12. The price of pizza is $2, but the hourly wage rate rises from $10 to $15. Use a diagram to determine how Patty’s demand for workers responds as a result of this wage rate increase. 3. The accompanying diagram shows the value of the marginal product of labor curve and the wage rates of $10 and $15. As the wage rate increases from $10 to $15, Patty’s demand for workers decreases from 2 workers to 1 worker. So, as the wage rate increases, Patty should hire fewer workers. Wage rate $18 New wage rate Old wage rate 15 12 10 8 6 4 0 VMPL 1 2 3 4 5 Quantity of labor (workers) 4. Jameel runs a driver education school. The more driving instructors he hires, the more driving lessons he can sell. But because he owns a limited number of training automobiles, each additional driving instructor adds less to Jameel’s output of driving lessons. The accompanying table shows Jameel’s production function per day. Each driving lesson can be sold at $35 per hour. Quantity of labor (driving instructors) Quantity of driving lessons (hours) 0 0 1 8 2 15 3 21 4 26 5 30 6 33 Determine Jameel’s labor demand schedule (his demand schedule for driving instructors) for each of the following daily wage rates for driving instructors: $160, $180, $200, $220, $240, and $260. 4. The accompanying table calculates the marginal product of labor (MPL) and the value of the marginal product of labor (VMPL). Quantity of labor (driving instructors) Quantity of driving lessons (hours) 0 0 1 8 2 15 3 21 4 26 5 30 6 33 MPL (hours per driving instructor) VMPL (per driving instructor) 8 $280 7 245 6 210 5 175 4 140 3 105 If the daily wage rate of driving instructors is $160, Jameel should hire 4 instructors: the fourth instructor has a value of the marginal product of $175, which is greater than the wage rate; but the fifth instructor would have a value of the marginal product of only $140, which is less than the wage rate. By similar reasoning for the other wage rates, Jameel’s demand schedule for labor is as shown in the accompanying table. Daily wage rate Quantity of labor demanded (driving instructors) $160 4 180 3 200 3 220 2 240 2 260 1 5. Dale and Dana work at a self-service gas station and convenience store. Dale opens up every day, and Dana arrives later to help stock the store. They are both paid the current market wage of $9.50 per hour. But Dale feels he should be paid much more because the revenue generated from the gas pumps he turns on every morning is much higher than the revenue generated by the items that Dana stocks. Assess this argument. 5. Dale’s argument is incorrect because the owner of the business will hire workers until the hourly value of the marginal product of the last person hired equals $9.50. This implies that all other workers hired will have an hourly value of the marginal product higher than $9.50 but will be paid a wage of $9.50. Or to put it a slightly different way, any worker who opens the station, regardless of whether it is Dale or Dana, will have a higher value of the marginal product than the ­second person to report for work. 6. A New York Times article observed that the wage of farmworkers in Mexico was $11 an hour but the wage of immigrant Mexican farmworkers in California was $9 an hour. a. Assume that the output sells for the same price in the two countries. Does this imply that the marginal product of labor of farmworkers is higher in Mexico or in California? Explain your answer, and illustrate with a diagram that shows the demand and supply curves for labor in the respective markets. In your diagram, assume that the quantity supplied of labor for any given wage rate is the same for Mexican farmworkers as it is for immigrant Mexican farmworkers in California. b. Now suppose that farmwork in Mexico is more arduous and more dangerous than farmwork in California. As a result, the quantity supplied of labor for any given wage rate is not the same for Mexican farmworkers as it is for immigrant Mexican farmworkers in California. How does this change your answer to part a? What concept best accounts for the difference between wage rates for Mexican farmworkers and immigrant Mexican farmworkers in California? c. Illustrate your answer to part b with a diagram. In this diagram, assume that the quantity of labor demanded for any given wage rate is the same for Mexican employers as it is for Californian employers. 6. a. We know that farmworkers are employed up to the point where the value of the marginal product of labor is just equal to the wage: VMPL = P × MPL = W. In Mexico, this means that P × MPLMexico = $11 and in California P × MPLCalifornia = $9. Since the price, P, is the same in Mexico and in California, this means that the marginal product of labor in Mexico has to be higher than in California. Assuming that the quantity supplied for any given wage rate is the same for Mexican farmworkers as it is for immigrant Mexican farmworkers in California implies that the two groups have equivalent supply curves. Therefore, one supply curve can be drawn to illustrate the supply responses of both types of workers. The different wage rates received by the two groups of workers is a result of differences in the demand curves for labor. Because Mexican farmworkers have a higher marginal product of labor, the demand curve for their labor lies above and to the right of the demand curve for their peers in California, as shown in the accompanying diagram. Supply Wage $11 9 Demand for Mexican farmworkers in Mexico Higher MPL of Mexican farmworkers in Mexico Demand for immigrant Mexican farmworkers in California Quantity of labor 0 b. Because farmwork in Mexico is more arduous and dangerous than farmwork in California, we can no longer infer that the higher wages paid to Mexican farmworkers is evidence that they have a higher marginal product of labor than their peers in California. Rather, the difference in wages is a compensating differential that compensates Mexican farmworkers for the greater difficulty and danger they face. c. Assuming that the quantity of labor demanded for any given wage rate is the same for the two groups means that one demand curve can be drawn to represent employers’ demand responses in both markets. The compensating differential that Mexican farmworkers demand relative to their peers in California is illustrated by their supply curve of labor in the accompanying diagram, which lies above and to the left of the supply curve of their Californian peers. Wage Labor supply of Mexican farmworkers in Mexico Labor supply of immigrant Mexican farmworkers in California $11 9 Compensating differential 0 Demand Quantity of labor 7. Kendra is the owner of Wholesome Farms, a commercial dairy. Kendra employs labor, land, and capital. In her operations, Kendra can substitute between the amount of labor she employs and the amount of capital she employs. That is, to produce the same quantity of output she can use more labor and less capital; similarly, to produce the same quantity of output she can use less labor and more capital. Let w* represent the annual cost of labor in the market, let r*L represent the annual cost of a unit of land in the market, and let rK* represent the annual cost of a unit of capital in the market. a. Suppose that Kendra can maximize her profits by employing less labor and more capital than she is currently using but the same amount of land. What three conditions must now hold for Kendra’s operations (involving her value of the marginal product of labor, land, and capital) for this to be true? b. Kendra believes that she can increase her profits by renting and using more land. However, if she uses more land she must use more of both labor and capital; if she uses less land, she can use less of both labor and capital. What three conditions must hold (involving her value of the marginal product of labor, land, and capital) for this to be true? 7. a. The three conditions are: (1) Kendra’s current value of the marginal product of land = r*L. Only if this is satisfied should Kendra leave the amount of land she employs unchanged. (2) Kendra’s current value of the marginal product of labor rK* . Only if this is satisfied should Kendra increase the amount of capital she uses. b. The three conditions are: (1) Kendra’s current value of the marginal product of land > r*L. Only if this is satisfied should Kendra increase the amount of land she employs. (2) Kendra’s current value of the marginal product of labor > w*. Kendra must hire more labor if she employs more land. Thus, only if this condition is satisfied should Kendra increase the amount of labor she employs along with the amount of land. (3) Kendra’s current value of the marginal product of capital > rK* . Kendra must use more capital if she employs more land. Thus, only if this condition is satisfied should Kendra increase the amount of capital she uses along with the amount of land. 8. For each of the following situations in which similar workers are paid different wages, give the most likely explanation for these wage differences. a. Test pilots for new jet aircraft earn higher wages than airline pilots. b. College graduates usually have higher earnings in their first year on the job than workers without college degrees have in their first year on the job. c. Full professors command higher salaries than assistant professors for teaching the same class. d. Unionized workers are generally better paid than non-unionized workers. 8. a. This is most likely because being a test pilot for a new aircraft design is more dangerous than flying a commercial airliner. So the most likely explanation is that of compensating differentials. b. This is probably due to differences in human capital. More education gives a worker greater amounts of human capital. So more education usually translates into greater earnings. c. This is also probably due to differences in human capital. Because full professors have been teaching longer than assistant professors, their greater onthe-job experience has given them greater human capital. And greater human capital translates into higher salaries. d. Unions exercise considerable bargaining power in negotiating wages for their members. This results in higher wages and therefore wage differences that are not explained by marginal productivity theory. 9. Research consistently finds that despite nondiscrimination policies, AfricanAmerican workers on average receive lower wages than White workers do. What are the possible reasons for this? Are these reasons consistent with marginal productivity theory? 9. One possible reason is that this is the result of discrimination in the workplace. And, as you know, discrimination is not consistent with marginal productivity theory. But another possible reason for this income disparity is that it may be a result of past discrimination, which is consistent with marginal productivity theory. In the past, because of overt discrimination, the educational opportunities for African-American children were severely limited. These children are today’s workers, and if their educational attainment is lower, they embody less human capital and are therefore paid a lower wage. So the current income disparity may imply past discrimination but be consistent with marginal productivity theory. But even if this is true, keep in mind that marginal productivity theory does not give moral justification to the current distribution of income. 10. Greta is an enthusiastic amateur gardener and spends a lot of her free time working in her yard. She also has a demanding and well-paid job as a freelance advertising consultant. Because the advertising business is going through a difficult time, the hourly consulting fee Greta can charge falls. Greta decides to spend more time gardening and less time consulting. Explain her decision in terms of income and substitution effects. 10. As Greta’s hourly consulting fee falls, the opportunity cost of leisure—time spent working in her yard—also falls. So the substitution effect will push Greta toward spending more time gardening and less time consulting. However, the income effect of a fall in the consulting fee makes Greta poorer and—since leisure is a normal good—less inclined to consume leisure. That is, the income effect will push Greta toward working more. If, overall, Greta decides to work less, the ­substitution effect must have dominated the income effect. 11. You are the governor’s economic policy adviser. The governor wants to put in place policies that encourage employed people to work more hours at their jobs and that encourage unemployed people to find and take jobs. Assess each of the following policies in terms of reaching that goal. Explain your reasoning in terms of income and substitution effects, and indicate when the impact of the policy may be ambiguous. a. The state income tax rate is lowered, which has the effect of increasing workers’ after-tax wage rate. b. The state income tax rate is increased, which has the effect of decreasing workers’ after-tax wage rate. c. The state property tax rate is increased, which reduces workers’ after-tax income. 11. a. The effect of this policy on the incentive to work is ambiguous. A lower income tax rate has the effect of raising workers’ wages in a real sense. The substitution effect will induce people to work more, but the income effect will induce them to work less. So this is an effective policy only if the substitution effect is stronger than the income effect. b. The effect of this policy on the incentive to work is also ambiguous. A higher income tax rate has the effect of reducing workers’ wages in a real sense. The substitution effect will induce people to work less, but the income effect will induce them to work more. So this is an effective policy only if the income effect is stronger than the substitution effect. c. This policy will unambiguously encourage people to work more. The increase in the property tax rate makes people feel poorer, and as a result, they will consume less of all normal goods. Since leisure is a normal good, people will consume less leisure and work more. This policy influences how much labor is supplied only through the income effect. There is no substitution effect on the quantity of labor supplied in this case since the opportunity cost of leisure has not changed. WORK IT OUT Interactive step-by-step help with solving this problem can be found online. 12. Patty’s Pizza Parlor has the production function per hour shown in the accompanying table. The hourly wage rate for each worker is $10. Each pizza sells for $2. Quantity of labor (workers) Quantity of pizza 0 0 1 9 2 15 3 19 4 22 5 24 a. Calculate the marginal product of labor for each worker and the value of the marginal product of labor per worker. b. Draw the value of the marginal product of labor curve. Use your diagram to determine how many workers Patty should employ. c. The price of pizza increases to $4. Calculate the value of the marginal product of labor per worker, and draw the new value of the marginal product of labor curve in your diagram. Use your diagram to determine how many workers Patty should employ now. Now let’s assume that Patty buys a new high-tech pizza oven that allows her workers to become twice as productive as before. That is, the first worker now produces 18 pizzas per hour instead of 9, and so on. d. Calculate the new marginal product of labor and the new value of the marginal product of labor at the original price of $2 per pizza. e. Use a diagram to determine how Patty’s hiring decision responds to this increase in the productivity of her workforce. 12. a. The accompanying table shows the marginal product of labor (MPL) and the value of the marginal product of labor (VMPL1). Number of workers Quantity of pizza 0 0 1 9 2 15 3 19 4 22 5 24 MPL (pizzas per worker) VMPL1 (per worker) (price of pizza = $2) VMPL2 (per worker) (price of pizza = $4) 9 $18 $36 6 12 24 4 8 16 3 6 12 2 4 8 b. The accompanying diagram shows the value of the marginal product of labor curve (VMPL1). The value of the marginal product of labor equals the wage rate at 2 workers. So Patty should employ 2 workers. Wage rate $36 24 18 16 12 10 6 4 Wage rate 0 VMPL2 VMPL1 1 2 3 4 5 Quantity of labor (workers) c. The table shows the new value of the marginal product of labor (VMPL2). The value of the marginal product of labor curve is labeled VMPL2 in the diagram. The new value of the marginal product of labor equals the wage rate at 4 workers. So Patty should employ 4 workers. d. The accompanying table shows the new production function for Patty’s Pizza Parlor, the new marginal product of labor (MPL3), and the new value of the marginal product of labor (VMPL3). Quantity of labor (workers) Quantity of pizza 0 0 1 18 2 30 3 38 4 44 5 48 MPL3 (pizzas per worker) VMPL3 (per worker) 18 $36 12 24 8 16 6 12 4 8 e. The accompanying diagram shows the original value of the marginal product of labor curve from part b (VMPL1) and the new value of the marginal product of labor curve (VMPL3). The value of the marginal product of labor now equals the wage rate at 4 workers. So Patty should employ 4 workers. As the value of the marginal product of labor increases—in this case as a result of a technological innovation (the new pizza oven)—Patty should hire more workers. Wage rate $36 24 Wage rate 18 16 12 10 6 4 0 VMPL3 VMPL1 1 2 3 4 5 Quantity of labor (workers) Indifference Curve 19 Appendix Analysis of Labor Supply 1. Leandro has 16 hours per day that he can allocate to work or leisure. His job pays a wage rate of $20. Leandro decides to consume 8 hours of leisure. His indifference curves have the usual shape: they slope downward, they do not cross, and they have the characteristic convex shape. a. Draw Leandro’s time allocation budget line for a typical day. Then illustrate the indifference curve at his optimal choice. Now Leandro’s wage rate falls to $10. b. Draw Leandro’s new budget line. c. Suppose that Leandro now works only 4 hours as a result of his reduced wage rate. Illustrate the indifference curve at his new optimal choice. d. Leandro’s decision to work less as the wage rate falls is the result of a substitution effect and an income effect. In your diagram, show the income effect and the substitution effect from this reduced wage rate. Which effect is stronger? 1. a. If Leandro spends all his time—all 16 hours—in leisure activities, he has no income. If he spends all 16 hours working, he has total income of 16 × $20 = $320. This gives him the time allocation budget line labeled BL1 in the accompanying diagram. The opportunity cost of leisure—minus the slope of his budget line—is 20: for each additional hour of leisure, Leandro gives up $20 of income. Since he consumes 8 hours of leisure (and works the remaining 8 hours), his indifference curve, I2, has to be tangent to his time allocation ­budget line at point A. Income $320 BL1 160 BL2 BLS A S I2 B I1 8 0 Substitution effect Income effect 12 16 Quantity of leisure (hours per day) b. If Leandro spends all his time working, he now has income of only 16 × $10 = $160. This gives him the time allocation budget line labeled BL2 in the ­diagram. The opportunity cost of leisure—minus the slope of his budget line— is 10: for each additional hour of leisure, Leandro gives up $10 of income. c. If Leandro works 4 hours, he has 12 hours of leisure. That is, his indifference curve, I1, is tangent to his time allocation budget line at point B in the diagram. d. The substitution effect is Leandro’s change in leisure consumption from point A to point S in the diagram: we constructed it by holding Leandro’s ­utility constant—by keeping him on the same indifference curve he was on originally, I2—but allowing the opportunity cost of leisure to change from 20 to 10. This is illustrated by the dashed budget line labeled BLS. The opportunity cost has fallen, pushing Leandro toward consuming more leisure by the substitution effect. The income effect is Leandro’s change in leisure consumption from point S to point B: the reduced wage rate has made Leandro poorer, so he should consume less leisure since it is a normal good. Since his overall leisure consumption has increased (from 8 hours to 12 hours), the substitution effect is stronger than the income effect. 2. Florence is a highly paid fashion consultant who earns $100 per hour. She has 16 hours per day that she can allocate to work or leisure, and she decides to work for 12 hours. a. Draw Florence’s time allocation budget line for a typical day, and illustrate the indifference curve at her optimal choice. One of Florence’s clients is featured on the front page of Vague, an influential fashion magazine. As a result, Florence’s consulting fee now rises to $500 per hour. Florence decides to work only 10 hours per day. b. Draw Florence’s new time allocation budget line, and illustrate the ­indifference curve at her optimal choice. c. In your diagram, show the income effect and the substitution effect from this increase in the wage rate. Which effect is stronger? 2. a. If Florence spends all 16 hours in leisure activities, she earns no income. If she spends all 16 hours working, her income is $1,600. This gives her the time allocation budget line labeled BL1 in the accompanying diagram. Since she works for 12 hours, she consumes 4 hours of leisure. That is, her indifference curve, I1, is tangent to her budget line at point A. Income $8,000 B I2 S 1,600 0 A I1 BL1 BL2 BLS 4 6 16 Quantity Substitution effect Income effect of leisure (hours per day) b. If Florence were to work all 16 hours now, her income would be $8,000. This gives her the time allocation budget line labeled BL2 in the diagram. Since she works 10 hours now, she consumes 6 hours of leisure. That is, she is at point B. c. The change in Florence’s leisure consumption from point A to point S is the substitution effect. Keeping her on the same indifference curve, I1, that she was originally on, we changed just the opportunity cost of leisure. This is represented by the dashed budget line, BLS. The opportunity cost of leisure has risen, so the substitution effect pushes Florence toward consuming less leisure. The income effect is the change in Florence’s consumption from point S to point B. The income effect pushes her toward consuming more leisure: Florence has become richer as her hourly consulting fee increased, so she chooses to consume more leisure, a normal good. In this case, the income effect is stronger than the substitution effect, and Florence consumes more leisure overall. 3. Wendy works at a fast-food restaurant. When her wage rate was $5 per hour, she worked 30 hours per week. When her wage rate rose to $6 per hour, she decided to work 40 hours. But when her wage rate rose further to $7, she decided to work only 35 hours. a. Draw Wendy’s individual labor supply curve. b. Is Wendy’s behavior irrational, or can you find a rational explanation? Explain your answer. 3. a. Wendy’s individual labor supply curve has the backward-bending shape shown in the accompanying diagram. Wage rate $7 Individual labor supply curve 6 5 0 30 35 40 Quantity of labor (hours) b. Wendy’s behavior has a perfectly rational explanation. As the wage rate increases, the opportunity cost of leisure increases. So the substitution effect says to consume less leisure and work more. At the same time, an increase in the wage rate makes Wendy richer in a real sense. And since leisure is a normal good, the income effect says to consume more leisure and work less. Income and substitution effects work in opposite directions. As Wendy’s wage rate rises from $5 to $6, the substitution effect dominates the income effect. As her wage rate rises further to $7, the income effect dominates the substitution effect. 4. Over the past fifty years the average American’s leisure time has increased by between 4 and 8 hours a week. Some economists think that this increase is ­primarily driven by a rise in wage rates. a. Use the income and substitution effects to describe the labor supply for the average American. Which effect dominates? b. In addition to increasing wages, a study by the Bureau of Labor Statistics finds labor force participation for women is projected to steadily increase through 2024. For the average woman who has entered the labor force, which effect dominates? c. Draw typical individual labor supply curves that illustrate your answers to part a and part b above. 4. a. As wage rates rise, the substitution effect says to consume less leisure, because leisure has just become relatively more expensive. However, the income effect says to consume more leisure, because a wage rate increase makes ­consumers richer and leisure is a normal good. Since the overall effect has been for ­leisure time to increase as a result of the wage rate increase, the income effect must have been stronger than the substitution effect. b. As wage rates rise, income and substitution effects work in the same ways as in part a. However, since female labor force participation has increased, the substitution effect must have been stronger for new female workers. (Why is this? For individuals who are not participating in the labor market, an increase in the wage rate has only a substitution effect, leading them to consume less ­leisure since its opportunity cost has risen—that is, leading them to work more. Since they are not earning income from work, an increase in the wage rate has no income effect.) c. The accompanying diagram shows a typical labor supply curve for all workers in panel (a) and for new female workers in panel (b). (a) All Workers Wage rate (b) New Female Workers Wage rate Quantity of labor Quantity of labor WORK IT OUT Interactive step-by-step help with solving this problem can be found online. 5. Tamara has 80 hours per week that she can allocate to work or leisure. Her job pays a wage rate of $20 per hour, but Tamara is being taxed on her income in the following way. On the first $400 that Tamara makes, she pays no tax. That is, for the first 20 hours she works, her net wage—what she takes home after taxes—is $20 per hour. On all income above $400, Tamara pays a 75% tax. That is, for all hours above the first 20 hours, her net wage rate is only $5 per hour. Tamara decides to work 30 hours. Her indifference curves have the usual shape. a. Draw Tamara’s time allocation budget line for a typical week. Also illustrate the indifference curve at her optimal choice. The government changes the tax scheme. Now only the first $100 of income is tax-exempt. That is, for the first 5 hours she works, Tamara’s net wage rate is $20 per hour. But the government reduces the tax rate on all other income to 50%. That is, for all hours above the first 5 hours, Tamara’s net wage rate is now $10. After these changes, Tamara finds herself exactly equally as well off as before. That is, her new optimal choice is on the same indifference curve as her initial optimal choice. b. Draw Tamara’s new time allocation budget line on the same diagram. Also illustrate her optimal choice. Bear in mind that she is equally as well off (on the same indifference curve) as before the tax changes occurred. c. Will Tamara work more or less than before the changes to the tax scheme? Why? 5. a. If Tamara consumes 80 hours of leisure, she has no income. For every hour she works up to 20 hours, she earns a net $20 per hour. That is, if she works 20 hours—she consumes 60 hours of leisure—her income is $400. In the accompanying diagram, the opportunity cost of leisure (equal to minus the slope of her budget line, BL1) during the first 20 hours of work is 20: for each hour of leisure, she gives up $20 of income. For any hours she works beyond the first 20 hours, she earns a net $5 per hour. If she works for all ­remaining 60 hours, in those 60 hours she makes $300. The opportunity cost of leisure (equal to minus the slope of her budget line, BL1) during those 60 hours is 5: for each hour of leisure, she gives up $5 of income. That is, if she works 80 hours per week, her total net income will be $400 + $300 = $700. So her ­budget line has a kink in it at 60 hours of leisure. Since she works for 30 hours, Tamara consumes 50 hours of leisure. This is point A in the diagram. At point A she earns $400 (for the first 20 hours worked at $20 per hour) plus $50 (for the last 10 hours worked at $5 per hour), equal to $450 in total. Income $850 BL2 700 BL1 B A 450 400 I 100 0 50 60 75 80 Quantity of leisure (hours per week) b. If Tamara consumes 80 hours of leisure, she has no income. For every hour she works up to 5 hours, she earns a net $20 per hour. That is, if she works 5 hours—she consumes 75 hours of leisure—her income is $100. The opportunity cost of leisure (equal to minus the slope of her budget line, BL2) during the first 5 hours of work is 20: for each hour of leisure, she gives up $20 of income. For any hours she works beyond the first 5 hours, she earns a net $10 per hour. If she works for all the remaining 75 hours, she makes $750. The opportunity cost of leisure (equal to minus the slope of her budget line, BL2) during those 75 hours is 10: for each hour of leisure, she gives up $10 of income. That is, if she works 80 hours per week, her total net income will be $100 + $750 = $850. Since after these changes she is equally as well off as before (she is on the same indifference curve as at point A), her new optimal consumption bundle has to be at a point like B on the indifference curve I. c. As a result of the tax changes, Tamara works more (she consumes less leisure). This is because the tax changes in effect have isolated just the substitution effect. As a result of the cut in the tax rate, her net wage rate (the opportunity cost of leisure) has increased. This has both a substitution effect and an income effect. Tamara should consume less leisure by the substitution effect and more leisure by the income effect. However, the cut in the tax-exempt amount has made Tamara poorer by an amount that leaves her equally as well off as she was before the tax changes. That is, the cut in the tax-exempt amount has just offset the income effect of the increase in her net wage rate. So the only effect at work here is the substitution effect. And the substitution effect says, unambiguously, that Tamara should consume less leisure and work more. Uncertainty, Risk, and Private Information 1. For each of the following situations, calculate the expected value. a. Tanisha owns one share of IBM stock, which is currently trading at $80. There is a 50% chance that the share price will rise to $100 and a 50% chance that it will fall to $70. What is the expected value of the future share price? b. Sharon buys a ticket in a small lottery. There is a probability of 0.7 that she will win nothing, of 0.2 that she will win $10, and of 0.1 that she will win $50. What is the expected value of Sharon’s winnings? c. Aaron is a farmer whose rice crop depends on the weather. If the weather is favorable, he will make a profit of $100. If the weather is unfavorable, he will make a profit of −$20 (that is, he will lose money). The weather forecast reports that the probability of weather being favorable is 0.9 and the probability of weather being unfavorable is 0.1. What is the expected value of Aaron’s profit? 1. a. The expected value of the share price is (0.5 × $100) + (0.5 × $70) = $50 + $35 = $85. b. The expected value of Sharon’s winnings is (0.7 × $0) + (0.2 × $10) + (0.1 × $50) = $0 + $2 + $5 = $7. c. The expected value of Aaron’s profit is (0.9 × $100) + (0.1 × (−$20)) = $90 + (−$2) = $88. 2. Vicky N. Vestor is considering investing some of her money in a startup ­company. She currently has income of $4,000, and she is considering investing $2,000 of that in the company. There is a 0.5 probability that the company will succeed and will pay out $8,000 to Vicky (her original investment of $2,000 plus $6,000 of the company’s profits). And there is a 0.5 probability that the company will fail and Vicky will get nothing (and lose her investment). The accompanying table illustrates Vicky’s utility function. Income $0 Total utility (utils) 0 1,000 50 2,000 85 3,000 115 4,000 140 5,000 163 6,000 183 7,000 200 8,000 215 9,000 229 10,000 241 a. Calculate Vicky’s marginal utility of income for each income level. Is Vicky risk-averse? b. Calculate the expected value of Vicky’s income if she makes this investment. c. Calculate Vicky’s expected utility from making the investment. d. What is Vicky’s utility from not making the investment? Will Vicky therefore invest in the company? Chapter 20 2. a. Vicky’s marginal utility of income is given in the accompanying table. Since her marginal utility declines, she is risk-averse. Income Total utility (utils) $0 0 1,000 50 2,000 85 3,000 115 4,000 140 5,000 163 6,000 183 7,000 200 8,000 215 9,000 229 10,000 241 Marginal utility (utils) 50 35 30 25 23 20 17 15 14 12 b. If the company succeeds, Vicky will have income of $10,000 (the $2,000 she did not invest plus the $8,000 the company pays out to her). If the company fails, Vicky will have income of $2,000 (the $2,000 she has not invested). The expected value of Vicky’s income is (0.5 × $10,000) + (0.5 × $2,000) = $5,000 + $1,000 = $6,000. c. Vicky’s expected utility from making the investment is (0.5 × 241) + (0.5 × 85) = 120.5 + 42.5 = 163. d. If she does not make the investment, Vicky’s utility is the utility of ­having $4,000 income, that is, 140. Since the expected utility from making the ­investment is greater than her utility from not making the investment, she will invest in the company. 3. Vicky N. Vestor’s utility function was given in Problem 2. As in Problem 2, Vicky currently has income of $4,000. She is considering investing in a startup company, but the investment now costs $4,000 to make. If the company fails, Vicky will get nothing from the company. But if the company succeeds, she will get $10,000 from the company (her original investment of $4,000 plus $6,000 of the company’s profits). Each event has a 0.5 probability of occurring. Will Vicky invest in the company? 3. If the company succeeds, Vicky will have income of $10,000. If the company fails, Vicky will have income of $0 (she loses her entire investment). Vicky’s expected utility from making the investment is (0.5 × 241) + (0.5 × 0) = 120.5 + 0 = 120.5. Since this is less than her utility from not investing (140 utils), she will not invest in the company. 4. You have $1,000 that you can invest. If you buy Ford stock, you face the following returns and probabilities from holding the stock for one year: with a probability of 0.2 you will get $1,500; with a probability of 0.4 you will get $1,100; and with a probability of 0.4 you will get $900. If you put the money into the bank, in one year’s time you will get $1,100 for certain. a. What is the expected value of your earnings from investing in Ford stock? b. Suppose you are risk-averse. Can we say for sure whether you will invest in Ford stock or put your money into the bank? 4. a. The expected value of your earnings from investing in Ford stock is (0.2 × $1,500) + (0.4 × $1,100) + (0.4 × $900) − $1,000 = $300 + $440 + $360 − $1,000 = $100. b. You have a choice between getting $1,100 for certain by putting your money into the bank or getting $1,100 on average by investing in Ford stock. Both investments pay the same on average, but investing in Ford stock is risky. Since you are risk-averse, you would prefer to get $1,100 for certain. So you will definitely put your money in the bank. 5. Wilbur is an airline pilot who currently has income of $60,000. If he gets sick and loses his flight medical certificate, he loses his job and has only $10,000 income. His probability of staying healthy is 0.6, and his probability of getting sick is 0.4. Wilbur’s utility function is given in the accompanying table. Income Total utility (utils) $0 0 10,000 60 20,000 110 30,000 150 40,000 180 50,000 200 60,000 210 a. What is the expected value of Wilbur’s income? b. What is Wilbur’s expected utility? ilbur thinks about buying “loss-of-license” insurance that will compensate him W if he loses his flight medical certificate. c. One insurance company offers Wilbur full compensation for his income loss (that is, the insurance company pays Wilbur $50,000 if he loses his flight medical certificate), and it charges a premium of $40,000. That is, regardless of whether he loses his flight medical certificate, Wilbur’s income after insurance will be $20,000. What is Wilbur’s utility? Will he buy the insurance? d. What is the highest premium Wilbur would just be willing to pay for full insurance (insurance that completely compensates him for the income loss)? 5. a. The expected value of Wilbur’s income is (0.6 × $60,000) + (0.4 × $10,000) = $36,000 + $4,000 = $40,000. b. Wilbur’s expected utility is (0.6 × 210) + (0.4 × 60) = 126 + 24 = 150. c. If Wilbur’s income is $20,000 for certain, his utility is 110. This is lower than his expected utility from not being insured, so he would not buy this insurance. d. If Wilbur had $30,000 after insurance for certain, his utility would be 150, which is just the same as his expected utility from not being insured. So if an insurance company offered him full insurance (to compensate him completely if he loses his flight medical certificate) and charged him a premium of $30,000, then Wilbur would have $30,000 income available for consumption for certain. So a premium of $30,000 is the highest he is willing to pay. 6. According to the FBI’s Uniform Crime Reports, approximately 1 in 379 cars was stolen in the United States in 2014. Beth owns a car worth $20,000 and is considering purchasing an insurance policy to protect herself from car theft. For the following questions, assume that the chance of car theft is the same in all regions and across all car models. a. What should the premium for a fair insurance policy have been in 2014 for a policy that replaces Beth’s car if it is stolen? (Hint: In your calculation, round up to three decimal places.) b. Suppose an insurance company charges 0.6% of the car’s value for a policy that pays for replacing a stolen car. How much will the policy cost Beth? c. Will Beth purchase the insurance in part b if she is risk-neutral? d. Discuss a possible moral hazard problem facing Beth’s insurance company if she purchases the insurance. 6. a. The premium for a fair insurance policy is equal to the expected value of Beth’s claim. Since the probability of having her car stolen is 1/379 = 0.003, the expected value of Beth’s claim is 0.003 × $20,000 = $60. b. The premium for this insurance policy is 0.006 × $20,000 = $120. c. Since this is a less than fair insurance policy, Beth will not purchase it unless she is risk-averse. d. If Beth is completely insured against loss of her car, she has no incentive to take care: she may leave it unlocked or park it in badly lit side streets instead of in a secure garage. 7. Hugh’s income is currently $5,000. His utility function is shown in the accompanying table. Income Total utility (utils) $0 0 1,000 100 2,000 140 3,000 166 4,000 185 5,000 200 6,000 212 7,000 222 8,000 230 9,000 236 10,000 240 a. Calculate Hugh’s marginal utility of income. What is his attitude toward risk? b. Hugh is thinking about gambling in a casino. With a probability of 0.5 he will lose $3,000, and with a probability of 0.5 he will win $5,000. What is the expected value of Hugh’s income? What is Hugh’s expected utility? Will he decide to gamble? (Suppose that he gets no extra utility from going to the casino.) c. Suppose that the “spread” (how much he can win versus how much he can lose) of the gamble narrows, so that with a probability of 0.5 Hugh will lose $1,000, and with a probability of 0.5 he will win $3,000. What is the expected value of Hugh’s income? What is his expected utility? Is this gamble better for him than the gamble in part b? Will he decide to gamble? 7. a. Hugh’s marginal utility is given in the accompanying table. Since his marginal utility is diminishing, he is risk-averse. Income Total utility (utils) $0 0 1,000 100 2,000 140 3,000 166 4,000 185 5,000 200 6,000 212 7,000 222 8,000 230 9,000 236 10,000 240 Marginal utility (utils) 100 40 26 19 15 12 10 8 6 4 b. Hugh will have $2,000 income with probability 0.5 and $10,000 income with probability 0.5. The expected value of his income is (0.5 × $2,000) + (0.5 × $10,000) = $1,000 + $5,000 = $6,000. His expected utility is (0.5 × 140) + (0.5 × 240) = 70 + 120 = 190. His utility from not gambling is the utility of having $5,000 for certain, which is 200. That is, he will not take the gamble. c. Hugh will have $4,000 income with probability 0.5 and $8,000 income with probability 0.5. The expected value of his income is (0.5 × $4,000) + (0.5 × $8,000) = $2,000 + $4,000 = $6,000. This gamble has the same expected value as that in part b. However, Hugh’s expected utility is (0.5 × 185) + (0.5 × 230) = 92.5 + 115 = 207.5. This gamble is better for him than that in part b because it has less risk associated with it: his expected utility is higher than for the gamble in part b. And it is sufficiently less risky that he will now take the gamble: he prefers it over having $5,000 for certain, which yields him only 200 utils. 8. Eva is risk-averse. Currently she has $50,000 to invest. She faces the following choice: she can invest in the stock of a start-up company, or she can invest in IBM stock. If she invests in the start-up company, then with probability 0.5 she will lose $30,000, but with probability 0.5 she will gain $50,000. If she invests in IBM stock, then with probability 0.5 she will lose $10,000, but with ­probability 0.5 she will gain $30,000. Can you tell which investment she will prefer to make? 8. If Eva invests in the start-up company, with probability 0.5 she has $50,000 − $30,000 = $20,000 in stock value, and with probability 0.5 she has $50,000 + $50,000 = $100,000 in stock value. So the expected value of Eva’s stock when she invests in the start-up company is (0.5 × $20,000) + (0.5 × $100,000) = $10,000 + $50,000 = $60,000. Similarly, if Eva invests in IBM stock, the expected value of her stock is (0.5 × $40,000) + (0.5 × $80,000) = $20,000 + $40,000 = $60,000. Both investments give Eva the same expected value, but the investment in IBM is less risky. She will therefore prefer to invest in IBM stock. 9. Suppose you have $1,000 that you can invest in Ted and Larry’s Ice Cream Parlor and/or Ethel’s House of Cocoa. The price of a share of stock in either company is $100. The fortunes of each company are closely linked to the weather. When it is warm, the value of Ted and Larry’s stock rises to $150 but the value of Ethel’s stock falls to $60. When it is cold, the value of Ethel’s stock rises to $150 but the value of Ted and Larry’s stock falls to $60. There is an equal chance of the weather being warm or cold. a. If you invest all your money in Ted and Larry’s, what is your expected stock value? What if you invest all your money in Ethel’s? b. Suppose you diversify and invest half of your $1,000 in each company. How much will your total stock be worth if the weather is warm? What if it is cold? c. Suppose you are risk-averse. Would you prefer to put all your money in Ted and Larry’s, as in part a? Or would you prefer to diversify, as in part b? Explain your reasoning. 9. a. If you put all your money in Ted and Larry’s, you can purchase ten shares of stock. The ten shares will be worth $1,500 if the weather is warm and $600 if it is cold. Since there is an equal chance of it being cold or warm, the expected stock value is (0.5 × $1,500) + (0.5 × $600) = $750 + $300 = $1,050. This is the same as the expected stock value you would receive if you put all your money in Ethel’s. b. If you put $500 in each company, you would initially have five shares of each. Suppose the weather turned out to be warm and sunny. The five shares of Ted and Larry’s would be worth $750, and the five shares of Ethel’s would be worth $300. So your total stock value would be $1,050. What would happen if it was cold? Now the five shares of Ted and Larry’s would be worth $300 and the five shares of Ethel’s would be worth $750, for a total stock value of $1,050. This illustrates the importance of diversification. c. If you invest all your money in Ted and Larry’s, you will get, on average, $1,050, but there is risk attached. By investing your money in both stocks, you get the same payoff whether the weather is warm or cold. That is, you can earn $1,050 for certain instead of an expected stock value of $1,050. A riskaverse individual would diversify his or her risk by investing in both stocks. In this example, diversification eliminates all risk. 10. LifeStrategy Conservative Growth and Energy are two portfolios constructed and managed by the Vanguard Group of mutual funds, comprised of stocks of conservatively managed U.S. companies and stocks of U.S. energy companies. The accompanying table shows historical annualized return from the period 2004 to 2014, which suggest the expected value of the annual percentage returns associated with these portfolios. Portfolio LifeStrategy Conservative Growth Energy Expected value of return (percent) 5.88% 12.66 a. Which portfolio would a risk-neutral investor prefer? b. Juan, a risk-averse investor, chooses to invest in the LifeStrategy Conservative Growth portfolio. What can be inferred about the risk of the two portfolios from Juan’s choice of investment? Based on historical performance, would a risk-neutral investor ever choose LifeStrategy Conservative Growth? c. Juan is aware that diversification can reduce risk. He considers a portfolio in which half his investment is in conservatively managed companies and the other half in Energy companies. What is the expected value of the return for this combined portfolio? Would you expect this combined portfolio to be more risky or less risky than the LifeStrategy Conservative Growth portfolio? Why or why not? 10. a. A risk-neutral investor—someone who does not care about risk—is interested only in the expected value of the return. Since the expected value of the U.S. Energy portfolio (12.66%) is greater than the expected value of the LifeStrategy Conservative Growth portfolio (5.88%), a risk-neutral investor would prefer the Energy portfolio. b. Since Juan is risk-averse and chooses the portfolio with the lower expected return, this portfolio must be considerably less risky than the Energy portfolio. As you saw in part a of this question, a risk-neutral investor would always choose the Energy portfolio, regardless of the level of risk associated with the portfolios. c. The expected value of the return of this combined portfolio is ((0.5 × 0.0588) + (0.5 × 0.1266)) × 100 = 9.27%. If the two portfolios are not correlated (what happens to one portfolio is an independent event from what happens to the other portfolio), then the combined portfolio would be less risky. However, if there is positive correlation between the two portfolios, then the risk of the combined portfolio could still be higher than the risk of the LifeStrategy ­Conservative Growth portfolio on its own. 11. You are considering buying a second-hand Volkswagen. From reading car magazines, you know that half of all Volkswagens have problems of some kind (they are “lemons”) and the other half run just fine (they are “plums”). If you knew that you were getting a plum, you would be willing to pay $10,000 for it: this is how much a plum is worth to you. You would also be willing to buy a lemon, but only if its price was no more than $4,000: this is how much a lemon is worth to you. And someone who owns a plum would be willing to sell it at any price above $8,000. Someone who owns a lemon would be willing to sell it for any price above $2,000. a. For now, suppose that you can immediately tell whether the car that you are being offered is a lemon or a plum. Suppose someone offers you a plum. Will there be trade? ow suppose that the seller has private information about the car she is selling: N the seller knows whether she has a lemon or a plum. But when the seller offers you a Volkswagen, you do not know whether it is a lemon or a plum. So this is a situation of adverse selection. b. Since you do not know whether you are being offered a plum or a lemon, you base your decision on the expected value to you of a Volkswagen, assuming you are just as likely to buy a lemon as a plum. Calculate this expected value. c. Suppose, from driving the car, the seller knows she has a plum. However, you don’t know whether this particular car is a lemon or a plum, so the most you are willing to pay is your expected value. Will there be trade? 11. a. You value a plum at $10,000: you would be willing to pay any price up to $10,000 to buy it. The seller values a plum at $8,000: she would be willing to sell her car at any price above $8,000. So there is room for trade: at some price between $8,000 and $10,000, both buyer and seller will want to engage in trade with each other. b. With probability 0.5 the car you are being offered is worth $10,000 to you. And with probability 0.5 the car you are being offered is worth $4,000 to you. So the expected value to you is (0.5 × $10,000) + (0.5 × $4,000) = $5,000 + $2,000 = $7,000. c. The most you are willing to pay for a car whose quality you do not know is $7,000. But the seller who knows she has a plum will only want to sell it for a price upwards of $8,000. So there is no trade, although it would be mutually beneficial. 12. You own a company that produces chairs, and you are thinking about hiring one more employee. Each chair produced gives you revenue of $10. There are two potential employees, Fred Ast and Sylvia Low. Fred is a fast worker who produces ten chairs per day, creating revenue for you of $100. Fred knows that he is fast and so will work for you only if you pay him more than $80 per day. Sylvia is a slow worker who produces only five chairs per day, creating revenue for you of $50. Sylvia knows that she is slow and so will work for you if you pay her more than $40 per day. Although Sylvia knows she is slow and Fred knows he is fast, you do not know who is fast and who is slow. So this is a situation of adverse selection. a. Since you do not know which type of worker you will get, you think about what the expected value of your revenue will be if you hire one of the two. What is that expected value? b. Suppose you offered to pay a daily wage equal to the expected revenue you calculated in part a. Whom would you be able to hire: Fred, or Sylvia, or both, or neither? c. If you know whether a worker is fast or slow, which one would you prefer to hire and why? Can you devise a compensation scheme to guarantee that you employ only the type of worker you prefer? 12. a. When you hire an additional worker, there is a 0.5 chance you will get a fast worker and a 0.5 chance you will get a slow worker. So the expected value of your additional revenue is (0.5 × $100) + (0.5 × $50) = $50 + $25 = $75. b. If you offered to pay $75, you will be able to hire only Sylvia: Fred would not want to work for that wage. That is, you will attract only an adverse selection of slow workers. c. You prefer to hire a fast worker. With a fast worker you earn $100 − $80 = $20 per day, but only earn $50 − $40 = $10 per day with a slow worker. Any compensation scheme that pays a worker $80 per day if at least 10 chairs are produced, but less than $40 per day if less than 10 chairs are produced, will guarantee that only a fast worker will choose to work for you. 13. For each of the following situations, do the following: first describe whether it is a situation of moral hazard or of adverse selection. Then explain what inefficiency can arise from this situation and explain how the proposed solution reduces the inefficiency. a. When you buy a second-hand car, you do not know whether it is a lemon (low quality) or a plum (high quality), but the seller knows. A solution is for sellers to offer a warranty with the car that pays for repair costs. b. Some people are prone to see doctors unnecessarily for minor complaints like headaches, and health maintenance organizations do not know how urgently you need a doctor. A solution is for insurees to have to make a co-payment of a certain dollar amount (for example, $10) each time they visit a health care provider. All insurees are risk-averse. c. When airlines sell tickets, they do not know whether a buyer is a business traveler (who is willing to pay a lot for a seat) or a leisure traveler (who has a low willingness to pay). A solution for a profit-maximizing airline is to offer an expensive ticket that is very flexible (it allows date and route changes) and a cheap ticket that is very inflexible (it has to be booked in advance and cannot be changed). d. A company does not know whether workers on an assembly line work hard or whether they slack off. A solution is to pay the workers “piece rates,” that is, pay them according to how much they have produced each day. All workers are risk-averse, but the company is not risk-neutral. e. When making a decision about hiring you, prospective employers do not know whether you are a productive or unproductive worker. A solution is for productive workers to provide potential employers with references from previous employers. 13. a. This is a situation of adverse selection: although the seller knows what type of car she has to sell, you don’t. If you don’t know the quality of a car you are offered, you are willing to pay only the average of what a lemon and a plum are worth to you. So sellers of plums are not able to get a price that is high enough for them to want to sell their car, even though—if you knew that you were getting a plum—you would be willing to pay enough for them to want to sell it. This is inefficient. By offering a warranty, a seller can signal to you that she has a plum: offering a warranty would be very expensive for the seller of a lemon, so only sellers of plums can afford to offer a warranty. So if you see a car being offered with a warranty, you know it must be a plum and you are willing to pay more for it. b. This is a situation of moral hazard: the insurer does not know whether you are doing the right thing (seeing a doctor only if you are genuinely sick). If the insurance company covered your visit fully, you might visit your physician even for minor headaches, leading to an excessively high level of claims. The co-­payment gives you an incentive to visit your physician only if you are sick enough to be willing to make the co-payment. An inefficiency arises in the allocation of risk because you are bearing risk (the risk of paying the deductible) that you would prefer, and be willing to pay the insurance company, to bear. c. This is a situation of adverse selection: although the buyer knows what type of traveler he is (business or leisure), the airline does not know. If the airline sold all seats at the same price, it would lose potential revenue from business travelers, and some leisure travelers might decide not to travel at all because the fare is too high. When different tickets are offered, business travelers (who need flexibility in their travel plans) will buy the high-priced flexible tickets and leisure travelers will buy the low-priced inflexible tickets. d. This is a situation of moral hazard: the company does not know how much effort a worker expends. By paying piece rates, a worker now has a stake in how much effort he or she expends: higher output means more pay, and lower output means less pay. But this is an inefficient allocation of risk. Because the worker is risk-averse, he or she would prefer a certain level of salary for sure, a level that the company would be willing to pay except for the problem of moral hazard. So workers are forced to bear more risk than is efficient. e. This is a situation of adverse selection. Employers do not know what type of employee you are (productive or unproductive). This is inefficient because they will offer a wage that is the average between what unproductive and productive workers should be paid. If you are a productive worker, that might not be enough to compensate you and you might decide not to work at all. The solution is for productive workers to provide references from previous employers. Unproductive workers will be unable to provide good references, so they will not supply any references at all. So having references signals that you are a productive worker and induces firms to pay you a higher salary. 14. Kory owns a house that is worth $300,000. If the house burns down, she loses all $300,000. If the house does not burn down, she loses nothing. Her house burns down with a probability of 0.02. Kory is risk-averse. a. What would a fair insurance policy cost? b. Suppose an insurance company offers to insure her fully against the loss from the house burning down, at a premium of $1,500. Can you say for sure whether Kory will or will not take the insurance? c. Suppose an insurance company offers to insure her fully against the loss from the house burning down, at a premium of $6,000. Can you say for sure whether Kory will or will not take the insurance? d. Suppose that an insurance company offers to insure her fully against the loss from the house burning down, at a premium of $9,000. Can you say for sure whether Kory will or will not take the insurance? 14. a. A fair insurance policy is one with a premium equal to the expected value of the claim. The expected value of Kory’s claim is (0.02 × $300,000) + (0.98 × $0) = $6,000. b. Kory will take this insurance. It is better than fair: the expected value of her claim is $6,000, but she only pays $1,500 for this insurance. Taking this insurance will increase Kory’s expected income. Since we know that she is riskaverse, we know for sure that she will take this insurance. c. Kory will take this insurance. It is fair insurance: the expected value of her claim is $6,000, and the premium is also $6,000. Taking this insurance will leave Kory’s expected income unchanged. Since we know that she is riskaverse, we know for sure that she will take this insurance. d. Kory may or may not take this insurance. It is “unfair”: the expected value of her claim is $6,000, but she would have to pay $9,000 for this insurance. Taking this insurance will reduce Kory’s expected income. She might still take this insurance if she is sufficiently risk-averse, but without more information about how risk-averse she is, we cannot tell for sure. WORK IT OUT Interactive step-by-step help with solving this problem can be found online. 15. You have $1,000 that you can invest. If you buy General Motors stock, then, in one year’s time: with a probability of 0.4 you will get $1,600; with a probability of 0.4 you will get $1,100; and with a probability of 0.2 you will get $800. If you put the money into the bank, in one year’s time you will get $1,100 for certain. a. What is the expected value of your earnings from investing in General Motors stock? b. Suppose you prefer putting your money into the bank to investing it in ­General Motors stock. What does that tell us about your attitude toward risk? 15. a. The expected value of your earnings from investing in General Motors stock is (0.4 × $1,600) + (0.4 × $1,100) + (0.2 × $800) − $1,000 = $640 + $440 + $160 − $1,000 = $240. b. Since getting $1,100 for certain is better for you than getting an average (but risky) $1,240, you must be risk-averse: you are willing to take a lower (but certain) payoff instead of a higher (but risky) one. Solution Manual for Microeconomics Paul Krugman, Robin Wells 9781319098780