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with each level of education, as shown in Figure 17.2. Observe that B(y) is 0 initially, which represents the $100,000 base 10-year earnings that are earned without any college education. For an education level less than y, B(y) remains 0, because 10-year earnings remain at the $100,000 base level. But when the education level reaches y or greater, 10-year earnings increase to $200,000, increasing B(y) to $100,000. How much education should a person obtain? Clearly the choice is between no education (i.e., y = 0) and an education level of y. Why? Any level of education less than y results in the same base earnings of $100,000. Thus there is no benefit from obtaining an education at a level above 0 but below y. Similarly, there is no benefit from obtaining an educational level above y because y* is sufficient to allow one to enjoy the higher total earnings of $200,000. COST–BENEFIT COMPARISON In deciding how much education to obtain, people compare the benefit of education with the cost. People in each group make the following cost-benefit calculation: Obtain the education level y* if the (a) Group I CI (y) = $40,000y Value of college education $200,000 $100,000 CHAPTER 17 • Markets with Asymmetric Information 641 (b) Group II Value of college education $200,000 $100,000 CII (y) = $20,000y B(y) B(y) 0 1 2 3 Optimal choice of y for group I 4 y* 5 6 Years of college 0 1 2 3 Optimal choice of y for group II 4 y* 5 6 Years of college FIGURE 17.2 SIGNALING Education can be a useful signal of the high productivity of a group of workers if education is easier to obtain for this group than for a low-productivity group. In (a), the low-productivity group will choose an education level of y = 0 because the cost of education is greater than the increased earnings resulting from education. However, in (b), the high-productivity group will choose an education level of y * = 4 because the gain in earnings is greater than the cost. benefit (i.e., the increase in earnings) is at least as large as the cost of this education. For
both groups, the benefit (the increase in earnings) is $100,000. The costs, however, differ. For Group I, the cost is $40,000y, but for Group II it is only $20,000y. Therefore, Group I will obtain no education as long as $100,000 6 $40,000y* or y* 7 2.5 and Group II will obtain an education level y* as long as $100,000 7 $20,000y* or y* 6 5 These results give us an equilibrium as long as y* is between 2.5 and 5. Suppose, for example, that y* is 4.0, as in Figure 17.2. In that case, people in Group I will find that education does not pay and will not obtain any, whereas people in Group II will find that education does pay and will obtain the level y = 4.0. Now, when a firm interviews job candidates who have no college education, it correctly assumes they have low productivity and offers them a wage of $10,000. Similarly, when the firm interviews people who have four years of college, it correctly assumes their productivity is high, warranting a wage of $20,000. We therefore have an equilibrium. High-productivity people will obtain a college education to signal their productivity; firms will read this signal and offer them a high wage. 642 PART 4 • Information, Market Failure, and the Role of Government This is a highly simplified model, but it illustrates a significant point: Education can be an important signal that allows firms to sort workers according to productivity. Some workers (those with high productivity) will want to obtain a college education even if that education does nothing to increase their productivity. These workers simply want to identify themselves as highly productive, so they obtain the education needed to send a signal. In the real world, of course, education does provide useful knowledge and does increase one’s ultimate productivity. (We wouldn’t have written this book if we didn’t believe that.) But education also serves a signaling function. For example, many firms insist that a prospective manager have an MBA. One reason is that MBAs learn economics, finance, and other useful subjects. But there is a second reason: To complete an MBA program takes intelligence, discipline, and hard work, and people with those qualities tend to be very productive. Guarantees and Warranties We have stressed the role of signaling in labor markets, but it can
also play an important role in many other markets in which there is asymmetric information. Consider the markets for such durable goods as televisions, stereos, cameras, and refrigerators. Many firms produce these items, but some brands are more dependable than others. If consumers could not tell which brands tend to be more dependable, the better brands could not be sold for higher prices. Firms that produce a higher-quality, more dependable product must therefore make consumers aware of this difference. But how can they do it in a convincing way? The answer is guarantees and warranties. Guarantees and warranties effectively signal product quality because an extensive warranty is more costly for the producer of a low-quality item than for the producer of a high-quality item. The low-quality item is more likely to require servicing under the warranty, for which the producer will have to pay. In their own self-interest, therefore, producers of low-quality items will not offer extensive warranties. Thus consumers can correctly view extensive warranties as signals of high quality and will pay more for products that offer them. E XAM PLE 17.3 WORKING INTO THE NIGHT Job market signaling does not end when one is hired. Even after a few years of employment, a worker will still know more about his abilities than will the employer. This is especially true for workers in knowledgebased fields such as engineering, computer programming, finance, law, management, and consulting. Although an unusually talented computer programmer, for example, will be more skilled than his co-workers at writing programs that are efficient and bug-free, it may take several years before the firm fully recognizes this talent. Given this asymmetric information, what policy should employers use to determine promotions and salary increases? Can workers who are unusually talented and productive signal this fact and thereby receive earlier promotions and larger salary increases? Workers can often signal talent and productivity by working harder and longer hours. Because more talented and productive workers tend to get more enjoyment and satisfaction from their jobs, it is less costly for them to send this signal than it is for CHAPTER 17 • Markets with Asymmetric Information 643 other workers. The signal is therefore strong: It conveys information. As a result, employers can—and do—rely on this signal when making promotion and salary decisions. This signalling process has affected the way many people work. Rather than an hourly wage, knowledge-based workers are typically paid a fixed salary for a 35- or 40-hour week and do not receive overtime pay if they work
additional hours. Yet such workers increasingly work well beyond their weekly schedules. Surveys by the U.S. Labor Department, for example, found that the percentage of all workers who toil 49 hours or more a week rose from 13 percent in 1976 to over 16 percent in 2011.6 Many young lawyers, accountants, consultants, investment bankers, and computer programmers regularly work into the night and on weekends, putting in 60- or 70-hour weeks. Is it surprising that these people are working so hard? Not at all. They are trying to send signals that can greatly affect their careers. Employers rely increasingly on the signaling value of long hours as rapid technological change makes it harder for them to find other ways of assessing workers’ skills and productivity. A study of software engineers at the Xerox Corporation, for example, found that many people work into the night because they fear that otherwise their bosses will conclude that they are shirkers who choose the easiest assignments. As the bosses make clear, this fear is warranted: “We don’t know how to assess the value of a knowledge worker in these new technologies,” says one Xerox manager, “so we value those who work into the night.” As corporations become more reluctant to offer lifetime job security, and as competition for promotion intensifies, salaried workers feel more and more pressure to work long hours. If you find yourself working 60- or 70-hour weeks, look at the bright side—the signal you’re sending is a strong one.7 17.3 Moral Hazard When one party is fully insured and cannot be accurately monitored by an insurance company with limited information, the insured party may take an action that increases the likelihood that an accident or an injury will occur. For example, if my home is fully insured against theft, I may be less diligent about locking doors when I leave, and I may choose not to install an alarm system. The possibility that an individual’s behavior may change because she has insurance is an example of a problem known as moral hazard. The concept of moral hazard applies not only to problems of insurance, but also to problems of workers who perform below their capabilities when employers cannot monitor their behavior (“job shirking”). In general, moral hazard occurs when a party whose actions are unobserved affects the probability or magnitude of a payment. For example, if I have complete medical insurance coverage, I may visit the doctor more often than I would if my coverage
were limited. If the insurance provider can monitor its insurees’ behavior, it can charge higher fees for those who make more claims. But if the company cannot monitor behavior, it may find its payments to be larger than expected. Under conditions of moral hazard, insurance companies may be forced to increase premiums for everyone or even to refuse to sell insurance at all. 6“At the Desk, Off the Clock and Below Statistical Radar,” New York Times, July 18, 1999. Data on hours worked are available from the Current Population Survey (CPS), Bureau of Labor Statistics (BLS), at http://www.bls.gov/cps/#charemp; Persons at Work in Agriculture and Nonagricultural Industries by Hours of Work. 7For an interesting study of “time stress,” see Daniel Hamermesh and Jungmin Lee, “Stressed Out on Four Continents: Time Crunch or Yuppie Kvetch?” Review of Econ. and Stat., May 2007, 89, 374–383. • moral hazard When a party whose actions are unobserved can affect the probability or magnitude of a payment associated with an event. 644 PART 4 • Information, Market Failure, and the Role of Government Consider, for example, the decisions faced by the owners of a warehouse valued at $100,000 by their insurance company. Suppose that if they run a $50 fireprevention program for their employees, the probability of a fire is.005. Without this program, the probability increases to.01. Knowing this, the insurance company faces a dilemma if it cannot monitor the company’s decision to conduct a fire-prevention program. The policy that the insurance company offers cannot include a clause stating that payments will be made only if there is a fire-prevention program. If the program were in place, the company could insure the warehouse for a premium equal to the expected loss from a fire—an expected loss equal to.005 * $100,000 = $500. Once the insurance policy is purchased, however, the owners no longer have an incentive to run the program. If there is a fire, they will be fully compensated for their financial loss. Thus, if the insurance company sells a policy for $500, it will incur losses because the expected loss from the fire will be $1000 (.01 * $100,000). Moral hazard is a problem not only for insurance companies. It also alters the ability of markets to allocate resources efficiently
. In Figure 17.3, for example, D gives the demand for automobile driving in miles per week. The demand curve, which measures the marginal benefits of driving, is downward sloping because some people switch to alternative transportation as the cost of driving increases. Suppose that initially, the cost of driving includes the insurance cost and that insurance companies can accurately measure miles driven. In this case, there is no moral hazard and the marginal cost of driving is given by MC. Drivers know that more driving will increase their insurance premiums and so increase their total cost of driving (the cost per mile is assumed to be constant). For example, if the cost of driving is $1.50 per mile (50 cents of which is insurance cost), drivers will go 100 miles per week. A moral hazard problem arises when insurance companies cannot monitor individual driving habits, so that insurance premiums do not depend on miles driven. In that case, drivers assume that any additional accident costs that they incur will be spread over a large group, with only a negligible portion accruing to each of them individually. Because their insurance premiums do not vary with the number of miles that they drive, an additional mile of transportation will cost $1.00, as shown by the marginal cost curve MC’, rather than $1.50. The number of miles driven will increase from 100 to the socially inefficient level of 140. FIGURE 17.3 THE EFFECTS OF MORAL HAZARD Moral hazard alters the ability of markets to allocate resources efficiently. D gives the demand for automobile driving. With no moral hazard, the marginal cost of transportation MC is $1.50 per mile; the driver drives 100 miles, which is the efficient amount. With moral hazard, the driver perceives the cost per mile to be MC = $1.00 and drives 140 miles. Cost per mile $2.00 $1.50 $1.00 $0.50 0 MC MC D = MB 50 100 140 Miles per week CHAPTER 17 • Markets with Asymmetric Information 645 Moral hazard not only alters behavior; it also creates economic inefficiency. The inefficiency arises because the insured individual perceives either the cost or the benefit of the activity differently from the true social cost or benefit. In the driving example of Figure 17.3, the efficient level of driving is given by the intersection of the marginal benefit (MB) and marginal cost (MC) curves. With moral hazard, however, the individual’s perceived marginal cost (MC’) is less
than actual cost, and the number of miles driven per week (140) is higher than the efficient level at which marginal benefit is equal to marginal cost (100). EXAM PLE 17.4 REDUCING MORAL HAZARD: WARRANTIES OF ANIMAL HEALTH For buyers of livestock, information about the animals’ health is very important.8 Unhealthy animals gain weight more slowly and are less likely to reproduce. Because of asymmetric information in the livestock market (sellers know the health of an animal better than buyers do), most states require warranties on the sale of livestock. Under these laws, sellers not only promise (warrant) that animals are free from hidden diseases, but are responsible for all costs arising from any diseased animals. Although warranties solve the problem of the seller having better information than the buyer, they also create a form of moral hazard. Guaranteeing reimbursement to the buyer for all costs associated with diseased animals means that insurance rates are not tied to the level of care that buyers or their agents take to protect their livestock against disease. As a result of these warranties, livestock buyers avoid paying for early diagnoses of diseased livestock, and losses increase. In response to the moral hazard problem, many states have modified their animal warranty laws by requiring sellers to tell buyers whether livestock are diseased at the time of sale. Some states also require sellers to comply with state and federal animal health regulations, thereby reducing disease. Beyond these measures, however, warranties that animals are free from hidden disease must be in the form of explicit written or oral guarantees to buyers. Following an outbreak of Mad Cow Disease in 2003, the U.S. Department of Agriculture introduced the National Animal Identification System (NAIS) as a means to further reduce moral hazard. NAIS is designed to make the entire supply chain more transparent so that disease outbreaks can be traced to the responsible party. 17.4 The Principal–Agent Problem If monitoring the productivity of workers were costless, the owners of a business would ensure that their managers and workers were working effectively. In most firms, however, owners can’t monitor everything that employees do—employees are better informed than owners. This information asymmetry creates a principal–agent problem. • principal–agent problem Problem arising when agents (e.g., a firm’s managers) pursue their own goals rather than the goals of principals (e.g., the firm’s owners). 8This example is based on Terence J. Centner and Michael E
. Wetzstein, “Reducing Moral Hazard Associated with Implied Warranties of Animal Health,” American Journal of Agricultural Economics 69 (1987): 143–50. 646 PART 4 • Information, Market Failure, and the Role of Government Individual employed • agent by a principal to achieve the principal’s objective. Individual who • principal employs one or more agents to achieve an objective. An agency relationship exists whenever there is an arrangement in which one person’s welfare depends on what another person does. The agent is the person who acts, and the principal is the party whom the action affects. A principal– agent problem arises when agents pursue their own goals rather than the goals of the principal. In our example, the manager and the workers are the agents, and the owners of the firm are the principals. In this case, the principal-agent problem results from the fact that managers may pursue their own goals, even at the cost of lower profits for the owners. Agency relationships are widespread in our society. For example, doctors serve as agents for hospitals and, as such, may select patients and do procedures which, though consistent with their personal preferences, are not necessarily consistent with the objectives of the hospital. Similarly, managers of housing properties may not maintain the property the way that the owners would like. And sometimes insured parties may be seen as agents and insurance companies as principals. How does incomplete information and costly monitoring affect the way agents act? And what mechanisms can give managers the incentives to operate in the owner’s interest? These questions are central to any principal–agent analysis. In this section, we study the principal–agent problem from several perspectives. First, we look at the owner–manager problem within private and public enterprises. Second, we discuss ways in which owners can use contractual relationships with their employees to deal with principal–agent problems. The Principal–Agent Problem in Private Enterprises Most large companies are controlled by management. Individual stockholders, who are not part of management, typically own only a small percentage of the equity of these companies, and thus they have little or no power to fire managers who are performing poorly. Indeed, it is difficult or impossible for stockholders to even learn much about what the managers are doing and how well they are performing. Monitoring managers is costly, and information can be expensive to gather. The result is that managers can often pursue their own objectives, rather than focusing on the objective of the stockholders, which is to maximize the value of the firm.9 But, what are
objectives of managers? One view is that managers are more concerned with growth than with profit per se: More rapid growth and larger market share provide more cash flow, which in turn allows managers to enjoy more perks. Another view emphasizes the utility that managers get from their jobs, not only from profit but also from the respect of their peers, the power to control the corporation, the fringe benefits and other perks, and long job tenure. However, there are limitations to managers’ ability to deviate from the objectives of owners. First, stockholders can complain loudly when they feel that managers are behaving improperly. In exceptional cases, they can oust the current management (perhaps with the help of the board of directors, whose job it is to monitor managerial behavior). Second, a vigorous market for corporate control can develop. If a takeover bid becomes more likely when the firm is poorly managed, managers will have a strong incentive to pursue the goal of profit maximization. Third, there can be a highly developed market for managers. If managers who maximize profit are in great demand, they will earn high wages and so give other managers an incentive to pursue the same goal. 9See Merritt B. Fox, Finance and Industrial Performance in a Dynamic Economy (New York: Columbia University Press, 1987). CHAPTER 17 • Markets with Asymmetric Information 647 Unfortunately, the means by which stockholders control managers’ behavior are limited and imperfect. Corporate takeovers may be motivated by personal and economic power, for example, instead of economic efficiency. The managerial labor market may also work imperfectly because top managers are frequently near retirement and have long-term contracts. The problem of limited stockholder control shows up most dramatically in executive compensation, which has grown very rapidly over the past several decades. In 2002, a Business Week survey of the 365 largest U.S. companies showed that the average CEO earned $13.1 million in 2000, and executive pay has continued to increase at a double-digit rate. Even more disturbing is the fact that for the 10 public companies led by the highest-paid CEOs, there was a negative correlation between CEO pay and company performance. It is clear that shareholders have been unable to adequately control managers’ behavior. What can be done to address this problem? In theory, the answer is simple: One must find mechanisms that more closely align the interests of managers and shareholders. In practice, however, this is likely to prove difficult. Among those suggestions put into effect recently by the Securities and Exchange Commission, which regulates public companies
, are reforms that grant more authority to independent outside directors. Other possible reforms would tie executive pay more closely to the long-term performance of the company. EXAM PLE 17.5 CEO SALARIES Washington Mutual, an upstart savings and loan company, saw incredible growth throughout the 1990s and early 2000s. A housing boom was in full swing, and the bank, led by CEO Kerry Killinger, was aggressive in pursuing new mortgages. By 2007, however, Washington Mutual was in trouble. As the housing market slumped and home values fell, it became clear that the bank had a dangerous number of sub-prime mortgages on its books. By the fall of 2008, Washington Mutual’s assets had been seized by the FDIC and sold to competitor JP Morgan Chase at the fire sale price of $1.9 billion to avert what at the time would have been the largest bank failure in U.S. history. Less than three weeks before this sale, Washington Mutual’s board of directors fired Killinger. Still, he received a severance package totaling over $15.3 million.10 Killinger’s successor, Alan Fishman, led the bank for just 17 days, but received $11.6 million in severance pay, in addition to a $7.5 million signing bonus.11 Washington Mutual’s shareholders were wiped out in the sale. Killinger and Fishman were not the only bankers, or even the only CEOs, to receive large compensation packages, regardless of their performance and the health of the companies they led. CEO compensation has increased sharply over the past few decades. The average annual salary for production workers in the U.S. went from $18,187 in 1990 to $32,093 in 2009. But in constant dollar terms, the 2009 average salary was only $19,552 (in 1990 dollars), which represents only a 7.5% increase. At the same time, the average annual compensation for CEOs has grown from $2.9 million to $8.5 million, or about $5.2 million in 1990 dollars.12 In other words, while production workers have seen a 7.5% increase in their real wages over the past two decades, real CEO compensation has risen nearly 80%. Why? Have top managers become more productive, or are CEOs simply becoming more effective at extracting economic rents from their companies? The answer lies in the principal–agent problem, which is at the heart of CEO salary determination. 10http://seattlet
imes.nwsource.com/html/businesstechnology/2011590001_wamuside13.html 11http://www.nytimes.com/2008/09/26/business/26wamu.html 12Source: Bureau of Labor Statistics, Institute for Policy Studies—United for a Fair Economy (2006). Average CEO pay peaked at $11 million in 2005, only to decrease during the 2007–2009 recession. After 2009, it began to increase again. 648 PART 4 • Information, Market Failure, and the Role of Government For years, many economists believed that executive compensation reflected an appropriate reward for talent. Recent evidence, however, suggests that managers have been able to increase their power over boards of directors and have used that power to extract compensation packages that are far out of line with their performance and contributions to the growth of their firms. In essence, managers have steadily increased their ability to extract economic rents. How has this happened? First, most boards of directors do not have the necessary information or independence to negotiate effectively with managers. Directors often cannot monitor executives’ activities and therefore cannot negotiate compensation packages that are tightly linked to their performance. Furthermore, boards consist of a mix of inside members, who either are or represent top executives, and outside members, who are chosen by and are often on close terms with top executives.13 Therefore, directors have a strong incentive to support executives in order to be re-nominated to the board or otherwise rewarded. Research has shown that high levels of CEO pay are negatively correlated with a firm’s accounting value and profitability.14 In other words, the higher the CEO’s pay, the lower the firm’s profitability is likely to be. In addition, CEOs with unusually high pay were more likely to stay at a company despite poor economic results. These effects are intensified at companies where the board is entrenched and shareholder rights are limited. “Golden parachutes,” generous severance packages that CEOs can negotiate with their boards, have also come under fire recently. Some argue that such guarantees free CEOs from board and shareholder pressure to focus on short-term growth and enable them to focus instead on their firms’ longterm growth. However, it has been shown that CEOs with golden parachutes are less likely to worry about long-term growth, and—when negotiating the sale of their firm to another company—are more likely to agree to acquisition terms that hurt shareholders.15 Reward structures that focus on profitability over a 5- to 10
-year period are more likely to generate efficient incentives than more shortsighted reward structures. We will consider some additional solutions to this important principal–agent problem in the next section. The Principal–Agent Problem in Public Enterprises The principal–agent framework can also help us understand the behavior of the managers of public organizations. These managers may also be interested in power and perks, both of which can be obtained by expanding their organization beyond its “efficient” level. Because it is also costly to monitor the behavior of public managers, there are no guarantees that they will produce the efficient output. Legislative checks on a government agency are not likely to be effective as long as the agency has better information about its costs than the legislature has. Although the public sector lacks some of the market forces that keep private managers in line, government agencies can still be effectively monitored. 13Killinger was the chairman of Washington Mutual’s board until he was forced out two months before the bank failed. 14In 2007, Killinger, who was also chairman of Washington Mutual’s board of directors, was paid $18.1 million, making him the highest paid CEO of any publicly traded company (http://www. equilar.com/NewsArticles/062407_pay.pdf). This was especially true when the CEO took home the largest portion of the pay going to the firm’s top-five executives. For more detailed discussion and analysis, see Lucian A. Bebchuk, Martjin Cremers, and Urs Peyer, “The CEO Pay Slice,” Journal of Financial Economics (Spring 2012). 15Lucian A. Bebchuk, Alma Cohen, and Charles C. Y. Wang, "Golden Parachutes and the Wealth of Shareholders,” Harvard Law School Olin Discussion Paper No. 683, December 2010. CHAPTER 17 • Markets with Asymmetric Information 649 First, managers of government agencies care about more than just the size of their agencies. Indeed, many choose lower-paying public jobs because they are concerned about the “public interest.” Second, much like private managers, public managers are subject to the rigors of the managerial job market. If public managers are perceived to be pursuing improper objectives, their ability to obtain high salaries in the future might be impaired. Third, legislatures and other government agencies perform an oversight function. For example, the Government Accounting Office and the Office of Management and Budget spend much of their energy monitoring other agencies. At
the local rather than the federal level, public managers are subject to even more checks. Suppose, for example, that a city transit agency has expanded bus service beyond the efficient level. Citizens can vote the transit managers out of office, or, if all else fails, use alternative transportation (or even move). Competition among agencies can be as effective as competition among private firms in constraining the behavior of managers. EXAM PLE 17.6 MANAGERS OF NONPROFIT HOSPITALS AS AGENTS Do the managers of nonprofit organizations have the same goals as those of for-profit organizations? Are nonprofit organizations more or less efficient than for-profit firms? We can get some insight into these issues by looking at the provision of health care. In a study of 725 hospitals, from 14 major hospital chains, researchers compared the return on investment and average costs of nonprofit and for-profit hospitals to determine if they performed differently.16 The study found that the rates of return did indeed differ. In one year, for-profits earned an 11.6-percent return, while nonprofits earned 8.8 percent. Four years later, for-profits earned 12.7 percent and nonprofits only 7.4 percent. A straight comparison of returns and costs is not appropriate, however, because the hospitals perform different functions. For example, 24 percent of the nonprofit hospitals provide medical residency programs, as compared with only 6 percent of the for-profit hospitals. Similar differences can be found in the provision of specialty care, with 10 percent of the nonprofits having open-heart units, as compared to only 5 percent of the for-profits. In addition, while 43 percent of nonprofits have premature infant units, only 29 percent of the forprofits have equivalent units. Using a statistical regression analysis, which controls for differences in the services performed, one can determine whether differences in services account for the higher costs. The study found that after adjusting for services performed, the average cost of a patient day in nonprofit hospitals was 8 percent higher than in for-profit hospitals. This difference implies that the profit status of the hospital affects its performance in the way principal–agent theory predicts: Without the competitive forces faced by for-profit hospitals, nonprofit hospitals may be less cost-conscious and therefore less likely to serve appropriately as agents for their principals— namely, society at large. Of course, nonprofit hospitals provide services that society may well wish to subsidize. But the added cost of running a nonprofit hospital should be considered when determining whether it should be granted tax-exempt status.
16Regina E. Herzlinger and William S. Krasker, “Who Profits from Nonprofits?” Harvard Business Review 65 (January–February 1987): 93–106. 650 PART 4 • Information, Market Failure, and the Role of Government Incentives in the Principal–Agent Framework We have seen why managers’ and owners’ objectives are likely to differ within the principal-agent framework. How, therefore, can owners design reward systems so that managers and workers come as close as possible to meeting owners’ goals? To answer this question, let’s study a specific problem. A small manufacturer uses labor and machinery to produce watches. The owners want to maximize profit. They must rely on a machine repairperson whose effort will influence the likelihood that machines break down and thus affect the firm’s profit level. Revenue also depends on other random factors, such as the quality of parts and the reliability of other labor. As a result of high monitoring costs, the owners can neither measure the effort of the repairperson directly nor be sure that the same effort will always generate the same profit level. Table 17.2 describes these circumstances. The table shows that the repairperson can work with either a low or high amount of effort. Low effort (a = 0) generates either $10,000 or $20,000 in revenue (with equal probability), depending on the random factors that we mentioned. We’ve labeled the lower of the two revenue levels “bad luck” and the higher level “good luck.” When the repairperson makes a high effort (a = 1), revenue will be either $20,000 (bad luck) or $40,000 (good luck). These numbers highlight the problem of incomplete information: When the firm’s revenue is $20,000, the owners cannot know whether the repairperson has made a low or high effort. Suppose the repairperson’s goal is to maximize his wage payment less the cost (in terms of lost leisure and unpleasant work time) of the effort that he makes. To simplify, we’ll suppose that the cost of effort is 0 for low effort and $10,000 for high effort. (Formally, c = $10,000a.) Now we can state the principal–agent problem from the owners’ perspective. The owners’ goal is to maximize expected profit, given the uncertainty of outcomes and given the fact that the repairperson’s behavior cannot be
monitored. The owners can contract to pay the repairperson for his work, but the payment scheme must be based entirely on the measurable output of the manufacturing process, not on the repairperson’s effort. To signify this link, we describe the payment scheme as w(R), stressing that payments can depend only on measured revenue. What is the best payment scheme? And can that scheme be as effective as one based on effort rather than output? The best payment scheme depends on the nature of production, the degree of uncertainty, and the objectives of both owners and managers. The arrangement will not always be as effective as an ideal scheme directly tied to effort. A lack of information can lower economic efficiency because both the owners’ revenue and the repairperson’s payment may fall at the same time. Let’s see how to design a payment scheme when the repairperson wishes to maximize his payment received net of the cost of effort made.17 Suppose first TABLE 17.2 REVENUE FROM MAKING WATCHES Low effort (a = 0) High effort (a = 1) BAD LUCK $10,000 $20,000 GOOD LUCK $20,000 $40,000 17We assume that because the repairperson is risk neutral, no efficiency is lost. If, however, the repairperson were risk averse, there would be an efficiency loss. CHAPTER 17 • Markets with Asymmetric Information 651 that the owners offer a fixed wage payment. Any wage will do, but we can see things most clearly if we assume that the wage is 0. (Here, 0 could represent a wage equal to the wage paid in other comparable jobs.) Facing a wage of 0, the repairperson has no incentive to make a high level of effort. The reason is that the repairperson does not share in any of the gains that the owners enjoy from the increased effort. It follows, therefore, that a fixed payment will lead to an inefficient outcome. When a = 0 and w = 0, the owner will earn an expected revenue of $15,000 and the repairperson a net wage of 0. Both the owners and the repairperson will be better off if the repairperson is rewarded for his productive effort. Suppose, for example, that the owners offer the repairperson the following payment scheme: If R = $10,000 or $20,000, w = 0 If R = $40,000, w = $24,000 (17.1) Under this bonus arrangement, a low
effort generates no payment. A high effort, however, generates an expected payment of $12,000, and an expected payment less the cost of effort of $12,000 - $10,000 = $2000. Under this system, the repairperson will choose to make a high level of effort. This arrangement makes the owners better off than before because they get an expected revenue of $30,000 and an expected profit of $18,000. This is not the only payment scheme that will work for the owners, however. Suppose they contract to have the worker participate in the following revenuesharing arrangement. When revenues are greater than $18,000, w = R - $18,000 (17.2) (Otherwise the wage is zero.) In this case, if the repairperson makes a low effort, he receives an expected payment of $1000. But if he makes a high level of effort, his expected payment is $12,000, and his expected payment less the $10,000 cost of effort is $2000. (The owners’ profit is $18,000, as before.) Thus, in our example, a revenue-sharing arrangement achieves the same outcome as a bonus-payment system. In more complex situations, the incentive effects of the two types of arrangements will differ. However, the basic idea illustrated here applies to all principal–agent problems: When it is impossible to measure effort directly, an incentive structure that rewards the outcome of high levels of effort can induce agents to aim for the goals that the owners set. *17.5 Managerial Incentives in an Integrated Firm We have seen that owners and managers of firms can have asymmetric information about demand, cost, and other variables. We’ve also seen how owners can design reward structures to encourage managers to make appropriate efforts. Now we focus our attention on firms that are integrated—that consist of several divisions, each with its own managers. Some firms are horizontally integrated: Several plants produce the same or related products. Others are also vertically integrated: Upstream divisions produce materials, parts, and components that downstream divisions use to produce final products. Integration creates organizational problems. We addressed some of these problems in the appendix • horizontal integration Organizational form in which several plants produce the same or related products for a firm. • vertical integration Organizational form in which a firm contains several divisions, with some producing parts and components that others use to produce finished products. 652 PART 4 • Information, Market Failure, and the Role of
Government to Chapter 11, where we discussed transfer pricing in the vertically integrated firm—that is, how the firm sets prices for parts and components that upstream divisions supply to downstream divisions. Here we will examine problems that stem from asymmetric information. Asymmetric Information and Incentive Design in the Integrated Firm In an integrated firm, division managers are likely to have better information about their different operating costs and production potential than central management has. This asymmetric information causes two problems. 1. How can central management elicit accurate information about divisional operating costs and production potential from divisional managers? This information is important because the inputs into some divisions may be the outputs of other divisions, because deliveries must be scheduled to customers, and because prices cannot be set without knowing overall production capacity and costs. 2. What reward or incentive structure should central management use to encourage divisional managers to produce as efficiently as possible? Should they be given bonuses based on how much they produce? If so, how should they be structured? To understand these problems, consider a firm with several plants that all produce the same product. Each plant’s manager has much better information about its production capacity than central management has. In order to avoid bottlenecks and to schedule deliveries reliably, central management wants to learn more about how much each plant can produce. It also wants each plant to produce as much as possible. Let’s examine ways in which central management can obtain the information it wants while also encouraging plant managers to run the plants as efficiently as possible. One way is to give plant managers bonuses based on either the total output of their plant or its operating profit. Although this approach would encourage managers to maximize output, it would penalize managers whose plants have higher costs and lower capacity. Even if these plants produced efficiently, their output and operating profit—and thus their bonuses—would be lower than those of plants with lower costs and higher capacities. Plant managers would also have no incentive to obtain and reveal accurate information about cost and capacity. A second way is to ask managers about their costs and capacities and then base bonuses on how well they do relative to their answers. For example, each manager might be asked how much his or her plant can produce each year. Then at the end of the year, the manager receives a bonus based on how close the plant’s output was to this target. For example, if the manager’s estimate of the feasible production level is Qf, the annual bonus in dollars, B, might be B = 10,000
-.5(Qf - Q) (17.3) where Q is the plant’s actual output, 10,000 is the bonus when output is at capacity, and.5 is a factor chosen to reduce the bonus if Q is below Qf. Under this scheme, however, managers would have an incentive to underestimate capacity. By claiming capacities below what they know to be true, they CHAPTER 17 • Markets with Asymmetric Information 653 can more easily earn large bonuses even if they do not operate efficiently. For example, if a manager estimates capacity to be 18,000 rather than 20,000, and the plant actually produces only 16,000, her bonus increases from $8000 to $9000. Thus this scheme fails to elicit accurate information about capacity and does not ensure that plants will be run as efficiently as possible. Now let’s modify this scheme. We will still ask managers how much their plants can feasibly produce and tie their bonuses to this estimate. However, we will use a slightly more complicated formula than the one in (17.3) to calculate the bonus: If Q 7 Qf, B =.3Qf If Q … Qf, B =.3Qf +.2(Q - Qf) - Q) -.5(Qf (17.4) The parameters (.3,.2, and.5) have been chosen so that each manager has the incentive to reveal the true feasible production level and to make Q, the actual output of the plant, as large as possible. To see that this scheme does the job, look at Figure 17.4. Assume that the true production limit is Q* = 20,000 units per year. The bonus that the manager will receive if she states feasible capacity to be the true production limit is given by = 20,000. This line is continued for outputs beyond 20,000 to the line labeled Qf illustrate the bonus scheme but dashed to signify the infeasibility of such production. Note that the manager’s bonus is maximized when the firm produces at its limits of 20,000 units; the bonus is then $6000. Suppose, however, that the manager reports a feasible capacity of only 10,000. = 10,000. The maximum bonus Then the bonus is given by the line labeled Qf is now $5000, which is obtained by producing an output of 20,000. But note that this is less than the bonus that the manager would receive if she
correctly stated the feasible capacity to be 20,000. The same line of argument applies when the manager exaggerates available capacity. If the manager states feasible capacity to be 30,000 units per year, the Bonus (dollars per year) 10,000 8000 6000 4000 2000 Qf = 30,000 Qf = 20,000 Qf = 10,000 FIGURE 17.4 INCENTIVE DESIGN IN AN INTEGRATED FIRM A bonus scheme can be designed that gives a manager the incentive to estimate accurately the size of the plant. If the manager reports a feasible capacity of 20,000 units per year, equal to the actual capacity, then the bonus will be maximized (at $6000). 0 10,000 20,000 30,000 40,000 Output (units per year) 654 PART 4 • Information, Market Failure, and the Role of Government = 30,000. The maximum bonus of $4000, which bonus is given by the line Qf is achieved at an output of 20,000, is less than the bonus that she could have received by reporting feasible capacity correctly.18 Applications Because the problem of asymmetric information and incentive design comes up often in managerial settings, incentive schemes like the one described above arise in many contexts. How, for example, can managers encourage salespeople to set and reveal realistic sales targets and then work as hard as possible to meet them? Most salespeople cover specific territories. A salesperson assigned to a densely populated urban territory can usually sell more product than a salesperson assigned to a sparsely populated area. The company, however, wants to reward all salespeople equitably. It also wants to give them the incentive to work as hard as possible and to report realistic sales targets, so that it can plan production and delivery schedules. Companies have always used bonuses and commissions to reward salespeople, but incentive schemes have often been poorly designed. Typically, salespeople’s commissions were proportional to their sales. This approach elicited neither accurate information about feasible sales targets nor maximum performance. Today, companies are learning that bonus schemes like the one given by equation (17.4) provide better results. The salesperson can be given an array of numbers showing the bonus as a function of both the sales target (chosen by the salesperson) and the actual level of sales. (The numbers would be calculated from equation (17.4) or some similar formula.) Salespeople will quickly figure out that they do best by reporting feasible sales targets and then working as
hard as possible to meet them.19 Recall from §14.1 that in a perfectly competitive labor market, firms hire labor to the point at which the real wage (the wage divided by the price of the product) is equal to the marginal product of labor. • efficiency wage theory Explanation for the presence of unemployment and wage discrimination which recognizes that labor productivity may be affected by the wage rate. 17.6 Asymmetric Information in Labor Markets: Efficiency Wage Theory When the labor market is competitive, all who wish to work will find jobs for wages equal to their marginal products. Yet most countries have substantial unemployment even though many people are aggressively seeking work. Many of the unemployed would presumably work for an even lower wage rate than that being received by employed people. Why don’t we see firms cutting wage rates, increasing employment levels, and thereby increasing profit? Can our models of competitive equilibrium explain persistent unemployment? In this section, we show how the efficiency wage theory can explain the presence of unemployment and wage discrimination.20 We have thus far + a(Q - Qf) for Q 7 Qf, and B = bQf 18Any bonus of the form B = bQf - Q) for Q … Qf, with g 7 b 7 a 7 0 will work. See Martin L. Weitzman, “The New Soviet Incentive Model,” Bell Journal of Economics 7 (Spring 1976): 251–6. There is a dynamic problem with this scheme that we have ignored: Managers must weigh a large bonus for good performance this year against being assigned more ambitious targets in the future. This is discussed in Martin Weitzman, “The ’Ratchet Principle’ and Performance Incentives,” Bell Journal of Economics 11 (Spring 1980): 302–8. - g(Qf 19See Jacob Gonik, “Tie Salesmen’s Bonuses to Their Forecasts,” Harvard Business Review (May–June 1978): 116–23. 20See Janet L. Yellen, “Efficiency Wage Models of Unemployment,” American Economic Review 74 (May 1984): 200–5. The analysis relies on Joseph E. Stiglitz, “The Causes and Consequences of the Dependence of Quality on Price,” Journal of Economic Literature 25 (March 1987): 1–48. CHAPTER 17 • Markets with Asymmetric Information 655 determined labor productivity according to workers’ abilities and firms’ investment
in capital. Efficiency wage models recognize that labor productivity also depends on the wage rate. There are various explanations for this relationship. Economists have suggested that the productivity of workers in developing countries depends on the wage rate for nutritional reasons: Better-paid workers can afford to buy more and better food and are therefore healthier and can work more productively. A better explanation for the United States is found in the shirking model. Because monitoring workers is costly or impossible, firms have imperfect information about worker productivity, and there is a principal–agent problem. In its simplest form, the shirking model assumes perfectly competitive markets in which all workers are equally productive and earn the same wage. Once hired, workers can either work productively or slack off (shirk). But because information about their performance is limited, workers may not get fired for shirking. The model works as follows. If a firm pays its workers the market-clearing wage w, they have an incentive to shirk. Even if they get caught and are fired (and they might not be), they can immediately get hired somewhere else for the same wage. Because the threat of being fired does not impose a cost on workers, they have no incentive to be productive. As an incentive not to shirk, a firm must offer workers a higher wage. At this higher wage, workers who are fired for shirking will face a decrease in wages when hired by another firm at w. If the difference in wages is large enough, workers will be induced to be productive, and the employer will not have a problem with shirking. The wage at which no shirking occurs is the efficiency wage. Up to this point, we have looked at only one firm. But all firms face the problem of shirking. All firms, therefore, will offer wages greater than the marketclearing wage w—say, we (efficiency wage). Does this remove the incentive for workers not to shirk because they will be hired at the higher wage by other firms if they get fired? No. Because all firms are offering wages greater than w, the demand for labor is less than the market-clearing quantity, and there is unemployment. Consequently, workers fired for shirking will face spells of unemployment before earning we at another firm. Figure 17.5 shows shirking in the labor market. The demand for labor DL is downward-sloping for the traditional reasons. If there were no shirking, the intersection of DL with the supply of labor (
SL) would set the market wage at w, and full employment would result (L). With shirking, however, individual firms are unwilling to pay w. Rather, for every level of unemployment in the labor market, firms must pay some wage greater than w to induce workers to be productive. This wage is shown as the no-shirking constraint (NSC) curve. This curve shows the minimum wage, for each level of unemployment, that workers must earn in order not to shirk. Note that the greater the level of unemployment, the smaller the difference between the efficiency wage and w. Why is this so? Because with high levels of unemployment, people who shirk risk long periods of unemployment and therefore don’t need much inducement to be productive. In Figure 17.5, the equilibrium wage will be at the intersection of the NSC curve and DL curves, with Le workers earning we. This equilibrium occurs because the NSC curve gives the lowest wage that firms can pay and still discourage shirking. Firms need not pay more than this wage to get the number of workers they need, and they will not pay less because a lower wage will encourage shirking. Note that the NSC curve never crosses the labor supply curve. This means that there will always be some unemployment in equilibrium. • shirking model Principle that workers still have an incentive to shirk if a firm pays them a market-clearing wage, because fired workers can be hired somewhere else for the same wage. • efficiency wage Wage that a firm will pay to an employee as an incentive not to shirk. In §14.2, we explain that the equilibrium wage is given by the intersection of the demand for labor curve and the supply of labor curve. 656 PART 4 • Information, Market Failure, and the Role of Government Wage SL FIGURE 17.5 UNEMPLOYMENT IN A SHIRKING MODEL Unemployment can arise in otherwise competitive labor markets when employers cannot accurately monitor workers. Here, the “no shirking constraint” (NSC) gives the wage necessary to keep workers from shirking. The firm hires Le workers (at an efficiency wage we higher than the market-clearing wage w), creating L* - Le of unemployment. we w* No-Shirking Constraint (NSC) Demand for Labor DL Le L* Quantity of labor E XAM PLE 17.7 EFFICIENCY WAGES AT FORD MOTOR
COMPANY One of the early examples of the payment of efficiency wages can be found in the history of Ford Motor Company. Before 1913, automobile production depended heavily on skilled workers. But the introduction of the assembly line drastically changed the workplace. Now jobs demanded much less skill, and production depended on maintaining assemblyline equipment. But as automobile plants changed, workers became increasingly disenchanted. In 1913, turnover at Ford was 380 percent. The following year, it rose to 1000 percent, and profit margins fell sharply. Ford needed to maintain a stable workforce, and Henry Ford (and his business partner James Couzens) provided it. In 1914, when the going wage for a day’s work in industry averaged between $2 and $3, Ford introduced a pay policy of $5 a day. The policy was prompted by improved labor efficiency, not generosity. The goal was to attract better workers who would stay with their jobs—and eventually to increase profits. Although Henry Ford was attacked for it, his policy succeeded. His workforce did become more stable, and the publicity helped Ford’s sales. In addition, because Ford had his pick of workers, he could hire a group that was on average more productive. Ford stated that the wage increase did in fact increase the loyalty and personal efficiency of his workers, and quantitative estimates support his statements. According to calculations by Ford’s chief of labor relations, productivity increased by 51 percent. Another study found that absenteeism had been cut in half and discharges for cause had declined sharply. Thus the productivity increase more than offset the increase in wages. As a result, Ford’s profitability rose from $30 million in 1914 to $60 million in 1916. SUMMARY 1. The seller of a product often has better information about its quality than the buyer. Asymmetric information of this type creates a market failure in which bad products tend to drive good products out of the market. Market failure can be eliminated if sellers offer standardized products, provide guarantees or warranties, or find other ways to maintain good reputations for their products. CHAPTER 17 • Markets with Asymmetric Information 657 2. Insurance markets frequently involve asymmetric information because the party buying insurance has better information about the risk involved than the insurance company. This can lead to adverse selection, in which poor risks choose to insure and good risks do not. Another problem for insurance markets is moral hazard, in which the insured takes less care to avoid losses after being insured. 3. Sellers can deal with the problem of asymm
etric information by sending buyers signals about the quality of their products. For example, workers can signal high productivity by obtaining high levels of education. 4. Asymmetric information may make it costly for the owners of firms (principals) to monitor accurately the behavior of their managers (agents). Managers may seek higher fringe benefits for themselves or a goal of sales maximization, even though shareholders would prefer to maximize profit. 5. Owners can avoid some principal–agent problems by designing contracts that give their agents the incentive to perform productively. 6. Asymmetric information can explain why labor markets have unemployment even though some workers are actively seeking work. According to efficiency wage theory, a wage higher than the competitive wage (the efficiency wage) increases worker productivity by discouraging workers from shirking on the job. QUESTIONS FOR REVIEW 1. Why can asymmetric information between buyers and sellers lead to market failure when a market is otherwise perfectly competitive? 2. If the used car market is a “lemons” market, how would you expect the repair record of used cars that are sold to compare with the repair record of those not sold? 3. Explain the difference between adverse selection and moral hazard in insurance markets. Can one exist without the other? 4. Describe several ways in which sellers can convince buyers that their products are of high quality. Which methods apply to the following products: Maytag washing machines, Burger King hamburgers, large diamonds? 5. Why might a seller find it advantageous to signal the quality of a product? How are guarantees and warranties a form of market signaling? EXERCISES 6. Joe earned a high grade-point average during his four years of college. Is this achievement a strong signal to Joe’s future employer that he will be a highly productive worker? Why or why not? 7. Why might managers be able to achieve objectives other than profit maximization, which is the goal of the firm’s shareholders? 8. How can the principal–agent model be used to explain why public enterprises, such as post offices, might pursue goals other than profit maximization? 9. Why are bonus and profit-sharing payment schemes likely to resolve principal–agent problems, whereas a fixed-wage payment will not? 10. What is an efficiency wage? Why is it profitable for the firm to pay it when workers have better information about their productivity than firms do? 1. Many consumers view a well-known brand name as a signal of quality and will pay
more for a brand-name product (e.g., Bayer aspirin instead of generic aspirin, or Birds Eye frozen vegetables instead of the supermarket’s own brand). Can a brand name provide a useful signal of quality? Why or why not? 2. Gary is a recent college graduate. After six months at his new job, he has finally saved enough to buy his first car. a. Gary knows very little about the difference between makes and models. How could he use market signals, reputation, or standardization to make comparisons? b. You are a loan officer in a bank. After selecting a car, Gary comes to you seeking a loan. Because he has only recently graduated, he does not have a long credit history. Nonetheless, the bank has a long history of financing cars for recent college graduates. Is this information useful in Gary’s case? If so, how? 3. A major university bans the assignment of D or F grades. It defends its action by claiming that students tend to perform above average when they are free from the pressures of flunking out. The university states that it wants all its students to get As and Bs. If the goal is to raise overall grades to the B level or above, is this a good policy? Discuss this policy with respect to the problem of moral hazard. 4. Professor Jones has just been hired by the economics department at a major university. The president of the board of regents has stated that the university is committed to providing top-quality education for undergraduates. Two months into the semester, Jones fails to show up for his classes. It seems he is devoting all his time to research rather than to teaching. Jones argues that his research will bring prestige to the department and the university. Should he be allowed to continue exclusively with research? Discuss with reference to the principal–agent problem. 658 PART 4 • Information, Market Failure, and the Role of Government 5. Faced with a reputation for producing automobiles with poor repair records, a number of American companies have offered extensive guarantees to car purchasers (e.g., a seven-year warranty on all parts and labor associated with mechanical problems). a. In light of your knowledge of the lemons market, why is this a reasonable policy? b. Is the policy likely to create a moral hazard prob- lem? Explain. 6. To promote competition and consumer welfare, the Federal Trade Commission requires firms to advertise truthfully. How does truth in advertising promote competition? Why would a market be
less competitive if firms advertised deceptively? 7. An insurance company is considering issuing three types of fire insurance policies: (i) complete insurance coverage, (ii) complete coverage above and beyond a $10,000 deductible, and (iii) 90 percent coverage of all losses. Which policy is more likely to create moral hazard problems? 8. You have seen how asymmetric information can reduce the average quality of products sold in a market, as low-quality products drive out high-quality products. For those markets in which asymmetric information is prevalent, would you agree or disagree with each of the following? Explain briefly: a. The government should subsidize Consumer Reports. b. The government should impose quality standards— e.g., firms should not be allowed to sell low-quality items. c. The producer of a high-quality good will probably want to offer an extensive warranty. d. The government should require all firms to offer extensive warranties. 9. Two used car dealerships compete side by side on a main road. The first, Harry’s Cars, always sells highquality cars that it carefully inspects and, if necessary, services. On average, it costs Harry’s $8000 to buy and service each car that it sells. The second dealership, Lew’s Motors, always sells lower-quality cars. On average, it costs Lew’s only $5000 for each car that it sells. If consumers knew the quality of the used cars they were buying, they would pay $10,000 on average for Harry’s cars and only $7000 on average for Lew’s cars. Without more information, consumers do not know the quality of each dealership’s cars. In this case, they would figure that they have a 50–50 chance of ending up with a high-quality car and are thus willing to pay $8500 for a car. Harry has an idea: He will offer a bumper-tobumper warranty for all cars that he sells. He knows that a warranty lasting Y years will cost $500Y on average, and he also knows that if Lew tries to offer the same warranty, it will cost Lew $1000Y on average. a. Suppose Harry offers a one-year warranty on all of the cars he sells. i. What is Lew’s profit if he does not offer a oneyear warranty? If he does offer a one-year warranty? ii. What is Harry’s profit if Lew does not
offer a one-year warranty? If he does offer a one-year warranty? iii. Will Lew’s match Harry’s one-year warranty? iv. Is it a good idea for Harry to offer a one-year warranty? b. What if Harry offers a two-year warranty? Will this offer generate a credible signal of quality? What about a three-year warranty? c. If you were advising Harry, how long a warranty would you urge him to offer? Explain why. *10. As chairman of the board of ASP Industries, you estimate that your annual profit is given by the table below. Profit () is conditional upon market demand and the effort of your new CEO. The probabilities of each demand condition occurring are also shown in the table. MARKET DEMAND Market Probabilities LOW DEMAND MEDIUM DEMAND HIGH DEMAND.30.40.30 Low Effort = $5 million = $10 million = $15 million High Effort = $10 million = $15 million = $17 million You must design a compensation package for the CEO that will maximize the firm’s expected profit. While the firm is risk neutral, the CEO is risk averse. The CEO’s utility function is Utility = W.5 when making low effort Utility = W.5 - 100 when making high effort where W is the CEO’s income. (The -100 is the “utility cost” to the CEO of making a high effort.) You know the CEO’s utility function, and both you and the CEO know all of the information in the preceding table. You do not know the level of the CEO’s effort at time of compensation or the exact state of demand. You do see the firm’s profit, however. Of the three alternative compensation packages below, which do you as chairman of ASP Industries prefer? Why? Package 1: Pay the CEO a flat salary of $575,000 per year Package 2: Pay the CEO a fixed 6 percent of yearly firm profits CHAPTER 17 • Markets with Asymmetric Information 659 Package 3: Pay the CEO a flat salary of $500,000 per year and then 50 percent of any firm profits above $15 million 11. A firm’s short-run revenue is given by R = 10e - e 2, where e is the level of effort by a typical worker (all workers are assumed to be identical). A worker chooses his level of effort to maximize wage less effort w
- e (the per-unit cost of effort is assumed to be 1). Determine the level of effort and the level of profit (revenue less wage paid) for each of the following wage arrangements. Explain why these different principal– agent relationships generate different outcomes. a. w = 2 for e Ú 1; otherwise w = 0. b. w = R/2. c. w = R - 12.5. 12. UNIVERSAL SAVINGS & LOAN has $1000 to lend. Risk-free loans will be paid back in full next year with 4% interest. Risky loans have a 20% chance of defaulting (paying back nothing) and an 80% chance of paying back in full with 30% interest. a. How much profit can the lending institution expect to earn? Show that the expected profits are the same whether the lending institution makes risky or riskfree loans. b. Now suppose that the lending institution knows that the government will “bail out” UNIVERSAL if there is a default (paying back the original $1000). What type of loans will the lending institution choose to make? What is the expected cost to the government? c. Suppose that the lending institution doesn’t know for sure that there will be a bail out, but one will occur with probability P. For what values of P will the lending institution make risky loans? This page intentionally left blank C H A P T E R 18 Externalities and Public Goods In this chapter we study externalities—the effects of production and consumption activities not directly reflected in the market—and public goods—goods that benefit all consumers but that the market either undersupplies or does not supply at all. Externalities and public goods are important sources of market failure and thus raise serious public policy questions. For example, how much waste, if any, should firms be allowed to dump into rivers and streams? How strict should automobile emission standards be? How much money should the government spend on national defense? Education? Basic research? Public television? When externalities are present, the price of a good need not reflect its social value. As a result, firms may produce too much or too little, so that the market outcome is inefficient. We begin by describing externalities and showing exactly how they create market inefficiencies. We then evaluate remedies. While some remedies involve government regulation, others rely primarily on bargaining among individuals or on the legal right of those adversely affected to sue those who create an externality. Next,
we analyze public goods. The marginal cost of providing a public good to an additional consumer is zero, and people cannot be prevented from consuming it. We distinguish between those goods that are difficult to provide privately and those that could have been provided by the market. We conclude by describing the problem that policymakers face when trying to decide how much of a public good to provide. 18.1 Externalities Externalities can arise between producers, between customers, or between consumers and producers. They can be negative—when the action of one party imposes costs on another party—or positive—when the action of one party benefits another party. A negative externality occurs, for example, when a steel plant dumps its waste in a river that fishermen downstream depend on for their 18.1 Externalities 661 18.2 Ways of Correcting Market Failure 667 18.3 Stock Externalities 678 18.4 Externalities and Property Rights 684 18.5 Common Property Resources 687 18.6 Public Goods 690 18.7 Private Preferences for Public Goods 694 18.1 The Costs and Benefits of Sulfur Dioxide Emissions 665 18.2 Reducing Sulfur Dioxide Emissions in Beijing 672 18.3 Emissions Trading and Clean Air 673 18.4 Regulating Municipal Solid Wastes 678 18.5 Global Warming 682 18.6 The Coase Theorem at Work 687 18.7 Crawfish Fishing in Louisiana 689 18.8 The Demand for Clean Air 693 661 662 PART 4 • Information, Market Failure, and the Role of Government • externality Action by either a producer or a consumer which affects other producers or consumers, but is not accounted for in the market price. In §6.3, we explain that with a fixed-proportions production function, it is impossible to substitute among inputs because each level of output requires a specific combination of labor and capital. daily catch. The more waste the steel plant dumps in the river, the fewer fish will be supported. The firm, however, has no incentive to account for the external costs that it imposes on fishermen when making its production decision. Furthermore, there is no market in which these external costs can be reflected in the price of steel. A positive externality occurs when a home owner repaints her house and plants an attractive garden. All the neighbors benefit from this activity, even though the home owner’s decision to repaint and landscape probably did not take these benefits into account. Negative
Externalities and Inefficiency Because externalities are not reflected in market prices, they can be a source of economic inefficiency. When firms do not take into account the harms associated with negative externalities, the result is excess production and unnecessary social costs. To see why, let’s take our example of a steel plant dumping waste in a river. Figure 18.1 (a) shows the production decision of a steel plant in a competitive market. Figure 18.1 (b) shows the market demand and supply curves, assuming that all steel plants generate similar externalities. We assume that because the firm has a fixed-proportions production function, it cannot alter its input combinations; waste and other effluent can be reduced only by lowering output. (Without this assumption, firms would be jointly choosing among a variety of combinations of output and pollution abatement.) We will analyze the nature of the externality under two circumstances: first when only one steel plant pollutes and, second, when all steel plants pollute in the same way. Price P1 Price P* P1 MSC MC MEC MSCI S MCI MECI D q* q1 (a) Firm output Q* Q1 Industry output (b) FIGURE 18.1 EXTERNAL COST When there are negative externalities, the marginal social cost MSC is higher than the marginal cost MC. The difference is the marginal external cost MEC. In (a), a profit-maximizing firm produces at q1, where price is equal to MC. The efficient output is q, at which price equals MSC. In (b), the industry’s competitive output is Q1, at the intersection of industry supply MCI and demand D. However, the efficient output Q is lower, at the intersection of demand and marginal social cost MSCI. CHAPTER 18 • Externalities and Public Goods 663 In §8.3, we explain that because a competitive firm faces a horizontal demand curve, choosing its output so that marginal cost is equal to price is profit-maximizing. • marginal external cost Increase in cost imposed externally as one or more firms increase output by one unit. • marginal social cost Sum of the marginal cost of production and the marginal external cost. In §9.2, we explain that, absent market failure, a competitive market leads to the economically efficient output level. The price of steel is P1 at the intersection of the demand and supply curves in Figure 18.1
(b). The MC curve in (a) gives a typical steel firm’s marginal cost of production. The firm maximizes profit by producing output q1, at which marginal cost is equal to price (which equals marginal revenue because the firm takes price as given). As the firm’s output changes, however, the external cost imposed on fishermen downstream also changes. This external cost is given by the marginal external cost (MEC) curve in Figure 18.1 (a). It is intuitively clear why total external cost increases with output—there is more pollution. However, our analysis focuses on the marginal external cost, which measures the added cost of the externality associated with each additional unit of output produced. In practice, the MEC curve is upward sloping for most forms of pollution: As the firm produces additional output and dumps additional effluent, the incremental harm to the fishing industry increases. From a social point of view, the firm produces too much output. The efficient level of output is the level at which the price of the product is equal to the marginal social cost (MSC) of production: the marginal cost of production plus the marginal external cost of dumping effluent. In Figure 18.1 (a), the marginal social cost curve is obtained by adding marginal cost and marginal external cost for each level of output (i.e., MSC = MC + MEC). The marginal social cost curve MSC intersects the price line at output q. Because only one plant is dumping effluent into the river, the market price of the product is unchanged. However, the firm is producing too much output (q1 instead of q) and generating too much effluent. Now consider what happens when all steel plants dump their effluent into rivers. In Figure 18.1 (b), the MCI curve is the industry supply curve. The marginal external cost associated with the industry output, MECI, is obtained by summing the marginal cost of every person harmed at each level of output. The MSCI curve represents the sum of the marginal cost of production and the marginal external cost for all steel firms. As a result, MSCI = MCI + MECI. Is industry output efficient when there are externalities? As Figure 18.1 (b) shows, the efficient industry output level is the level at which the marginal benefit of an additional unit of output is equal to the marginal social cost. Because the demand curve measures the marginal benefit to consumers, the efficient output is Q
, at the intersection of the marginal social cost MSCI and demand D curves. The competitive industry output, however, is at Q1, the intersection of the demand curve and the supply curve, MCI. Clearly, industry output is too high. In our example, each unit of output results in some effluent being dumped. Therefore, whether we are looking at one firm’s pollution or the entire industry’s, the economic inefficiency is the excess production that results in too much effluent being dumped in the river. The source of the inefficiency is the incorrect pricing of the product. The market price P1 in Figure 18.1 (b) is too low— it reflects the firms’ marginal private cost of production, but not the marginal social cost. Only at the higher price P will steel firms produce the efficient level of output. What is the cost to society of this inefficiency? For each unit produced above Q*, the social cost is given by the difference between the marginal social cost and the marginal benefit (the demand curve). As a result, the aggregate social cost is shown in Figure 18.1 (b) as the shaded triangle between MSCI, D, and output Q1. When we move from the profit-maximizing to the socially efficient output, firms are worse off because their profits are reduced, and purchasers of steel are worse off because the price of steel has increased. However, these losses are less than the gain to those who were harmed by the adverse effect of the dumping of effluent in the river. 664 PART 4 • Information, Market Failure, and the Role of Government Externalities generate both long-run and short-run inefficiencies. In Chapter 8, we saw that firms enter a competitive industry whenever the price of the product is above the average cost of production and exit whenever price is below average cost. In long-run equilibrium, price is equal to (long-run) average cost. When there are negative externalities, the average private cost of production is less than the average social cost. As a result, some firms remain in the industry even when it would be efficient for them to leave. Thus, negative externalities encourage too many firms to remain in the industry. Positive Externalities and Inefficiency Externalities can also result in too little production, as the example of home repair and landscaping shows. In Figure 18.2, the horizontal axis measures the home owner’s investment (in dollars) in
repairs and landscaping. The marginal cost curve for home repair shows the cost of repairs as more work is done on the house; it is horizontal because this cost is unaffected by the amount of repairs. The demand curve D measures the marginal private benefit of the repairs to the homeowner. The home owner will choose to invest q1 in repairs, at the intersection of her demand and marginal cost curves. But repairs generate external benefits to the neighbors, as the marginal external benefit curve, MEB, shows. This curve is downward sloping in this example because the marginal benefit is large for a small amount of repair but falls as the repair work becomes extensive. The marginal social benefit curve, MSB, is calculated by adding the marginal private benefit and the marginal external benefit at every level of output. In short, MSB = D + MEB. The efficient level of output q, at which the marginal social benefit of additional repairs is equal to the marginal cost of those repairs, • marginal external benefit Increased benefit that accrues to other parties as a firm increases output by one unit. • marginal social benefit Sum of the marginal private benefit plus the marginal external benefit. FIGURE 18.2 EXTERNAL BENEFITS When there are positive externalities, marginal social benefits MSB are higher than marginal benefits D. The difference is the marginal external benefit MEB. A self-interested homeowner invests q1 in repairs, determined by the intersection of the marginal benefit curve D and the marginal cost curve MC. The efficient level of repair q is higher and is given by the intersection of the marginal social benefit and marginal cost curves. Value MSB D P1 P* MEB MC q1 q* Repair level CHAPTER 18 • Externalities and Public Goods 665 is found at the intersection of the MSB and MC curves. The inefficiency arises because the homeowner doesn’t receive all the benefits of her investment in repairs and landscaping. As a result, the price P1 is too high to encourage her to invest in the socially desirable level of house repair. A lower price, P, is required to encourage the efficient level of supply, q. Another example of a positive externality is the money that firms spend on research and development (R&D). Often the innovations resulting from research cannot be protected from other firms. Suppose, for example, that a firm designs a new product. If that design can be patented, the firm might earn a large profit by manufacturing and marketing the product. But if the new design can be
closely imitated by other firms, those firms can appropriate some of the developing firm’s profit. Because there is then little reward for doing R&D, the market is likely to underfund it. The externality concept is not new: In discussing demand in Chapter 4, we explained that positive and negative network externalities can arise if the quantity of a good demanded by a consumer increases or decreases in response to an increase in purchases by other consumers. Network externalities can also lead to market failures. Suppose, for example, that some individuals enjoy socializing at busy ski resorts when many other skiers are present. The resulting congestion could make the skiing experience unpleasant for those skiers who preferred short lift lines to pleasant social occasions. In §4.5, we explain that when there is a network externality, each individual’s demand depends on the purchases of other individuals. EXAMPLE 18.1 THE COSTS AND BENEFITS OF SULFUR DIOXIDE EMISSIONS Although sulfur dioxide gas can be produced naturally by volcanoes, almost two-thirds of all sulfur dioxide emissions in the United States come from electric power generation that depends on burning fossil fuels such as coal and petroleum. The effect of sulfur dioxide pollution on the environment has concerned policymakers for years, but these concerns reached new heights in the 1990s (with a series of amendments to the Clean Air Act) because of the potential adverse effects of acid rain. Acid rain—formed when sulfur dioxide and nitrogen oxides react with the atmosphere to form various acidic compounds—threatens property and health throughout the midwestern and northwestern United States.1 Acid rain can adversely affect human health either directly, from the atmosphere, or indirectly, through the soil in which our food is grown. Acid rain has been shown to increase risk of heart and lung disorders such as asthma and bronchitis and has been linked to premature death in both adults and children. According to one estimate, if sulfur dioxide emissions had been reduced by 50 percent of 1980s levels—a time when emissions were at a historic high in the United States—over 17,000 deaths per year would have been prevented. In addition to human health, acid rain causes damage to water and forests as well as to man-made structures. According to one study, a 50-percent reduction in sulfur dioxide levels in the 1980s would have translated into a $24 million annual value in improvements in recreational fishing, an $800 million annual value to the commercial timber sector, and a $700
million annual value to grain crop producers.2 Furthermore, sulfur dioxide emissions have been shown to cause damage to paint, steel, limestone, and marble through increased surface erosion. While the cost of acid rain to man-made materials is difficult 1Further information on sulfur dioxide and acid rain can be found at http://www.epa.gov. 2Spencer Banzhaf et al., “Valuation of Natural Resource Improvements in the Adirondacks,” (Washington: Resources for the Future, September 2004). 666 PART 4 • Information, Market Failure, and the Role of Government to quantify, automobile manufacturers are now offering acid-resistant paint on new automobiles at an average cost of $5 per car, or $61 million for all new cars and trucks sold in the United States. What about the costs of achieving reductions in sulfur dioxide emissions? To achieve these reductions, firms need to put emissions-control equipment into use. The incremental cost of achieving some emissions reduction is likely to be small, but that cost increases as greater and greater investments in capital equipment are needed to achieve further reductions. An example of the costs and benefits of reducing sulfur dioxide emissions is given in Figure 18.3, which is based on a study of pollution abatement in Philadelphia.3 It is easiest to read the graph from right to left, since we are looking to see how much of a reduction in sulfur dioxide concentrations from the existing level of.08 parts per million is socially desirable. The marginal abatement cost curve is increasing (from right to left); it jumps whenever new capital-intensive pollution-control equipment is needed to improve fuel efficiency. The marginal external cost curve reflects (again reading from right to left) the incremental reduction in the harms caused by acid rain. For moderate concentrations, studies of respiratory diseases, corrosion of materials, and lost visibility suggest that marginal social costs are high and relatively constant. However, for very low concentrations, the marginal external cost declines, and eventually there are relatively few adverse health, material, or aesthetic effects. The efficient level of reduced sulfur dioxide emissions is given by the number of ppm at which the marginal cost of reduced emissions is equal to the marginal external cost. We can see from Figure 18.3 that this level is approximately.0275 ppm. To sum up, there are clearly substantial benefits to reducing sulfur dioxide emissions. What if any policies are best utilized to achieve those reductions efficiently? We will return to these questions after we consider a variety of policy options for the treatment of externalities in Section
18.2. FIGURE 18.3 SULFUR DIOXIDE EMISSIONS REDUCTIONS The efficient sulfur dioxide concentration equates the marginal abatement cost to the marginal external cost. Here the marginal abatement cost curve is a series of steps, each representing the use of a different abatement technology. Dollars per unit of reduction 60 40 20 0 Marginal External Cost Marginal Abatement Cost 0.02 0.04 0.06 0.08 Sulfur dioxide concentration (ppm) 3Thomas R. Irvin, “A Cost Benefit Analysis of Sulfur Dioxide Abatement Regulations in Philadelphia,” Business Economics, September 1977, pp. 12–20. CHAPTER 18 • Externalities and Public Goods 667 18.2 Ways of Correcting Market Failure How can the inefficiency resulting from an externality be remedied? If the firm that generates the externality has a fixed-proportions production technology, the externality can be reduced only by encouraging the firm to produce less. As we saw in Chapter 8, this goal can be achieved through an output tax. Fortunately, most firms can substitute among inputs in the production process by altering their choices of technology. For example, a manufacturer can add a scrubber to its smokestack to reduce emissions. Consider a firm that sells its output in a competitive market. The firm emits pollutants that damage air quality in a neighborhood. The firm can reduce its emissions, but only at a cost. Figure 18.4 illustrates this trade-off. The horizontal axis represents the level of factory emissions and the vertical axis the cost per unit of emissions. To simplify, we assume that the firm’s output decision and its emissions decision are independent and that the firm has already chosen its profit-maximizing output level. The firm is therefore ready to choose its preferred level of emissions. The curve labeled MEC represents the marginal external cost of emissions. This social cost curve represents the increased harm associated with the emissions. We will use the terms marginal external cost and marginal social cost interchangeably in the discussion that follows. (Recall that we have assumed that the firm’s output is fixed, so that the private costs of production—as opposed to pollution abatement—are unchanged.) The MEC curve slopes upward because the marginal cost of the externality gets higher as the externality becomes more extensive. (Evidence from studies of the effects of air and water pollution suggests that
small levels of pollutants generate little harm. However, the harm increases substantially as the level of pollutants increases.) Because our emphasis will be on reducing emissions from existing levels, we will find it useful to read the MEC graph from right to left. From this perspective, we see that the MEC associated with a small reduction in emissions from a level of 26 units, which reflects the incremental benefit of reduced emissions, is Recall from §7.3 that a firm can substitute among inputs by changing technologies in response to an effluent fee. Dollars per unit of emissions 6 4 2 MEC FIGURE 18.4 THE EFFICIENT LEVEL OF EMISSIONS The efficient level of factory emissions is the level that equates the marginal external cost of emissions MEC to the benefit associated with lower abatement costs MCA. The efficient level of 12 units is E. 0 2 4 6 E0 8 10 12 E 14 16 18 20 22 24 26 E1 Level of emissions MCA 668 PART 4 • Information, Market Failure, and the Role of Government greater than $6 per unit. However, as emissions are reduced further and further, the marginal social cost falls (eventually) to below $2 per unit. At some point, the incremental benefit of reducing emissions becomes less than $2. The curve labeled MCA is the marginal cost of abating emissions. It measures the additional cost to the firm of installing pollution-control equipment. The MCA curve is downward sloping because the marginal cost of reducing emissions is low when the reduction has been slight and high when it has been substantial. (A slight reduction is inexpensive—the firm can reschedule production to generate the greatest emissions at night, when few people are outside. Large reductions require costly changes in the production process.) As with the MEC curve, reading the MCA curve from right to left will help with our intuition. From this perspective, the marginal cost of abatement increases as we seek to achieve greater and greater reductions in emissions. With no effort at abatement, the firm’s profit-maximizing level of emissions is 26, the level at which the marginal cost of abatement is zero. The efficient level of emissions, 12 units, is at point E, where the marginal external cost of emissions, $3, is equal to the marginal cost of abating emissions. Note that if emissions are lower than E—say, E0—the marginal cost of abating emissions, $7, is greater than the marginal
external cost of emissions, $2. Emissions, therefore, are too low relative to the social optimum. However, if the level of emissions is E1, the marginal external cost of emissions, $4, is greater than the marginal cost of abatement, $1. Emissions are then too high. We can encourage the firm to reduce emissions to E* in three ways: (1) emissions standards; (2) emissions fees; and (3) transferable emissions permits. We will begin by discussing standards and fees and comparing relative advantages and disadvantages. Then we will examine transferable emissions permits. An Emissions Standard An emissions standard is a legal limit on how much pollutant a firm can emit. If the firm exceeds the limit, it can face monetary and even criminal penalties. In Figure 18.5, the efficient emissions standard is 12 units, at point E. The firm will be heavily penalized for emissions greater than this level. The standard ensures that the firm produces efficiently. The firm meets the standard by installing pollution-abatement equipment. The increased abatement expenditure will cause the firm’s average cost curve to rise (by the average cost of abatement). Firms will find it profitable to enter the industry only if the price of the product is greater than the average cost of production plus abatement—the efficient condition for the industry.4 An Emissions Fee An emissions fee is a charge levied on each unit of a firm’s emissions. As Figure 18.5 shows, a $3 emissions fee will generate efficient behavior by our factory. Faced with this fee, the firm minimizes costs by reducing emissions from 26 to 12 units. To see why, note that the first unit of emissions can be reduced (from 26 to 25 units of emissions) at very little cost (the marginal cost of additional abatement is close to zero). For very little cost, therefore, the firm can avoid paying the $3 per-unit fee. In fact, for all levels of emissions above 12 units, the marginal cost 4This analysis assumes that the social costs of emissions do not change over time. If they do, the efficient standard will also change. • emissions standard Legal limit on the amount of pollutants that a firm can emit. • emissions fee Charge levied on each unit of a firm’s emissions. Dollars per unit of emissions Fee 3 CHAPTER 18 • Externalities and Public Goods 669 MEC Standard 12 E MCA 26 Level of emissions FIGURE
18.5 STANDARDS AND FEES The efficient level of emissions at E* can be achieved through either an emissions fee or an emissions standard. Facing a fee of $3 per unit of emissions, a firm reduces emissions to the point at which the fee is equal to the marginal cost of abatement. The same level of emissions reduction can be achieved with a standard that limits emissions to 12 units. of abatement is less than the emissions fee. Thus it pays to reduce emissions. Below 12 units, however, the marginal cost of abatement is greater than the fee. In that case, the firm will prefer to pay the fee rather than further reduce emissions. It will therefore pay a total fee given by the gray-shaded rectangle and incur a total abatement cost given by the blue-shaded triangle under the MCA curve to the right of E = 12. This cost is less than the fee that the firm would pay if it did not reduce emissions at all. Standards versus Fees The United States has historically relied on standards to regulate emissions. However, other countries, such as Germany, have used fees successfully. Which method is better? The relative advantages of standards and fees depend on the amount of information available to policymakers and on the actual cost of controlling emissions. To understand these differences, let’s suppose that because of administrative costs, the agency that regulates emissions must charge the same fee or set the same standard for all firms. THE CASE FOR FEES First, let’s examine the case for fees. Consider two firms that are located so that the marginal social cost of emissions is the same no matter which reduces its emissions. Because they have different abatement costs, however, their marginal cost of abatement curves are not the same. Figure 18.6 shows why emissions fees are preferable to standards in this case. MCA1 and MCA2 represent the marginal cost of abatement curves for the two firms. Each firm initially generates 14 units of emissions. Suppose we want to reduce total emissions by 14 units. Figure 18.6 shows that the cheapest way to do this is to have Firm 1 reduce emissions by 6 units and Firm 2 by 8. With these reductions, both firms have marginal costs of abatement of $3. But consider what happens if the regulatory agency asks both firms to reduce emissions by 7 units. In that case Firm 1’s marginal cost of abatement increases from $3 to $3.75, while Firm 2’s
marginal cost of abatement decreases from $3 to $2.50. This cannot be 670 PART 4 • Information, Market Failure, and the Role of Government FIGURE 18.6 THE CASE FOR FEES With limited information, a policymaker may be faced with the choice of either a single emissions fee or a single emissions standard for all firms. The fee of $3 achieves a total emissions level of 14 units more cheaply than a 7-unit-per-firm emissions standard. With the fee, the firm with a lower abatement cost curve (Firm 2) reduces emissions more than the firm with a higher cost curve (Firm 1). Dollars per unit of emissions MCA2 MCA1 6 5 4 3.75 3 2.50 2 1 Firm 2’s Reduced Abatement Costs Firm 1’s Increased Abatement Costs 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Level of emissions cost-minimizing because the second firm can reduce emissions more cheaply than the first. Only when the marginal cost of abatement is equal for both firms will emissions be reduced by 14 units at minimum cost. Now we can see why a fee ($3) might be preferable to a standard (7 units). Faced with a $3 fee, Firm 1 will reduce emissions by 6 units and Firm 2 by 8 units—the efficient outcome. By contrast, under an emissions standard, Firm 1 incurs additional abatement costs given by the green-shaded area between 7 and 8 units of emissions. But Firm 2 enjoys reduced abatement costs given by the purple-shaded area between 6 and 7 units. Clearly, Firm 1’s added abatement costs are larger than Firm 2’s reduced costs. The emissions fee thus achieves the same level of emissions at a lower cost than the equal per-firm emissions standard. In general, fees can be preferable to standards for several reasons. First, when standards must be applied equally to all firms, fees achieve the same emissions reduction at a lower cost. Second, fees give a firm a strong incentive to install new equipment that would allow it to reduce emissions even further. Suppose the standard requires that each firm reduce its emission by 6 units, from 14 to 8. Firm 1 is considering installing new emissions devices that would lower its marginal cost of abatement from MCA1 to MCA2. If the equipment is relatively inexpensive, the firm will install it because it will lower the cost of
meeting the standard. However, a $3 emissions fee would provide a greater incentive for the firm to reduce emissions. With the fee, not only will the firm’s cost of abatement be lower on the first 6 units of reduction, but it will also be cheaper to reduce emissions by 2 more units: The emissions fee is greater than the marginal abatement cost for emissions levels between 6 and 8. THE CASE FOR STANDARDS Now let’s examine the case for standards by looking at Figure 18.7. While the marginal external cost curve is very steep, the marginal cost of abatement is relatively flat. The efficient emissions fee is $8. But suppose that because of limited information, a lower fee of $7 is charged (this fee amounts to a 1/8 or 12.5 percent reduction). Because the MCA curve is flat, the firm’s emissions will be increased from 8 to 11 units. This increase lowers the CHAPTER 18 • Externalities and Public Goods 671 Dollars per unit of emissions 16 14 12 10 8 6 4 2 C Marginal External Cost E A D B Marginal Cost of Abatement 2 4 6 8 10 12 14 16 Level of emissions FIGURE 18.7 THE CASE FOR STANDARDS When the government has limited information about the costs and benefits of pollution abatement, either a standard or a fee may be preferable. The standard is preferable when the marginal external cost curve is steep and the marginal abatement cost curve is relatively flat. Here a 12.5 percent error in setting the standard leads to extra social costs of triangle ADE. The same percentage error in setting a fee would result in excess costs of ABC. firm’s abatement costs somewhat, but because the MEC curve is steep, there will be substantial additional social costs. The increase in social costs, less the savings in abatement costs, is given by the entire shaded (light and dark) triangle ABC. What happens if a comparable error is made in setting the standard? The efficient standard is 8 units of emissions. But suppose the standard is relaxed by 12.5 percent, from 8 to 9 units. As before, this change will lead to an increase in social costs and a decrease in abatement costs. But the net increase in social costs, given by the small triangle ADE, is much smaller than before. This example illustrates the difference between standards and fees. When the marginal external cost curve is relatively steep and the marginal cost of ab
atement curve relatively flat, the cost of not reducing emissions is high. In such cases, a standard is preferable to a fee. With incomplete information, standards offer more certainty about emissions levels but leave the costs of abatement uncertain. Fees, on the other hand, offer certainty about the costs of abatement but leave the reduction of emissions levels uncertain. The preferable policy depends, therefore, on the nature of uncertainty and on the shapes of the cost curves.5 Tradeable Emissions Permits If we knew the costs and benefits of abatement and if all firms’ costs were identical, we could apply a standard. Alternatively, if the costs of abatement varied among firms, an emissions fee would work. However, when firms’ costs vary 5Our analysis presumes that the emissions fee is levied as a fixed fee per unit of emissions. If the fee is set too low because of limited information, the firm will generate a substantial amount of excess emissions. Suppose, however, that a fixed fee were replaced with a fee schedule designed so that the higher the level of emissions the higher the per-unit fee. In this case, if the fee schedule is set too low, the increasing fee will discourage the firm from generating substantial excess emissions. In general, a variable fee is preferable to a standard if the fee schedule can be designed to match the environmental harm caused by the emissions. In this case, firms know that the payment they make will be approximately equal to the harm that they cause and will internalize that harm in making their production decisions. See Louis Kaplow and Steven Shavell, “On the Superiority of Corrective Taxes to Quantity Regulation,” American Law and Economics Review 4 (Spring 2002): 1–17. 672 PART 4 • Information, Market Failure, and the Role of Government • tradeable emissions permits System of marketable permits, allocated among firms, specifying the maximum level of emissions that can be generated. and we do not know the costs and benefits, neither a standard nor a fee will generate an efficient outcome. We can reach the goal of reducing emissions efficiently by using tradeable emissions permits. Under this system, each firm must have permits to generate emissions. Each permit specifies the number of units of emissions that the firm is allowed to put out. Any firm that generates emissions not allowed by permit is subject to substantial monetary sanctions. Permits are allocated among firms, with the total number of permits chosen to achieve the desired maximum level of emissions. Permits are marketable
: They can be bought and sold. Under the permit system, the firms least able to reduce emissions are those that purchase permits. Thus, suppose the two firms in Figure 18.6 (page 670) were given permits to emit up to 7 units. Firm 1, facing a relatively high marginal cost of abatement, would pay up to $3.75 to buy a permit for one unit of emissions, but the value of that permit is only $2.50 to Firm 2. Firm 2 should therefore sell its permit to Firm 1 for a price between $2.50 and $3.75. If there are enough firms and permits, a competitive market for permits will develop. In market equilibrium, the price of a permit equals the marginal cost of abatement for all firms; otherwise, a firm will find it advantageous to buy more permits. The level of emissions chosen by the government will be achieved at minimum cost. Those firms with relatively low marginal cost of abatement curves will be reducing emissions the most, and those with relatively high marginal cost of abatement curves will be buying more permits and reducing emissions the least. Marketable emissions permits create a market for externalities. This market approach is appealing because it combines some of the advantageous features of a system of standards with the cost advantages of a fee system. The agency that administers the system determines the total number of permits and, therefore, the total amount of emissions, just as a system of standards would do. But the marketability of the permits allows pollution abatement to be achieved at minimum cost.6 E XAM PLE 18.2 REDUCING SULFUR DIOXIDE EMISSIONS IN BEIJING Taken together, sulfur dioxide emissions produced through the burning of coal for use in electric power generation and the wide use of coal-based home furnaces have caused a huge problem in Beijing as well as other cities in China. Not only have emissions created an acid rain problem, but they have combined with emissions from the growing number of automobiles to make Beijing one of the most polluted cities not only in China, but in the world. In 1995, for example, the level of sulfur dioxide in Beijing was 90 milligrams per cubic meter, which compares unfavorably to Berlin (18 mg/m3), Copenhagen (7), London (25), New York (26), Tokyo (18), and Mexico City (74). Of the major cities in the world, only Moscow had higher sulfur dioxide levels (109 mg/m3).
Over the long term, the key to solving Beijing’s problem is to replace coal with cleaner fuels, to encourage the use of public transportation, and, when necessary, to 6With limited information and costly monitoring, a marketable permit system is not always ideal. For example, if the total number of permits is chosen incorrectly and the marginal cost of abatement rises sharply for some firms, a permit system could drive those firms out of business by imposing high abatement costs. (This would also be a problem for fees.) CHAPTER 18 • Externalities and Public Goods 673 introduce fuel-efficient hybrid vehicles. But prior to its hosting of the Olympics in 2008, Beijing had a problem. What could it do to reduce sulfur dioxide emissions so as to offer a cleaner environment to the Olympic athletes and to the visiting public? Beijing’s choice was to shut down a large number of coal-fired plants. The air quality in Beijing improved 30 percent in 2008 for the Olympics, at a cost of about $10 billion. But a year after the Games, when many of the environmental regulations were no longer in effect, about 60 percent of the improvement was lost. Was the shutdown of plants the most efficient policy choice? Our study of pollutionabatement strategies suggests not. For one thing, we have experience with the use of standards for regulating sulfur dioxide emissions in Philadelphia (recall Example 18.1). In 1968, Philadelphia imposed air-quality regulations that limited the maximum allowable sulfur content in fuel oil to 1.0 percent or less. This regulation decreased sulfur dioxide levels in the air substantially—from 0.10 parts per million (ppm) in 1968 to below 0.030 ppm in 1973. Improved air quality led to better human health, less damage to materials, and higher property values. Example 18.1 shows that the imposed standards made sense on cost-benefit grounds. Would the imposition of a system of emissions fees—or better yet a regime of tradeable emissions permits—do even better in Beijing? A study of the regulation of electric-utility sulfur dioxide tradeable emissions shows that marketable permits in the United States can cut in half the cost of complying with a regulatory-based standard.7 Can similar gains be achieved in Beijing? The answer lies in part on whether the market for tradeable emissions will itself work efficiently. But it also depends on the shape of the marginal abatement cost and marginal external cost curves. As our prior discussion has shown, the case for emissions fees (and for trade
able permits) is strongest (1) when firms vary substantially in their marginal abatement costs; and (2) when the marginal external cost of emissions curve is relatively steep and the marginal cost of abatement curve relatively flat. EXAM PLE 18.3 EMISSIONS TRADING AND CLEAN AIR Controlling emissions cost companies approximately $18 billion during the 1980s, and it cost even more during the first half of the 1990s.8 An effective emissions trading system could reduce those costs substantially in the decades to come. The Environmental Protection Agency’s “bubble” and “offset” programs were modest attempts to use a trading system to lower cleanup costs. A bubble allows an individual firm to adjust its pollution controls for individual sources of pollutants as long as a total pollutant limit for the firm is not exceeded. In theory, a bubble could be used to set pollutant limits for many firms or for an entire geographic region; in practice, however, it has been applied to individual firms. As a result “permits” are, in effect, traded within the firm: If one part of the firm can reduce its emissions, another part will be allowed to emit more. Abatement cost savings associated with the EPA’s program of 42 bubbles have been approximately $300 million per year since 1979. Under the offset program, new sources of emissions may be located in geographic regions in which air-quality standards have not been met, but only if they offset their new emissions by reducing emissions from existing sources by at least as much. Offsets can be obtained by internal trading, but external trading among firms is also allowed. A total of more than 2000 offset transactions have occurred since 1976. Because of their limited natures, bubble and offset programs substantially understate the 7Don Fullerton, Shaun P. McDermott, and Jonathan P. Caulkins, “Sulfur Dioxide Compliance of a Regulated Utility,” NBER Working Paper No. 5542, April 1996. 8See Robert W. Hahn and Gordon L. Hester, “The Market for Bads: EPA’s Experience with Emissions Trading,” Regulation (1987): 48–53; Brian J. McKean, “Evolution of Marketable Permits: The U.S. Experience with Sulfur-Dioxide Allowance Trading,” Environmental Protection Agency, December, 1996. 674 PART 4 • Information, Market Failure,
and the Role of Government potential gain from a broad-based emissions trading program. In one study, the cost of achieving an 85-percent reduction in hydrocarbon emissions in all U.S. DuPont plants was estimated under three alternative policies: (1) each source at each plant must reduce emissions by 85 percent; (2) each plant must reduce its overall emissions by 85 percent with only internal trading possible; and (3) total emissions at all plants must be reduced by 85 percent, with both internal and external trading possible.9 When no trading was allowed, the cost of emissions reduction was $105.7 million. Internal trading reduced the cost to $42.6 million. Allowing for both external and internal trading reduced the cost even further, to $14.6 million. Clearly, the potential cost savings from an effective tradeable emissions program can be substantial. This may explain why Congress focused on transferable permits as a way of dealing with “acid rain” in the 1990 Clean Air Act. Acid rain can be extremely harmful to people, animals, vegetation, and buildings. The government initially authorized a permit system to reduce annual sulfur dioxide emissions by 10 million tons and nitrogen oxide emissions by 2.5 million tons by the year 2000. That program remains in place today. Under the plan, each tradeable permit allows a maximum of one ton of sulfur dioxide to be released into the air. Electric utilities and other polluting entities are allocated permits in proportion to their current level of emissions. Companies can make the capital investments necessary to reduce emissions, perhaps by selling excess permits, or they can buy permits and avoid having to make costly emissionsreducing investments. In the early 1990s, economists expected these permits to trade for around $300. In fact, as Figure 18.8 shows, between 1993 and 2003, prices fluctuated between $100 and $200. Why? It 1600 1400 1200 1000 800 600 400 200 ) 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 Year FIGURE 18.8 PRICE OF TRADEABLE EMISSIONS PERMITS The price of tradeable permits for sulfur dioxide emissions fluctuated between $100 and $200 from 1993 to 2003, but then increased sharply in 2005 and 2006 in response to an increased demand for permits. The price fluctuated between $400 and $500 per ton for the next few years, before the market crashed in 2008, after the EPA was forced to revise the permit program. 9M. T. Maloney and Bruce Yandle, “Bub
bles and Efficiency: Cleaner Air at Lower Cost,” Regulation (May/June 1980): 49–52. CHAPTER 18 • Externalities and Public Goods 675 turned out that reducing sulfur dioxide emissions was less costly than anticipated (it had become cheaper to mine low-sulfur coal), and many electric utilities took advantage of this development to reduce emissions. From 2005 to 2006, however, the price of permits rose sharply, hitting a high of nearly $1600 in December 2005. This was the result of an increase in the price of lowsulfur coal and, more importantly, the increased demand for permits that resulted as more electric power plants were required to meet tight emissions standards.10 Starting in 2007, however, the market price of emission permits began to decline, in part because the EPA lost a lawsuit brought by a group of utilities. The court ruled that the EPA had overstepped its authority by expanding the sulfur permit market beyond its initial scope. The permit market could be expanded, the court ruled, but the EPA must rewrite its rules to comply with existing Clean Air Act regulations. Permit prices fell precipitously after the ruling, and the market finally bottomed out in 2010, when the EPA issued new rules that require most emissions reductions to come from changes at individual plants and that limit the use of permit allowances. By 2011, you could buy a permit (perhaps as a gift for a close friend) for as little as $2 per ton. Will the prices of emission permits remain so low that the entire program might be dismantled? The answer depends on the amount of sulfur dioxide emissions we are willing to allow in the United States. If emission limits are tightened, permit prices could eventually rise. Recycling To the extent that the disposal of waste products involves little or no private cost to either consumers or producers, society will dispose of too much waste material. The overutilization of virgin materials and the underutilization of recycled materials will result in a market failure that may require government intervention. Fortunately, given the appropriate incentive to recycle products, this market failure can be corrected.11 To see how recycling incentives can work, consider a typical household’s decision with respect to the disposal of glass containers. In many communities, households are charged a fixed annual fee for trash disposal. As a result, these households can dispose of glass and other garbage at very low cost—only the time and effort to put the materials in a trash receptacle. The low cost of disposal creates a divergence between the private and the social cost
of disposal. The marginal private cost, which is the cost to the household of throwing out the glass, is likely to be constant (independent of the amount of disposal) for low to moderate levels of disposal. It will then increase for large disposal levels involving additional shipping and dump charges. In contrast, the social cost of disposal includes the harm to the environment from littering, as well as the injuries caused by sharp glass objects. Marginal social cost is likely to increase, in part because the marginal private cost is increasing and in part because the environmental 10Our thanks to Elizabeth Bailey, Denny Ellerman, and Paul Joskow for providing the emissions permit price data and for helpful comments. For a more detailed explanation of permit prices, see A. D. Ellerman, P. L. Joskow, R. Schmalensee, J. P. Montero, and E. M. Bailey, Markets for Clean Air: The U.S. Acid Rain Program (Boston: MIT Center for Energy and Environmental Policy Research, 1999). For more information on tradeable permits generally, go to the EPA Web site at www.epa.gov. 11Even without market intervention, some recycling will occur if the price of virgin material is sufficiently high. For example, recall from Chapter 2 that when the price of copper is high, there is more recycling of scrap copper. 676 PART 4 • Information, Market Failure, and the Role of Government and aesthetic costs of littering are likely to increase sharply as the level of disposal increases. Both cost curves are shown in Figure 18.9. The horizontal axis measures, from left to right, the amount of scrap material m that the household disposes, up to a maximum of 12 pounds per week. Consequently, the amount recycled can be read from right to left. As the amount of scrap disposal increases, the marginal private cost, MC, increases, but at a much lower rate than the marginal social cost MSC. Recycling of containers can be accomplished by a municipality or a private firm that arranges for collection, consolidation, and processing of materials. The marginal cost of recycling is likely to increase as the amount of recycling grows, in part because collection, separation, and cleaning costs grow at an increasing rate. The marginal cost of recycling curve, MCR, in Figure 18.9 is best read from right to left. Thus, when there are 12 pounds of disposed material, there is no recycling; the marginal cost is zero. As the amount of disposal decreases
, the amount of recycling increases; the marginal cost of recycling increases. The efficient amount of recycling occurs at the point at which the marginal cost of recycling, MCR, is equal to the marginal social cost of disposal, MSC. As Figure 18.9 shows, the efficient amount of scrap for disposal m* is less than the amount that will arise in a private market, m1. Why not utilize a disposal fee, a disposal standard, or even transferable disposal permits to resolve this externality? Any of these policies can help in theory, but they are not easy to put into practice and are rarely used. For example, a disposal fee is difficult to implement because it would be very costly for a community to sort through trash to separate and then to collect glass materials. Pricing and billing for scrap disposal would also be expensive, because the weight and composition of materials would affect the social cost of the scrap and, therefore, the appropriate price to be charged. Cost (dollars) MCR MSC MC + per-unit refund MC 4 m* m1 8 12 Scrap FIGURE 18.9 THE EFFICIENT AMOUNT OF RECYCLING The efficient amount of recycling of scrap material is the amount that equates the marginal social cost of scrap disposal, MSC, to the marginal cost of recycling, MCR. The efficient amount of scrap for disposal m* is less than the amount that will arise in a private market, m1. $ P P CHAPTER 18 • Externalities and Public Goods 677 FIGURE 18.10 REFUNDABLE DEPOSITS The supply of virgin glass containers is given by Sv and the supply of recycled glass by Sr. The market supply S is the horizontal sum of these two curves. Initially, equilibrium in the market for glass containers involves a price P and a supply of recycled glass M1. By raising the relative cost of disposal and encouraging recycling, the refundable deposit increases the supply of recycled glass from Sr to S’r and the aggregate supply of glass from S to S’. The price of glass then falls to P’, the quantity of recycled glass increases to M, and the amount of disposed glass decreases. Sr Sr Sv S S D M1 M Amount of glass REFUNDABLE DEPOSITS One policy solution that has been used with some success to encourage recycling is the refundable deposit.12 Under a refundable deposit system, an initial deposit is paid to the store owner when the glass container product is purchased.
The deposit is refunded if and when the container is returned to the store or to a recycling center. Refundable deposits create a desirable incentive: The per-unit refund can be chosen so that households (or firms) recycle more material. From an individual’s point of view, the refundable deposit creates an additional private cost of disposal: the opportunity cost of failing to obtain a refund. As shown in Figure 18.9, with the higher cost of disposal, the individual will reduce disposal and increase recycling to the optimal social level m. A similar analysis applies at the industry level. Figure 18.10 shows a downward-sloping market demand for glass containers, D. The supply of virgin glass containers is given by Sv and the supply of recycled glass by Sr. The market supply S is the horizontal sum of these two curves. As a result, the market price of glass is P and the equilibrium supply of recycled glass is M1. By raising the relative cost of disposal and encouraging recycling, the refundable deposit increases the supply of recycled glass from Sr, to S’r, the aggregate supply increases from S to S’, and the price of glass falls to P’. As a result, the quantity of recycled glass increases to M, resulting in a decrease in the amount of disposed glass. The refundable deposit scheme has another advantage: A market for recycled products is created. In many communities, public or private firms as well as private individuals specialize in collecting and returning recyclable materials. As this market becomes larger and more efficient, the demand for recycled rather than virgin materials increases, therefore increasing the benefit to the environment. 12See Frank Ackerman, Why Do We Recycle: Markets, Values, and Public Policy (Washington: Island Press, 1997), for a general discussion of recycling. 678 PART 4 • Information, Market Failure, and the Role of Government E XAM PLE 18.4 REGULATING MUNICIPAL SOLID WASTES By 1990, the average resident of Los Angeles was generating about 6.4 pounds of solid waste per day, and residents of other large American cities were not far behind. By contrast, residents of Tokyo, Paris, Hong Kong, and Rome generated 3 pounds, 2.4 pounds, 1.9 pounds, and 1.5 pounds, respectively.13 Some of these differences are due to variations in consumption levels, but most are due to the efforts that many other countries have made to encourage recycling. In the United States, only
about 25 percent of aluminum, 23 percent of paper, and 8.5 percent of glass scrap are recycled. A number of policy proposals have been introduced to encourage recycling in the United States. The first is the refundable deposit described above. A second is a curbside charge, in which communities charge individuals a fee for refuse disposal that is proportional to the weight (or the volume) of the refuse. To encourage separation of recyclable materials, all separable glass materials are collected for free. Curbside charges encourage recycling, but they fail to discourage consumption of products that might require recycling. A third alternative is to require the mandatory separation of recyclable materials such as glass. Random spot checks with substantial penalties for violations are required to make the system effective. Mandatory separation is perhaps the least desirable of the three alternatives, not only because it is difficult to implement, but also because individuals, if the cost of separation is sufficiently high, may be encouraged to shift to alternative containers such as plastic, which are environmentally damaging and cannot readily be recycled. The potential effectiveness of each of these three policies is illustrated by a study that focused on the mix between glass and plastic. Consumers were assumed to have varying preferences, with half preferring glass and half preferring plastic, for products that are otherwise identical in price, quantity, and quality. Without any incentive to recycle, a 50–50 division between glass and plastic would result. From a social perspective, however, greater use of recyclable glass would be preferred. Mandatory separation fails as a policy in this case: The cost of separation is so high that the percentage of glass container materials purchased actually falls to 40 percent. A curbside charge, however, does much better: It leads to a 72.5 percent use of recyclable glass. Finally, a refundable deposit system does best, with 78.9 percent of consumers purchasing recyclable glass containers. A recent case in Perkasie, Pennsylvania, shows that recycling programs can indeed be effective. Prior to implementation of a program combining all three economic incentives just described, the total amount of unseparated solid waste was 2573 tons per year. When the program was implemented, this amount fell to 1038 tons—a 59-percent reduction. As a result, the town saved $90,000 per year in disposal costs. Recycling efforts have expanded in the past decade. By 2009, 50.7 percent of aluminum, 74.2 percent of office paper, and 31.1 percent of glass containers were recycled.
In total, Americans created 4.34 pounds of solid waste per person per day. 1.46 pounds of that total was either recycled or composted. 18.3 Stock Externalities We have studied the negative externalities that result directly from flows of harmful pollution. For example, we saw how sulfur dioxide emissions from power plants can adversely affect the air that people breathe, so that government 13This example is based on Peter S. Menell, “Beyond the Throwaway Society: An Incentive Approach to Regulating Municipal Solid Waste,” Ecology Law Quarterly (1990): 655–739. See also Marie Lynn Miranda et al., “Unit Pricing for Residential Municipal Solid Waste: An Assessment of the Literature,” U.S. Environmental Protection Agency, March 1996. CHAPTER 18 • Externalities and Public Goods 679 intervention in the form of emissions fees or standards might be warranted. Recall that we compared the marginal cost of reducing the flow of emissions to the marginal benefit in order to determine the socially optimal level of emissions. Sometimes, however, the damage to society comes not directly from the emissions flow, but rather from the accumulated stock of the pollutant. A good example is global warming. Global warming is thought to result from the accumulation of carbon dioxide and other greenhouse gasses (GHGs) in the atmosphere. (As the GHG concentration grows, more sunlight is absorbed into the atmosphere rather than being reflected away, causing an increase in average temperatures.) GHG emissions do not cause the kind of immediate harm that sulfur dioxide emissions cause. Rather, it is the stock of accumulated GHGs in the atmosphere that ultimately causes harm. Furthermore, the dissipation rate for accumulated GHGs is very low: Once the GHG concentration in the atmosphere has increased substantially, it will remain high for many years, even if further GHG emissions were reduced to zero. That is why there is concern about reducing GHG emissions now rather than waiting for concentrations to build up (and temperatures to start rising) fifty or more years from now. Stock externalities (like flow externalities) can also be positive. An example is the stock of “knowledge” that accumulates as a result of investments in R&D. Over time, R&D leads to new ideas, new products, more efficient production techniques, and other innovations that benefit society as a whole, and not just those who undertake the R&D. Because of this positive externality, there is a strong argument for the government to subsidize R&
D. Keep in mind, however, that it is the stock of knowledge and innovations that benefits society, and not the flow of R&D that creates the stock. We examined the distinction between a stock and a flow in Chapter 15. As we explained in Section 15.1 (page 560), the capital that a firm owns is measured as a stock, i.e., as a quantity of plant and equipment that the firm owns. The firm can increase its stock of capital by purchasing additional plant and equipment, i.e., by generating a flow of investment expenditures. (Recall that inputs of labor and raw materials are also measured as flows, as is the firm’s output.) We saw that this distinction is important, because it helps the firm decide whether to invest in a new factory, equipment, or other capital. By comparing the present discounted value (PDV) of the additional profits likely to result from the investment to the cost of the investment, i.e., by calculating the investment’s net present value (NPV), the firm can decide whether or not the investment is economically justified. The same net present value concept applies when we want to analyze how the government should respond to a stock externality—though with an additional complication. For the case of pollution, we must determine how any ongoing level of emissions leads to a buildup of the stock of pollutant, and we must then determine the economic damage likely to result from that higher stock. We will then be able to compare the present value of the ongoing costs of reducing emissions each year to the present value of the economic benefits resulting from a reduced future stock of the pollutant. Stock Buildup and Its Impact Let’s focus on pollution to see how the stock of a pollutant changes over time. With ongoing emissions, the stock will accumulate, but some fraction of the stock, d, will dissipate each year. Thus, assuming the stock starts at zero, in the first year, the stock of pollutant (S) will be just the amount of that year’s emissions (E): S1 = E1 • stock externality Accumulated result of action by a producer or consumer which, though not accounted for in the market price, affects other producers or consumers. Recall from §15.1 that a firm’s capital is measured as a stock, while the investment that creates the capital is a flow. The firm’s output is also measured as a flow. Recall from §15.
2 that the present discounted value (PDV) of a series of expected future cash flows is the sum of those cash flows discounted by the appropriate interest rate. Moreover, we observe in §15.4 that, according to the net present value (NPV) rule, a firm should invest if the PDV of the expected future cash flow from an investment is greater than the cost. 680 PART 4 • Information, Market Failure, and the Role of Government In the second year, the stock of pollutant will equal the emissions that year plus the nondissipated stock from the first year— S2 = E2 + (1 - d)S1 —and so on. In general, the stock in any year t is given by the emissions generated that year plus the nondissipated stock from the previous year: St = Et + (1 - d)St - 1 If emissions are at a constant annual rate E, then after N years, the stock of pollutant will be14: SN = E[1 + (1 - d) + (1 - d)2 + c + (1 - d)N - 1] As N becomes infinitely large, the stock will approach the long-run equilibrium level E/d. The impact of pollution results from the accumulating stock. Initially, when the stock is small, the economic impact is small; but the impact grows as the stock grows. With global warming, for example, higher temperatures result from higher concentrations of GHGs: thus the concern that if GHG emissions continue at current rates, the atmospheric stock of GHGs will eventually become large enough to cause substantial temperature increases—which, in turn, could have adverse effects on weather patterns, agriculture, and living conditions. Depending on the cost of reducing GHG emissions and the future benefits of averting these temperature increases, it may make sense for governments to adopt policies that would reduce emissions now, rather than waiting for the atmospheric stock of GHGs to become much larger. NUMERICAL EXAMPLE We can make this concept more concrete with a simple example. Suppose that, absent government intervention, 100 units of a pollutant will be emitted into the atmosphere every year for the next 100 years; the rate at which the stock dissipates, d, is 2 percent per year, and the stock of pollutant is initially zero. Table 18.1 shows how the stock builds up over time. Note that after 100 years, the stock will reach a level of 4,337 units. (If this level of emissions
continued forever, the stock will eventually approach E/d = 100/.02 = 5,000 units.) Suppose that the stock of pollutant creates economic damage (in terms of health costs, reduced productivity, etc.) equal to $1 million per unit. Thus, if the total stock of pollutant were, say, 1000 units, the resulting economic damage for that year would be $1 billion. And suppose that the annual cost of reducing emissions is $15 million per unit of reduction. Thus, to reduce emissions from 100 units per year to zero would cost 100 * $15 million = $1.5 billion per year. Would it make sense, in this case, to reduce emissions to zero starting immediately? To answer this question, we must compare the present value of the annual cost of $1.5 billion with the present value of the annual benefit resulting from a reduced stock of pollutant. Of course, if emissions were reduced to zero starting immediately, the stock of pollutant would likewise be equal to zero over the entire 100 years. Thus, the benefit of the policy would be the savings of social 14To see this, note that after 1 year, the stock of pollutant is S1 year the stock is S2 = E + (1 - d)S2 S3 stock approaches E/d. = E, in the second = E + (1 - d)E, in the third year, the stock is = E + (1 - d)E + (1 - d)2E, and so on. As N becomes infinitely large, the = E + (1 - d)S1 CHAPTER 18 • Externalities and Public Goods 681 TABLE 18.1 BUILDUP IN THE STOCK OF POLLUTANT YEAR 2010 2011 2012 … 2110 … E 100 100 100 … 100 … 100 St 100 198 296 … 4,337 … 5,000 DAMAGE ($ BILLION) Cost of E 0 ($ BILLION) NET BENEFIT ($ BILLION) 0.100 0.198 0.296 … 4.337 … 5.000 1.5 1.5 1.5 … 1.5 … 1.5 - 1.400 - 1.302 - 1.204 … 2.837 … 3.500 cost associated with a growing stock of pollutant. Table 18.1 shows the annual cost of reducing emissions from 100 units to zero, the annual benefit from averting damage, and the annual net benefit (the annual benefit net of the
cost of eliminating emissions). As you would expect, the annual net benefit is negative in the early years because the stock of pollutant is low; the net benefit becomes positive only later, after the stock of pollutant has grown. To determine whether a policy of zero emissions makes sense, we must calculate the NPV of the policy, which in this case is the present discounted value of the annual net benefits shown in Table 18.1. Denoting the discount rate by R, the NPV is: NPV = (-1.5 +.1) + (-1.5 +.198) 1 + R + (-1.5 +.296) (1 + R)2 + c + (-1.5 + 4.337) (1 + R)99 Is this NPV positive or negative? The answer depends on the discount rate, R. Table 18.2 shows the NPV as a function of the discount rate. (The middle row of Table 18.2, in which the dissipation rate d is 2 percent, corresponds to Table 18.1. Table 18.2 also shows NPVs for dissipation rates of 1 percent and 4 percent.) For discount rates of 4 percent or less, the NPV is clearly positive, but if the discount rate is large, the NPV will be negative. Table 18.2 also shows how the NPV of a “zero emissions” policy depends on the dissipation rate, d. If d is lower, the accumulated stock of pollutant will reach higher levels and cause more economic damage, so the future benefits of reducing emissions will be greater. Note from Table 18.2 that for any given discount rate, the NPV Recall from §15.1 that the NPV of an investment declines as the discount rate becomes larger. Figure 15.3 shows the NPV for an electric motor factory; note the similarity to our environmental policy problem. TABLE 18.2 NPV OF “ZERO EMISSIONS” POLICY Discount Rate, R Dissipation Rate, D.01 108.81 65.93 15.48.01.02.04.02 54.07 31.20 3.26.04 12.20 4.49 - 5.70.06 - 0.03 - 3.25 - 7.82.08 - 4.08 - 5.69 - 8.11 Note: Entries in table are NPVs in $billions. Entries for d =.02 correspond to net benefit numbers
in Table 18.1. 682 PART 4 • Information, Market Failure, and the Role of Government • social rate of discount Opportunity cost to society as a whole of receiving an economic benefit in the future rather than the present. of eliminating emissions is much larger if d =.01 and much smaller if d =.04. As we will see, one of the reasons why there is so much concern over global warming is the fact that the stock of GHGs dissipates very slowly; d is only about.005. Formulating environmental policy in the presence of stock externalities therefore introduces an additional complicating factor: What discount rate should be used? Because the costs and benefits of a policy apply to society as a whole, the discount rate should likewise reflect the opportunity cost to society of receiving an economic benefit in the future rather than today. This opportunity cost, which should be used to calculate NPVs for government projects, is called the social rate of discount. But as we will see in Example 18.5, there is little agreement among economists as to the appropriate number to use for the social rate of discount. In principle, the social rate of discount depends on three factors: (1) the expected rate of real economic growth; (2) the extent of risk aversion for society as a whole; and (3) the “rate of pure time preference” for society as a whole. With rapid economic growth, future generations will have higher incomes than current generations, and if their marginal utility of income is decreasing (i.e., they are risk-averse), their utility from an extra dollar of income will be lower than the utility to someone living today; that’s why future benefits provide less utility and should thus be discounted. In addition, even if we expected no economic growth, people may simply prefer to receive a benefit today than in the future (the rate of pure time preference). Depending on one’s beliefs about future real economic growth, the extent of risk aversion for society as a whole, and the rate of pure time preference, one could conclude that the social rate of discount should be as high as 6 percent—or as low as 1 percent. And herein lies the difficulty. With a discount rate of 6 percent, it is hard to justify almost any government policy that imposes costs today but yields benefits only 50 or 100 years in the future (e.g., a policy to deal with global warming). Not so, however, if the discount rate is only 1 or 2 percent.15 Thus for
problems involving long time horizons, the policy debate often boils down to a debate over the correct discount rate. E XAM PLE 18.5 GLOBAL WARMING Emissions of carbon dioxide and other greenhouse gases have increased dramatically over the past century as economic growth has been accompanied by the greater use of fossil fuels, which has in turn led to an increase in atmospheric concentrations of GHGs. Even if worldwide GHG emissions were to be stabilized at current levels, atmospheric GHG concentrations would continue to grow throughout the next century. By trapping sunlight, these higher GHG concentrations are likely to cause a significant increase in global mean temperatures in 50 years or so and could have severe environmental consequences—flooding of low- lying areas as the polar ice caps melt and sea levels rise, more extreme weather patterns, disruption of ecosystems, and reduced agricultural output. GHG emissions could be reduced from their current levels—governments, for example, could impose stiff taxes on the use of gasoline and other fossil fuels—but this solution would be costly. The problem is that the costs of 15For example, with a discount rate of 6 percent, $100 received 100 years from now is worth only $0.29 today. With a discount rate of 1 percent, that same $100 is worth $36.97 today, i.e., 127 times as much. CHAPTER 18 • Externalities and Public Goods 683 reducing GHG emissions would occur today, but the benefits from reduced emissions would be realized only in some 50 or more years. Should the world’s industrialized countries agree to adopt policies to dramatically reduce GHG emissions, or is the present discounted value of the likely benefits of such policies simply too small? Many climate scientists and economists have studied the probable build-up of GHG concentrations and resulting increases in global temperatures if no steps are taken to reduce emissions. Although there is considerable uncertainty over the economic impact of higher temperatures, the consensus view is that the impact could be significant, so that there would be a future benefit from reducing emissions today.16 The cost of reducing emissions (or preventing them from growing above current levels) can be assessed as well, although here too there is uncertainty over the specific numbers. Table 18.3 shows GHG emissions and average global temperature change at ten-year intervals for two scenarios. The first is a “business as usual” scenario in which GHG emissions are projected to more than double over the next century so that the average GHG concentration rises considerably, and by 21
10 the average temperature is 4 degrees Celsius above its current level. The resulting damage each year from this temperature increase is estimated to be 1.3 percent of world GDP per degree Celsius of temperature increase. World GDP is in turn assumed to grow at 2.5 percent per year in real terms from its 2010 value of $65 trillion, reaching $768 trillion in 2110. Thus the annual damage from global warming reaches about (.01)(4)(768) = +40 trillion in 2110. The second scenario shown in Table 18.3 is one in which the GHG concentration is stabilized at 550 ppm so that the temperature increase is limited to only 2 degrees Celsius, which is reached in 2060. To achieve this, GHG emissions must be reduced by 1 percent per year starting in 2010. The annual cost of this emissions reduction policy is estimated to be TABLE 18.3 REDUCING GHG EMISSIONS “BUSINESS AS USUAL” EMISSIONS REDUCED BY 1% PER YEAR YEAR 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 2110 Et 50 55 62 73 85 90 95 100 105 110 115 St 430 460 490 520 550 580 610 640 670 700 730 Tt 0° 0.5° 1° 1.5° 2° 2.3° 2.7° 3° 3.3° 3.7° 4° DAMAGE 0 0.54 1.38 2.66 4.54 6.77 9.91 14.28 20.31 28.59 39.93 Et 50 45 41 37 33 30 27 25 22 20 18 St 430 460 485 510 530 550 550 550 550 550 550 Tt 0° 0.5° 1° 1.4° 1.8° 2° 2° 2° 2° 2° 2° DAMAGE COST NET BENEFIT 0 0.43 1.11 2.13 3.63 5.81 7.44 9.52 12.18 15.60 19.97 0.65 0.83 1.07 1.36 1.75 2.23 2.86 3.66 4.69 6.00 7.68 - 0.65 - 0.72 - 0.79 - 0.83 - 0.84 - 1.27 - 0.38 1.10 3.44 7.00 12.28 Notes: Et is measured in gigatonnes (billions of metric tons) of CO2 equivalent (CO2e), St is measured
in parts per million (ppm) of atmospheric CO2e, the change in temperature Tt is measured in degrees Celsius, and costs, damages, and net benefits are measured in trillions of 2007 dollars. Cost of reducing emissions is estimated to be 1% of GDP each year. World GDP is projected to grow at 2.5% in real terms from a level of $65 trillion in 2010. Damage from warming is estimated to be 1.3% of GDP per year for every 1°C of temperature increase. 16For a consensus view, see the 2007 Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press or online at http://www.ipcc.ch. 684 PART 4 • Information, Market Failure, and the Role of Government 1 percent of world GDP.17 (Because world GDP is assumed to increase each year, so too does the cost of this policy.) Also shown in the table is the annual net benefit from the policy, which equals the damage under the “business as usual” scenario minus the (smaller) damage when emissions are reduced minus the cost of reducing emissions. Does this emissions-reduction policy make sense? To answer that question, we must calculate the present value of the flow of net benefits, which depends critically on the discount rate. A review conducted in the United Kingdom recommends a social rate of discount of 1.3 percent. With that discount rate, the NPV of the policy is $21.3 trillion, which shows that the emissions-reduction policy is clearly economical. The NPV is smaller but still positive ($1.63 trillion) if we use a discount rate of 2 percent. But with a discount rate of 3 percent, the NPV is - +9.7 trillion; with a discount rate of 5 percent, the NPV is - +12.7 trillion. We have examined a particular policy—and a rather stringent one at that—to reduce GHG emissions. Whether that policy or any other policy to restrict GHG emissions makes economic sense clearly depends on the rate used to discount future costs and benefits. Be warned, however, that economists disagree about what rate to use, and as a result, they disagree about what should be done about global warming.18 • property rights Legal rules stating what people or firms may do with their property. 18.4 Externalities and Property Rights We have seen how government regulation can deal with the inefficiencies that arise from externalities. Emissions fees and transferable emissions permits work because they
change a firm’s incentives, forcing it to take into account the external costs that it imposes. But government regulation is not the only way to deal with externalities. In this section we show that in some circumstances, inefficiencies can be eliminated through private bargaining among the affected parties or by a legal system in which parties can sue to recover the damages they suffer. Property Rights Property rights are the legal rules that describe what people or firms may do with their property. If you have property rights to land, for example, you may build on it or sell it and are protected from interference by others. To see why property rights are important, let’s return to our example of the firm that dumps effluent into the river. We assumed both that it had a property right to use the river to dispose of its waste and that the fishermen did not have a property right to “effluent-free” water. As a result, the firm had no incentive to include the cost of effluent in its production calculations. In other words, the firm externalized the costs generated by the effluent. But suppose that the fishermen had a property right to clean water. In that case, they could demand that the firm pay them for the right to dump effluent. The firm would either cease production 17This policy is the one recommended by the Stern Review, commissioned by the U.K. Government, and available online at http://www.hm-treasury.gov.uk/stern_review_report.htm. The cost estimate of 1 percent of GDP is from the Stern Review, and is probably too optimistic. The estimate of the damage from higher temperatures (1.3 percent of GDP for each 1 degree Celsius increase) is an amalgam of estimates from the Stern Review and the IPCC Report. 18This disagreement over the discount rate and its crucial role in assessing policies to reduce GHG emissions is spelled out quite nicely in Martin Weitzman, “The Stern Review of the Economics of Climate Change,” Journal of Economic Literature (September 2007). Also, there are many uncertainties about the size of possible future temperature increases and their social and economic impact. Those uncertainties can have implications for policy but have been ignored in this example. See, for example, R. S. Pindyck, “Uncertainty in Environmental Economics,” Journal of Environmental Economics and Policy (Winter 2007), R.S. Pindyck, “Uncertain Outcomes and Climate Change Policy,
” Journal of Environmental Economics and Management, 2012. CHAPTER 18 • Externalities and Public Goods 685 TABLE 18.4 PROFITS UNDER ALTERNATIVE EMISSIONS CHOICES (DAILY) FACTORY’S PROFIT ($) FISHERMEN’S PROFIT ($) TOTAL PROFIT ($) No filter, no treatment plant Filter, no treatment plant No filter, treatment plant Filter, treatment plant 500 300 500 300 100 500 200 300 600 800 700 600 or pay the costs associated with the effluent. These costs would be internalized and an efficient allocation of resources achieved. Bargaining and Economic Efficiency Economic efficiency can be achieved without government intervention when the externality affects relatively few parties and when property rights are well specified. To see how, let’s consider a numerical version of our effluent example. Suppose the steel factory’s effluent reduces the fishermen’s profit. As Table 18.4 shows, the factory can install a filter system to reduce its effluent, or the fishermen can pay for the installation of a water treatment plant.19 The efficient solution maximizes the joint profit of the factory and the fishermen. Maximization occurs when the factory installs a filter and the fishermen do not build a treatment plant. Let’s see how alternative property rights lead these two parties to negotiate different solutions. Suppose the factory has the property right to dump effluent into the river. Initially, the fishermen’s profit is $100 and the factory’s $500. By installing a treatment plant, the fishermen can increase their profit to $200, whereby the joint profit, without cooperation, is $700 ($500 + $200). Moreover, the fishermen are willing to pay the factory up to $300 to install a filter—the difference between the $500 profit with a filter and the $200 profit without cooperation. Because the factory loses only $200 in profit by installing a filter, it will be willing to do so because it is more than compensated for its loss. In this case, the gain to both parties by cooperating is equal to $100: the $300 gain to the fishermen less the $200 cost of a filter. Suppose the factory and the fishermen agree to split this gain equally by having the fishermen pay the factory $250 to install the filter. As Table 18.5 shows, this bargaining solution achieves the efficient outcome. Under the column “Right to Dump,” we see that without cooperation, the fishermen earn a profit of
$200 and the factory $500. With cooperation, the profit of both increases by $50. Now suppose the fishermen are given the property right to clean water, which requires the factory to install the filter. The factory earns a profit of $300 and the fishermen $500. Because neither party can be made better off by bargaining, having the factory install the filter is efficient. This analysis applies to all situations in which property rights are well specified. When parties can bargain without cost and to their mutual advantage, the resulting outcome will be efficient, regardless of how the property rights are specified. The italicized proposition is called the Coase theorem, after Ronald Coase who did much to develop it.20 19For a more extensive discussion of a variant of this example, see Robert Cooter and Thomas Ulen, Law and Economics (Prentice Hall, 2012), ch. 4. 20Ronald Coase, “The Problem of Social Cost,” Journal of Law and Economics 3 (1960): 1–44. • Coase theorem Principle that when parties can bargain without cost and to their mutual advantage, the resulting outcome will be efficient regardless of how property rights are specified. 686 PART 4 • Information, Market Failure, and the Role of Government TABLE 18.5 RIGHTS BARGAINING WITH ALTERNATIVE PROPERTY NO COOPERATION RIGHT TO DUMP ($) RIGHT TO CLEAN WATER ($) Profit of factory Profit of fishermen COOPERATION Profit of factory Profit of fishermen 500 200 550 250 300 500 300 500 Costly Bargaining—The Role of Strategic Behavior Bargaining can be time-consuming and costly, especially when property rights are not clearly specified. In that case, neither party is sure how hard to bargain before the other party will agree to a settlement. In our example, both parties knew that the bargaining process had to settle on a payment between $200 and $300. If the parties are unsure of the property rights, however, the fishermen might be willing to pay only $100, and the bargaining process would break down. Bargaining can break down even when communication and monitoring are costless if both parties believe they can obtain larger gains. For example, one party might demand a large share and refuse to bargain, assuming incorrectly that the other party will eventually concede. Another problem arises when many parties are involved. Suppose, for example, that the emissions from a factory are adversely affecting hundreds or thousands of households who live downstream. In that case, the costs of bargaining will make it very difficult for the
parties to reach a settlement. A Legal Solution—Suing for Damages In many situations involving externalities, a party who is harmed (the victim) by another has the legal right to sue. If successful, the victim can recover monetary damages equal to the harm that it has suffered. A suit for damages is different from an emissions or effluent fee because the victim, not the government, is paid. To see how the potential for a lawsuit can lead to an efficient outcome, let’s reexamine our fishermen–factory example. Suppose first that the fishermen are given the right to clean water. The factory, in other words, is responsible for harm to the fishermen if it does not install a filter. The harm to the fishermen in this case is $400: the difference between the profit that the fishermen make when there is no effluent ($500) and their profit when there is effluent ($100). The factory has the following options: 1. Do not install filter, pay damages: 2. Install filter, avoid damages: Profit = $100 ($500 - $400) Profit = $300 ($500 - $200) The factory will find it advantageous to install a filter, which is substantially cheaper than paying damages, and the efficient outcome will be achieved. An efficient outcome (with a different division of profits) will also be achieved if the factory is given the property right to emit effluent. Under the law, the fishermen would have the legal right to require the factory to install the filter, but CHAPTER 18 • Externalities and Public Goods 687 EXAM PLE 18.6 THE COASE THEOREM AT WORK As a September 1987 cooperative agreement between New York City and New Jersey illustrates, the Coase theorem applies to governments as well as to people and organizations. For many years, garbage spilling from waterfront trash facilities along New York harbor had adversely affected the quality of water along the New Jersey shore and occasionally littered the beaches. One of the worst instances occurred in August 1987, when more than 200 tons of garbage formed a 50-milelong slick off the New Jersey shore. New Jersey had the right to clean beaches and could have sued New York City to recover damages associated with garbage spills. New Jersey could have also asked the court to grant an injunction requiring New York City to stop using its trash facilities until the problem was removed. But New Jersey wanted cleaner beaches, not simply the recovery of damages. And New York wanted to be able to operate its trash facility. Consequently, there was room for mutually
beneficial exchange. After two weeks of negotiations, New York and New Jersey reached a settlement. New Jersey agreed not to bring a lawsuit against the city. New York City agreed to use special boats and other flotation devices to contain spills that might originate from Staten Island and Brooklyn. It also agreed to form a monitoring team to survey all trash facilities and to shut down those failing to comply. At the same time, New Jersey officials were allowed unlimited access to New York City trash facilities to monitor the program’s effectiveness. they would have to pay the factory for its $200 lost profit (not for the cost of the filter). This leaves the fishermen with three options: 1. Put in a treatment plant: 2. Have factory put in a filter but pay damages: 3. Do not put in treatment plant or require a filter: Profit = $200 Profit = $300 ($500 - $200) Profit = $100 The fishermen earn the highest profit if they take the second option. They will thus require the factory to put in a filter but compensate it $200 for its lost profit. Just as in the situation in which the fishermen had the right to clean water, this outcome is efficient because the filter has been installed. Note, however, that the $300 profit is substantially less than the $500 profit that the fishermen get when they have a right to clean water. This example shows that a suit for damages eliminates the need for bargaining because it specifies the consequences of the parties’ choices. Giving the party that is harmed the right to recover damages from the injuring party ensures an efficient outcome. (When information is imperfect, however, suing for damages may lead to inefficient outcomes.) 18.5 Common Property Resources Occasionally externalities arise when resources can be used without payment. Common property resources are those to which anyone has free access. As a result, they are likely to be overutilized. Air and water are the two most common examples. Others include fish, animal populations, mineral exploration, and extraction. Let’s look at some of the inefficiencies that can occur when resources are common property rather than privately owned. • common property resource Resource to which anyone has free access. 688 PART 4 • Information, Market Failure, and the Role of Government Consider a large lake with trout to which an unlimited number of fishermen have access. Each fisherman fishes up to the point at which the marginal revenue from fishing (or the marginal value, if fishing is for sport instead of profit) is equal to the cost. But the lake is
a common property resource, and no fisherman has the incentive to take into account how his fishing affects the opportunities of others. As a result, the fisherman’s private cost understates the true cost to society because more fishing reduces the stock of fish, making less available for others. This leads to an inefficiency—too many fish are caught. Figure 18.11 illustrates this situation. Suppose that because the catch is sufficiently small relative to demand, fishermen take the price of fish as given. Suppose also that someone can control the number of fishermen with access to the lake. The efficient level of fish per month F* is determined at the point at which the marginal benefit from fish caught is equal to the marginal social cost. The marginal benefit is the price taken from the demand curve. The marginal social cost shown in the diagram includes not only the private operating costs but also the social cost of depleting the stock of fish. Now compare the efficient outcome with what happens when the lake is common property. In this case, the marginal external costs are not taken into account, and each fisherman fishes until there is no longer any profit to be made. When only F* fish are caught, the revenue from fishing is greater than the cost, and there is a profit to be earned by fishing more. Entry into the fishing business occurs until the point at which the price is equal to the marginal cost, point Fc in Figure 18.11. At Fc, however, too many fish will be caught. There is a relatively simple solution to the common property resource problem—let a single owner manage the resource. The owner will set a fee for use of the resource that is equal to the marginal cost of depleting the stock of fish. Facing the payment of this fee, fishermen in the aggregate will no longer find it profitable to catch more than F* fish. Unfortunately, most common property resources are vast and single ownership is not always practical. Over the past several decades, government oversight has provided a partial resolution to the problem. In many fishing areas in the United States, the government deter- Benefits, Costs (dollars per fish) Marginal Social Cost FIGURE 18.11 COMMON PROPERTY RESOURCES When a common property resource, such as a fishery, is accessible to all, the resource is used up to the point Fc at which the private cost is equal to the additional revenue generated. This usage exceeds the efficient level F * at which the marginal social cost of using the resource is equal to the
marginal benefit (as given by the demand curve). Private Cost Demand F* Fc Fish per month mines the annual total allowable catch and then allocates that catch to fishermen through individual fishing quotas determined through an auction or other allocative process.21 CHAPTER 18 • Externalities and Public Goods 689 EXAM PLE 18.7 CRAWFISH FISHING IN LOUISIANA In recent years, crawfish have become a popular restaurant item. In 1950, for example, the annual crawfish harvest in the Atchafalaya River basin in Louisiana was just over 1 million pounds. By 1995, it had grown to over 30 million pounds. Because most crawfish grow in ponds to which fishermen have unlimited access, a common property resource problem has arisen: Too many crawfish have been trapped, causing the crawfish population to fall far below the efficient level.22 How serious is the problem? Specifically, what is the social cost of unlimited access to fishermen? The answer can be found by estimating the private cost of trapping crawfish, the marginal social cost, and the demand for crawfish. Figure 18.12 shows portions of the relevant curves. Private cost is upward-sloping: As the catch increases, so does the additional effort that must be made to obtain it. The demand curve is downward sloping but elastic because other shellfish are close substitutes. We can find the efficient crawfish catch both graphically and algebraically. Let F represent the catch of crawfish in millions of pounds per year (shown on the horizontal axis), and let C represent cost in dollars per pound (shown on the vertical C Cost (dollars per pound) 2.10 0.325 Marginal Social Cost Private Cost Demand 9.2 11.9 F Crawfish catch (millions of pounds) FIGURE 18.12 CRAWFISH AS A COMMON PROPERTY RESOURCE Because crawfish are bred in ponds to which fishermen have unlimited access, they are a common property resource. The efficient level of fishing occurs when the marginal benefit is equal to the marginal social cost. However, the actual level of fishing occurs at the point at which the price for crawfish is equal to the private cost of fishing. The shaded area represents the social cost of the common property resource. 21For details, see the Environmental Defense Fund report, “Sustaining America’s Fisheries and Fishing Communities: An Evaluation of Incentive-Based Management,” authored by Lawrence J. White (2007). 22
This example is based on Frederick W. Bell, “Mitigating the Tragedy of the Commons,” Southern Economic Journal 52 (1986): 653–64. 690 PART 4 • Information, Market Failure, and the Role of Government axis). In the region where the various curves intersect, the three curves in the graph are as follows: Demand C = 0.401 - 0.0064F Marginal C = -5.645 + 0.6509F social cost Private cost: C = -0.357 + 0.0573F The efficient crawfish catch of 9.2 million pounds, which equates demand to marginal social cost, is shown as the intersection of the two curves. The actual catch, 11.9 million pounds, is determined by equating demand to private cost and is shown as the intersection of those two curves. The yellow-shaded triangle in the figure measures the social cost of free access. This figure represents the excess of social cost above the private benefit of fishing summed from the efficient level (where demand is equal to marginal social cost) to the actual level (where demand is equal to private cost). In this case, the social cost is approximated by the area of a triangle with a base of 2.7 million pounds (11.9 - 9.2) and a height of $1.775 (+2.10 - +0.325), or $2,396,000. Note that by regulating the ponds— limiting either access or the size of the catch—this social cost could be avoided. • public good Nonexclusive and nonrival good: The marginal cost of provision to an additional consumer is zero and people cannot be excluded from consuming it. • nonrival good Good for which the marginal cost of its provision to an additional consumer is zero. • nonexclusive good Good that people cannot be excluded from consuming, so that it is difficult or impossible to charge for its use. 18.6 Public Goods We have seen that externalities, including common-property resources, create market inefficiencies that sometimes warrant government regulation. When, if ever, should governments replace private firms as a producer of goods and services? In this section we describe a set of conditions under which the private market either may not provide a good at all or may not price it properly once it is available. NONRIVAL GOODS As we saw in Chapter 16, public goods have two characteristics: They are nonrival and nonexclusive. A good is nonrival if for any
given level of production, the marginal cost of providing it to an additional consumer is zero. For most goods that are provided privately, the marginal cost of producing more of the good is positive. But for some goods, additional consumers do not add to cost. Consider the use of a highway during a period of low traffic volume. Because the highway already exists and there is no congestion, the additional cost of driving on it is zero. Or consider the use of a lighthouse by a ship. Once the lighthouse is built and functioning, its use by an additional ship adds nothing to its running costs. Finally, consider public television. Clearly, the cost of one more viewer is zero. Most goods are rival in consumption. For example, when you buy furniture, you have ruled out the possibility that someone else can buy it. Goods that are rival must be allocated among individuals. Goods that are nonrival can be made available to everyone without affecting any individual’s opportunity for consuming them. NONEXCLUSIVE GOODS A good is nonexclusive if people cannot be excluded from consuming it. As a consequence, it is difficult or impossible to charge people for using nonexclusive goods; the goods can be enjoyed without direct payment. One example of a nonexclusive good is national defense. Once a nation has provided for its national defense, all citizens enjoy its benefits. A lighthouse and public television are also examples of nonexclusive goods. Nonexclusive goods need not be national in character. If a state or city eradicates an agricultural pest, all farmers and consumers benefit. It would be virtually impossible to exclude a particular farmer from the benefits of the program. Automobiles are exclusive (as well as rival). If a dealer sells a new car to one consumer, then the dealer has excluded other individuals from buying it. CHAPTER 18 • Externalities and Public Goods 691 Some goods are exclusive but nonrival. For example, in periods of low traffic, travel on a bridge is nonrival because an additional car on the bridge does not lower the speed of other cars. But bridge travel is exclusive because bridge authorities can keep people from using it. A television signal is another example. Once a signal is broadcast, the marginal cost of making the broadcast available to another user is zero; thus the good is nonrival. But broadcast signals can be made exclusive by scrambling the signals and charging for the codes that unscramble them. Some goods are nonexclusive but rival. An ocean or large lake is nonexclusive, but fishing is rival because it imposes costs on others: the
more fish caught, the fewer fish available to others. Air is nonexclusive and often nonrival; but it can be rival if the emissions of one firm adversely affect the quality of the air and the ability of others to enjoy it. Public goods, which are both nonrival and nonexclusive, provide benefits to people at zero marginal cost, and no one can be excluded from enjoying them. The classic example of a public good is national defense. Defense is nonexclusive, as we have seen, but it is also nonrival because the marginal cost of providing defense to an additional person is zero. The lighthouse is also a public good because it is nonrival and nonexclusive; in other words, it would be difficult to charge ships for the benefits they receive from it.23 The list of public goods is much smaller than the list of goods that governments provide. Many publicly provided goods are either rival in consumption, exclusive, or both. For example, high school education is rival in consumption. Because other children get less attention as class sizes increase, there is a positive marginal cost of providing education to one more child. Likewise, charging tuition can exclude some children from enjoying education. Public education is provided by local government because it entails positive externalities, not because it is a public good. Finally, consider the management of a national park. Part of the public can be excluded from using the park by raising entrance and camping fees. Use of the park is also rival: because of crowded conditions, the entrance of an additional car into a park can reduce the benefits that others receive from it. Efficiency and Public Goods The efficient level of provision of a private good is determined by comparing the marginal benefit of an additional unit to the marginal cost of producing it. Efficiency is achieved when the marginal benefit and the marginal cost are equal. The same principle applies to public goods, but the analysis is different. With private goods, the marginal benefit is measured by the benefit that the consumer receives. With a public good, we must ask how much each person values an additional unit of output. The marginal benefit is obtained by adding these values for all people who enjoy the good. To determine the efficient level of provision of a public good, we must then equate the sum of these marginal benefits to the marginal cost of production. Figure 18.13 illustrates the efficient level of producing a public good. D1 represents the demand for the public good by one consumer and D2 the demand by a second consumer. Each demand curve tells us the marginal benefit that the consumer gets from consuming every level
of output. For example, when there are 2 units of the public good, the first consumer is willing to pay $1.50 for the 23Lighthouses need not be provided by the government. See Ronald Coase, “The Lighthouse in Economics,” Journal of Law and Economics 17 (1974): 357–76, for a description of how lighthouses were privately funded in nineteenth-century England. 692 PART 4 • Information, Market Failure, and the Role of Government FIGURE 18.13 EFFICIENT PUBLIC GOOD PROVISION When a good is nonrival, the social marginal benefit of consumption, given by the demand curve D, is determined by vertically summing the individual demand curves for the good, D1 and D2. At the efficient level of output, the demand and the marginal cost curves intersect. Benefits (dollars) 7.00 5.50 4.00 1.50 D2 Marginal Cost D D1 In §4.3, we show that a market demand curve can be obtained by summing individual demand curves horizontally 10 Output good, and $1.50 is the marginal benefit. Similarly, the second consumer has a marginal benefit of $4.00. To calculate the sum of the marginal benefits to both people, we must add each of the demand curves vertically. For example, when the output is 2 units, we add the marginal benefit of $1.50 to the marginal benefit of $4.00 to obtain a marginal social benefit of $5.50. When this sum is calculated for every level of public output, we obtain the aggregate demand curve for the public good D. The efficient amount of output is the one at which the marginal benefit to society is equal to the marginal cost. This occurs at the intersection of the demand and the marginal cost curves. In our example, because the marginal cost of production is $5.50, 2 is the efficient output level. To see why 2 is efficient, note what happens if only 1 unit of output is provided: Although the marginal cost remains at $5.50, the marginal benefit is approximately $7.00. Because the marginal benefit is greater than the marginal cost, too little of the good has been provided. Similarly, suppose 3 units of the public good have been produced. Now the marginal benefit of approximately $4.00 is less than the marginal cost of $5.50; too much of the good has been provided. Only when the marginal social benefit is equal to the marginal cost is
the public good provided efficiently.24 Public Goods and Market Failure Suppose you want to offer a mosquito abatement program for your community. You know that the program is worth more to the community than the $50,000 it will cost. Can you make a profit by providing the program privately? You would break even if you assessed a $5.00 fee to each of the 10,000 households 24We have shown that nonexclusive, nonrival goods are inefficiently provided. A similar argument would apply to nonrival but exclusive goods. CHAPTER 18 • Externalities and Public Goods 693 in your community. But you cannot force them to pay the fee, let alone devise a system in which those households that value mosquito abatement most highly pay the highest fees. Unfortunately, mosquito abatement is nonexclusive: There is no way to provide the service without benefiting everyone. As a result, households have no incentive to pay what the program really is worth to them. People can act as free riders, who understate the value of the program so that they can enjoy the benefit of the good without paying for it. With public goods, the presence of free riders makes it difficult or impossible for markets to provide goods efficiently. Perhaps if few people were involved and the program were relatively inexpensive, all households might agree voluntarily to share costs. However, when many households are involved, voluntary private arrangements are usually ineffective. The public good must therefore be subsidized or provided by governments if it is to be produced efficiently. • free rider Consumer or producer who does not pay for a nonexclusive good in the expectation that others will. EXAM PLE 18.8 THE DEMAND FOR CLEAN AIR In Example 4.6 (page 134), we used the demand curve for clean air to calculate the benefits of a cleaner environment. Now let’s examine the public-good characteristics of clean air. Many factors, including the weather, driving patterns, and industrial emissions, determine a region’s air quality. Any effort to clean up the air will generally improve air quality throughout the region. As a result, clean air is nonexclusive: It is difficult to stop any one person from enjoying it. Clean air is also nonrival: My enjoyment does not inhibit yours. Because clean air is a public good, there is no market and no observable price at which people are willing to trade clean air for other commodities. Fortunately, we can infer people’s willingness to pay for clean air from the housing market—households will pay more for
a home located in an area with good air quality than for an otherwise identical home in an area with poor air quality. Let’s look at the estimates of the demand for clean air obtained from a statistical analysis of housing data for the Boston metropolitan area.25 The analysis correlates housing prices with the quality of air and other characteristics of the houses and their neighborhoods. Figure 18.14 shows three demand curves in which the value put on clean air depends on the level of nitrogen oxides and on income. The horizontal axis measures the level of air pollution in terms of parts per hundred million (pphm) of nitrogen oxide in the air. The vertical axis measures each household’s willingness to pay for a onepart-per-hundred-million reduction in the nitrogen oxide level. The demand curves are upwardsloping because we are measuring pollution rather than clean air on the horizontal axis. As we would expect, the cleaner the air, the lower the willingness to pay for more of the good. These differences in the willingness to pay for clean air vary substantially. In Boston, for example, nitrogen oxide levels ranged from 3 to 9 pphm. A middle-income household would be willing to pay $800 for a 1 pphm reduction in nitrogen oxide levels when the level is 3 pphm, but the figure would jump to $2200 for a 1 pphm reduction when the level is 9 pphm. Note that higher-income households are willing to pay more than lower-income households to obtain a small improvement in air quality. At low nitrogen oxide levels (3 pphm), the differential between low- and middle-income households is only $200, but it increases to about $700 at high levels (9 pphm). 25David Harrison, Jr., and Daniel L. Rubinfeld, “Hedonic Housing Prices and the Demand for Clean Air,” Journal of Environmental Economics and Management 5 (1978): 81–102. 694 PART 4 • Information, Market Failure, and the Role of Government FIGURE 18.14 THE DEMAND FOR CLEAN AIR The three curves describe the willingness to pay for clean air (a reduction in the level of nitrogen oxides) for each of three different households (low income, middle income, and high income). In general, higher-income households have greater demands for clean air than lower-income households. Moreover, each household is less willing to pay for clean air as the level of air quality increases. Willingness to Pay 3000 2500 2000
1500 1000 500 High Income Middle Income Low Income 10 Nitrogen oxide (pphm) With quantitative information about the demand for clean air and separate estimates of the costs of improving air quality, we can determine whether the benefits of environmental regulations outweigh the costs. A study by the National Academy of Sciences of regulations on automobile emissions did just this. The study found that controls would lower the level of pollutants, such as nitrogen oxides, by approximately 10 percent. The benefit of this 10-percent improvement to all residents of the United States was calculated to be approximately $2 billion. The study also estimated that it would cost somewhat less than $2 billion to install pollution control equipment in automobiles to meet emissions standards. The study concluded, therefore, that the benefits of the regulations did outweigh the costs. 18.7 Private Preferences for Public Goods Government production of a public good is advantageous because the government can assess taxes or fees to pay for it. But how can government determine how much of a public good to provide when the free rider problem gives people an incentive to misrepresent their preferences? In this section we discuss one mechanism for determining private preferences for government-produced goods. Voting is commonly used to decide allocation questions. For example, people vote directly on some local budget issues and elect legislators who vote on others. Many state and local referenda are based on majority-rule voting: Each person has one vote, and the candidate or the issue that receives more than 50 percent of the votes wins. Let’s see how majority-rule voting determines the provision of public education. Figure 18.15 describes the preferences for spending on education (on a per-pupil basis) of three citizens who are representative of three interest groups in the school district. CHAPTER 18 • Externalities and Public Goods 695 Willingness to pay AW W3 W2 W1 0 600 1200 1800 2400 Education spending per pupil (in dollars) FIGURE 18.15 DETERMINING THE LEVEL OF EDUCATIONAL SPENDING The efficient level of educational spending is determined by summing the willingness to pay for education (net of tax payments) of each of three citizens. Curves W1, W2, and W3 represent their willingness to pay, and curve AW represents the aggregate willingness to pay. The efficient level of spending is $1200 per pupil. The level of spending actually provided is the level demanded by the median voter. In this particular case, the median voter’s preference (given by the peak of the W2 curve) is also the efficient
level. Curve W1 gives the first citizen’s willingness to pay for education, minus any required tax payments. The willingness to pay for each spending level is the maximum amount of money the citizen will pay to enjoy that spending level rather than no spending at all.26 In general, the benefit from increased spending on education increases as spending increases. But the tax payments required to pay for that education increase as well. The willingness-to-pay curve, which represents the net benefit of educational spending, initially slopes upward because the citizen places great value on low spending levels. When spending increases beyond $600 per pupil, however, the value that the household puts on education increases at a diminishing rate. The net benefit, therefore, actually declines. Eventually, the spending level becomes so great (at $2400 per pupil) that the citizen is indifferent between this level of spending and no spending at all. Curve W2, which represents the second citizen’s willingness to pay (net of taxes) is similarly shaped but reaches its maximum at a spending level of $1200 per pupil. Finally, W3, the willingness to pay of the third citizen, peaks at $1800 per pupil. The dark line labeled AW represents the aggregate willingness to pay for education—the vertical summation of the W1, W2, and W3 curves. The AW curve measures the maximum amount that all three citizens are willing to pay to enjoy each spending level. As Figure 18.15 shows, the aggregate willingness to pay is maximized when $1200 per pupil is spent. Because the AW curve measures the benefit of spending net of the tax payments required to pay for that spending, the maximum point, $1200 per pupil, also represents the efficient level of spending. Will majority-rule voting achieve the efficient outcome in this case? Suppose the public must vote whether to spend $1200 or $600 per pupil. The first citizen will vote for $600, but the other two citizens will vote for $1200, which will then have been chosen by majority rule. In fact, $1200 per pupil will beat any other alternative in a majority-rule vote. Thus, $1200 represents the most preferred alternative of the median voter—the citizen with the median or middle preference. (The first citizen prefers $600 and the third $1800.) Under majority rule voting, the preferred spending level of the median voter will always win an election against any other alternative. 26In other words, the willingness to pay measures the consumer surplus that the citizen enjoys when a particular level of
spending is chosen. 696 PART 4 • Information, Market Failure, and the Role of Government But will the preference of the median voter be the efficient level of spending? In this case yes, because $1200 is efficient. But the preference of the median voter is often not the efficient spending level. Suppose the third citizen’s preferences were the same as the second’s. In that case, although the median voter’s choice would still be $1200 per pupil, the efficient level of spending would be less than $1200 (because the efficient level involves an average of the preferences of all three citizens). In this case, majority rule would lead to too much spending on education. If we reversed the example so that the first and second citizens’ preferences were identical, majority rule would generate too little educational spending. Thus, although majority-rule voting allows the preferences of the median voter to determine referenda outcomes, these outcomes need not be economically efficient. Majority rule is inefficient because it weighs each citizen’s preference equally: The efficient outcome weighs each citizen’s vote by his or her strength of preference. SUMMARY 1. An externality occurs when a producer or a consumer affects the production or consumption activities of others in a manner that is not directly reflected in the market. Externalities cause market inefficiencies because they inhibit the ability of market prices to convey accurate information about how much to produce and how much to buy. 2. Pollution is a common example of an externality that leads to market failure. It can be corrected by emissions standards, emissions fees, marketable emissions permits, or by encouraging recycling. When there is uncertainty about costs and benefits, any one of these mechanisms can be preferable, depending on the shapes of the marginal social cost and marginal benefit curves. 3. Sometimes it is the accumulated stock of a pollutant, rather than current level of emissions, that causes damage. An example of such stock externality is the buildup of greenhouse gases, which may lead to global warming. 4. Inefficiencies due to market failure may be eliminated through private bargaining among the affected parties. According to the Coase theorem, the bargaining solution will be efficient when property rights are clearly specified, when transactions costs are zero, and when there is no strategic behavior. But bargaining is unlikely to generate an efficient outcome because parties frequently behave strategically. 5. Common property resources are not controlled by a single person and can be used without a price being paid. As a result of free usage, an
externality is created in which current overuse of the resource harms those who might use it in the future. 6. Goods that private markets are not likely to produce efficiently are either nonrival or nonexclusive. A good is nonrival if for any given level of production, the marginal cost of providing it to an additional consumer is zero. A good is nonexclusive if it is expensive or impossible to exclude people from consuming it. Public goods are both nonrival and nonexclusive. 7. A public good is provided efficiently when the vertical sum of the individual demands for the good is equal to the marginal cost of producing it. 8. Majority-rule voting is one way for citizens to voice their preference for public goods. Under majority rule, the level of spending provided will be that preferred by the median voter. This level need not be the efficient outcome. QUESTIONS FOR REVIEW 1. Which of the following describes an externality and which does not? Explain the difference. a. A policy of restricted coffee exports in Brazil causes the U.S. price of coffee to rise—an increase which in turn also causes the price of tea to rise. b. An advertising blimp distracts a motorist who then hits a telephone pole. 2. Compare and contrast the following three mechanisms for treating pollution externalities when the costs and benefits of abatement are uncertain: (a) an emissions fee, (b) an emissions standard, and (c) a system of transferable emissions permits. 3. When do externalities require government intervention? When is such intervention unlikely to be necessary? CHAPTER 18 • Externalities and Public Goods 697 4. Consider a market in which a firm has monopoly power. Suppose in addition that the firm produces under the presence of either a positive or a negative externality. Does the externality necessarily lead to a greater misallocation of resources? 5. Externalities arise solely because individuals are unaware of the consequences of their actions. Do you agree or disagree? Explain. 6. To encourage an industry to produce at the socially optimal level, the government should impose a unit tax on output equal to the marginal cost of production. True or false? Explain. 7. George and Stan live next door to each other. George likes to plant flowers in his garden, but every time he does, Stan’s dog comes over and digs them up. Stan’s dog is causing the damage, so if economic efficiency is to be achieved, it is necessary that Stan pay to put
up a fence around his yard to confine the dog. Do you agree or disagree? Explain. 8. An emissions fee is paid to the government, whereas an injurer who is sued and held liable pays damages directly to the party harmed by an externality. What differences in the behavior of victims might you expect to arise under these two arrangements? EXERCISES 1. A number of firms have located in the western portion of a town after single-family residences took up the eastern portion. Each firm produces the same product and in the process emits noxious fumes that adversely affect the residents of the community. a. Why is there an externality created by the firms? b. Do you think that private bargaining can resolve the problem? Explain. c. How might the community determine the efficient level of air quality? 2. A computer programmer lobbies against copyrighting software, arguing that everyone should benefit from innovative programs written for personal computers and that exposure to a wide variety of computer programs will inspire young programmers to create even more innovative programs. Considering the marginal social benefits possibly gained by this proposal, do you agree with this position? 3. Assume that scientific studies provide you with the following information concerning the benefits and costs of sulfur dioxide emissions: Benefits of abating (reducing) emissions: MB = 500 - 20A Costs of abating emissions: MC = 200 + 5A where A is the quantity abated in millions of tons and the benefits and costs are given in dollars per ton. 9. Why does free access to a common property resource generate an inefficient outcome? 10. Public goods are both nonrival and nonexclusive. Explain each of these terms and show clearly how they differ from each other. 11. A village is located next to 1000 acres of prime grazing land. The village presently owns the land and allows all residents to graze cows freely. Some members of the village council have suggested that the land is being overgrazed. Is this likely to be true? These same members have also suggested that the village should either require grazers to purchase an annual permit or sell off the land to the grazers. Would either of these be a good idea? 12. Public television is funded in part by private donations, even though anyone with a television set can watch for free. Can you explain this phenomenon in light of the free rider problem? 13. Explain why the median voter outcome need not be efficient when majority-rule voting determines the level of public spending. 14. Would you consider Wikipedia a public
good? Does it provide any positive or negative externalities? a. What is the socially efficient level of emissions abatement? b. What are the marginal benefit and marginal cost of abatement at the socially efficient level of abatement? c. What happens to net social benefits (benefits minus costs) if you abate one million more tons than the efficient level? One million fewer? d. Why is it socially efficient to set marginal benefits equal to marginal costs rather than abating until total benefits equal total costs? 4. Four firms located at different points on a river dump various quantities of effluent into it. The effluent adversely affects the quality of swimming for homeowners who live downstream. These people can build swimming pools to avoid swimming in the river, and the firms can purchase filters that eliminate harmful chemicals dumped in the river. As a policy adviser for a regional planning organization, how would you compare and contrast the following options for dealing with the harmful effect of the effluent: a. An equal-rate effluent fee on firms located on the river. b. An equal standard per firm on the level of effluent that each can dump. c. A transferable effluent permit system in which the aggregate level of effluent is fixed and all firms receive identical permits. 698 PART 4 • Information, Market Failure, and the Role of Government 5. Medical research has shown the negative health effects of “secondhand” smoke. Recent social trends point to growing intolerance of smoking in public areas. If you are a smoker and you wish to continue smoking despite tougher anti-smoking laws, describe the effect of the following legislative proposals on your behavior. As a result of these programs, do you, the individual smoker, benefit? Does society benefit as a whole? a. A bill is proposed that would lower tar and nicotine levels in all cigarettes. b. A tax is levied on each pack of cigarettes. c. A tax is levied on each pack of cigarettes sold. d. Smokers would be required to carry government- issued smoking permits at all times. 6. The market for paper in a particular region in the United States is characterized by the following demand and supply curves: QD = 160,000 - 2000P and QS = 40,000 + 2000P where QD is the quantity demanded in 100-pound lots, QS is the quantity supplied in 100-pound lots, and P is the price per 100-pound lot. Currently there is no attempt to regulate the dumping of effluent into
streams and rivers by the paper mills. As a result, dumping is widespread. The marginal external cost (MEC) associated with the production of paper is given by the curve MEC = 0.0006QS. a. Calculate the output and price of paper if it is produced under competitive conditions and no attempt is made to monitor or regulate the dumping of effluent. b. Determine the socially efficient price and output of paper. c. Explain why the answers you calculated in parts (a) and (b) differ. 7. In a market for dry cleaning, the inverse market demand function is given by P = 100 - Q, and the (private) marginal cost of production for the aggregation of all dry-cleaning firms is given by MC = 10 + Q. Finally, the pollution generated by the dry cleaning process creates external damages given by the marginal external cost curve MEC = Q. a. Calculate the output and price of dry cleaning if it is produced under competitive conditions without regulation. b. Determine the socially efficient price and output of dry cleaning. c. Determine the tax that would result in a competitive market producing the socially efficient output. d. Calculate the output and price of dry cleaning if it is produced under monopolistic conditions without regulation. e. Determine the tax that would result in a monopolistic market producing the socially efficient output. f. Assuming that no attempt is made to monitor or regulate the pollution, which market structure yields higher social welfare? Discuss. 8. Refer back to Example 18.5 on global warming. Table 18.3 (page 683) shows the annual net benefits from a policy that reduces GHG emissions by 1 percent per year. At what discount rate is the NPV of this policy just equal to zero? 9. A beekeeper lives adjacent to an apple orchard. The orchard owner benefits from the bees because each hive pollinates about one acre of apple trees. The orchard owner pays nothing for this service, however, because the bees come to the orchard without his having to do anything. Because there are not enough bees to pollinate the entire orchard, the orchard owner must complete the pollination by artificial means, at a cost of $10 per acre of trees. Beekeeping has a marginal cost MC = 10 + 5Q, where Q is the number of beehives. Each hive yields $40 worth of honey. a. How many beehives will the beekeeper maintain? b. Is this the
economically efficient number of hives? c. What changes would lead to a more efficient operation? 10. There are three groups in a community. Their demand curves for public television in hours of programming, T, are given respectively by W1 W2 W3 = +200 - T = +240 - 2T = +320 - 2T Suppose public television is a pure public good that can be produced at a constant marginal cost of $200 per hour. a. What is the efficient number of hours of public tel- evision? b. How much public television would a competitive private market provide? 11. Reconsider the common resource problem given in Example 18.7. Suppose that crawfish popularity continues to increase, and that the demand curve shifts from C = 0.401 - 0.0064F to C = 0.50 - 0.0064F. How does this shift in demand affect the actual crawfish catch, the efficient catch, and the social cost of common access? (Hint: Use the marginal social cost and private cost curves given in the example.) 12. The Georges Bank, a highly productive fishing area off New England, can be divided into two zones in terms of fish population. Zone 1 has the higher population per square mile but is subject to severe diminishing returns to fishing effort. The daily fish catch (in tons) in Zone 1 is F1 = 200(X1) - 2(X1)2 CHAPTER 18 • Externalities and Public Goods 699 where X1 is the number of boats fishing there. Zone 2 has fewer fish per mile but is larger, and diminishing returns are less of a problem. Its daily fish catch is F2 = 100(X2) - (X2)2 where X2 is the number of boats fishing in Zone 2. The marginal fish catch MFC in each zone can be represented as MFC1 MFC2 = 200 - 4(X1) = 100 - 2(X2) There are 100 boats now licensed by the U.S. government to fish in these two zones. The fish are sold at $100 per ton. Total cost (capital and operating) per boat is constant at $1000 per day. Answer the following questions about this situation: a. If the boats are allowed to fish where they want, with no government restriction, how many will fish in each zone? What will be the gross value of the catch? b. If the U.S. government can restrict the number and distribution of
the boats, how many should be allocated to each zone? What will be the gross value of the catch? Assume the total number of boats remains at 100. c. If additional fishermen want to buy boats and join the fishing fleet, should a government wishing to maximize the net value of the catch grant them licenses? Why or why not? A P P E N D I X The Basics of Regression • multiple regression analysis Statistical procedure for quantifying economic relationships and testing hypotheses about them. • linear regression Model specifying a linear relationship between a dependent variable and several independent (or explanatory) variables and an error term. 700 This appendix explains the basics of multiple regression analysis, using an example to illustrate its application in economics.1 Multiple regression is a statistical procedure for quantifying economic relationships and testing hypotheses about them. In a linear regression, the relationships are of the following form: Y = b0 + b1X1 + b2X2 + g + bkXk + e (A.1) Equation (A.1) relates a dependent variable Y to several independent (or explanatory) variables, X1, X2,…For example, in an equation with two independent variables, Y might be the demand for a good, X1 its price, and X2 income. The equation also includes an error term e that represents the collective influence of any omitted variables that may also affect Y (for example, prices of other goods, the weather, unexplainable shifts in consumers’ tastes, etc.). Data are available for Y and the Xs, but the error term is assumed to be unobservable. Note that equation (A.1) must be linear in the parameters, but it need not be linear in the variables. For example, if equation (A.1) represented a demand function, Y might be the logarithm of quantity (log Q), X1 the logarithm of price (log P), and X2 the logarithm of income (log I): log Q = b0 + b1 log P + b2 log I + e (A.2) Our objective is to obtain estimates of the parameters b0, b1,…, bk that provide a “best fit” to the data. We explain how this is done below. An Example Suppose we wish to explain and then forecast quarterly automobile sales in the United States. Let’s start with a simplified case in which sales S (in billions of dollars
) is the dependent variable that will be explained. The only explanatory variable is the price of new automobiles P (measured by a new car price index scaled so that 1967 = 100). We could write this simple model as S = b0 + b1P + e (A.3) In equation (A.3), b0 and b1 are the parameters to be determined from the data, and e is the random error term. The parameter b0 is the intercept, while 1For a textbook treatment of applied econometrics, it’s hard to think of a better reference than R. S. Pindyck and D. L. Rubinfeld, Econometric Models and Economic Forecasts, 4th ed. (New York: McGraw-Hill, 1998). APPENDIX • The Basics of Regression 701 b1 is the slope: It measures the effect of a change in the new car price index on automobile sales. If there is no error term, the relationship between S and P would be a straight line that describes the systematic relationship between the two variables. However, because not all the actual observations fall on the line, the error term e is required to account for omitted factors. Estimation In order to choose values for the regression parameters, we need a criterion for a “best fit.” The criterion most often used is to minimize the sum of squared residuals between the actual values of Y and the fitted values for Y obtained after equation (A.1) has been estimated. This is called the least-squares criterion. If we denote n the estimated parameters (or coefficients) for the model in (A.1) by b k, then the fitted values for Y are given by n 1, c, b n 0 1X1 n + g + b kXk (A.4) Figure A.1 illustrates this for our example, in which there is a single independent variable. The data are shown as a scatter plot of points with sales on the vertical axis and price on the horizontal. The fitted regression line is drawn through the data points. The fitted value for sales associated with any particular n value for the price values Pi is given by S i For each data point, the regression residual is the difference between the actual and fitted value of the dependent variable. The residual, en i, associated with data point A in the figure, is given by en i. The parameter values are chosen so that when all the residuals are squared and then added
, the resulting sum is minimized. In this way, positive errors and negative errors are treated symmetrically; large errors are given a more-than- proportional weight. 1Pi (at point B). n = b 0 = Si n - S n + b i • least-squares criterion Criterion of “best fit” used to choose values for regression parameters, usually by minimizing the sum of squared residuals between the actual values of the dependent variable and the fitted values. Sales (S) (billions of dollars) 60 Si 50 Si 40 Residual (Si – Si) A B 100 Pi Si = b0 + b1Pi FIGURE A.1 LEAST SQUARES The regression line is chosen to minimize the sum of squared residuals. The residual associated with price Pi is given by line AB. 110 120 P Price index ( ) 702 APPENDIX • The Basics of Regression As we will see shortly, this criterion lets us do some simple statistical tests to help interpret the regression. As an example of estimation, let’s return to the two-variable model of auto sales given by equation (A.3). The result of fitting this equation using the leastsquares criterion is n = -25.5 + 0.57P S (A.5) In equation (A.5), the intercept -225.5 indicates that if the price index were zero, sales would be $ -225.5 billion. The slope parameter indicates that a 1-unit increase in the price index for new cars leads to a $0.57 billion increase in auto sales. This rather surprising result—an upward-sloping demand curve—is inconsistent with economic theory and should make us question the validity of our model. Let’s expand the model to consider the possible effects of two additional explanatory variables: personal income I (in billions of dollars) and the rate of interest R (the three-month Treasury bill rate). The estimated regression when there are three explanatory variables is n = 51.1 - 0.42P + 0.046I - 0.84R S (A.6) The importance of including all relevant variables in the model is suggested by the change in the regression results after the income and interest rate variables are added. Note that the coefficient of the P variable has changed substantially, from 0.57 to - 0.42. The coefficient - 0.42 measures the effect of an increase in price on sales, with the effect of interest rates and income
held constant. The negative price coefficient is consistent with a downward-sloping demand curve. Clearly, the failure to control for interest rates and income leads to the false conclusion that sales and price are positively related. The income coefficient, 0.046, tells us that for every $1 billion increase in personal income in the United States, automobile sales are likely to increase by $46 million (or $0.046 billion). The interest rate coefficient reflects the fact that for every one percentage point increase in the rate of interest, automobile sales are likely to fall by $840 million. Clearly, automobile sales are very sensitive to the cost of borrowing. Statistical Tests Our estimates of the true (but unknown) parameters are numbers that depend on the set of observations that we started with—that is, with our sample. With a different sample we would obtain different estimates.2 If we continue to collect more and more samples and generate additional estimates, the estimates of each parameter will follow a probability distribution. This distribution can be summarized by a mean and a measure of dispersion around that mean, a standard deviation that we refer to as the standard error of the coefficient. Least-squares has several desirable properties. First, it is unbiased. Intuitively, this means that if we could run our regression over and over again with different samples, the average of the many estimates that we obtained for each coefficient would equal the true parameter. Second, least-squares is consistent. In other words, if our sample were very large, we would obtain estimates that came very close to the true parameters. 2The least-squares formula that generates these estimates is called the least-squares estimator, and its values vary from sample to sample. • sample Set of observations for study, drawn from a larger universe. APPENDIX • The Basics of Regression 703 In econometric work, we often assume that the error term, and therefore the estimated parameters, are normally distributed. The normal distribution has the property that the area within 1.96 standard errors of its mean is equal to 95 percent of the total area. With this information, we can ask the following question: Can n we construct an interval around b such that there is a 95-percent probability that the true parameter lies within that interval? The answer is yes, and this 95-percent confidence interval is given by n n { 1.96 (standard error of b b ) (A.7) Thus, when working with an estimated regression equation, we must not only look
at the point estimates but also examine the standard errors of the coefficients to determine bounds for the true parameters.3 If a 95-percent confidence interval contains 0, then the true parameter b may actually be zero (even if our estimate is not). This result implies that the corresponding independent variable may not really affect the dependent variable, even if we thought it did. We can test the hypothesis that a true parameter is actually equal to 0 by looking at its t-statistic, which is defined as t = n b n Standard error of b (A.8) If the t-statistic is less than 1.96 in magnitude, the 95-percent confidence interval n around b must include 0. This means that we cannot reject the hypothesis that the true parameter b equals 0. We therefore say that our estimate, whatever it may be, is not statistically significant. Conversely, if the t-statistic is greater than 1.96 in absolute value, we reject the hypothesis that b = 0 and call our estimate statistically significant. Equation (A.9) shows the multiple regression for the auto sales model (equa- tion A.6) with a set of standard errors and t-statistics added: n = 51.1 S (9.4) t = 5.44 -0.42P +0.046I (0.006) (0.13) -3.23 7.67 -0.84R (0.32) -2.63 (A.9) The standard error of each estimated parameter is given in parentheses just below the estimate, and the corresponding t-statistics appear below that. Let’s begin by considering the price variable. The standard error of 0.13 is small relative to the coefficient - 0.42. In fact, we can be 95 percent certain that the true value of the price coefficient is on the interval given by - 0.42 plus or minus 1.96 standard deviations (i.e., - 0.42 plus or minus [1.96][0.13] = - 0.42 ± 0.25). This puts the true value of the coefficient between - 0.17 and - 0.67. Because this range does not include zero, the effect of price is both significantly different from zero and negative. We can also arrive at this result from the t-statistic. The t of - 3.23 reported in equation (A.9) for the price variable is equal to - 0.42 divided by
0.13. Because this t-statistic exceeds 1.96 in absolute value, we conclude that price is a significant determinant of auto sales. 3When there are fewer than 100 observations, we multiply the standard error by a number somewhat larger than 1.96. 704 APPENDIX • The Basics of Regression • standard error of the regression Estimate of the standard deviation of the regression error. • R-squared (R2) Percentage of the variation in the dependent variable that is accounted for by all the explanatory variables. Note that the income and interest rate variables are also significantly different from zero. The regression results tell us that an increase in income is likely to have a statistically significant positive effect on auto sales, whereas an increase in interest rates will have a statistically significant negative effect. Goodness of Fit Reported regression results usually contain information that tells us how closely the regression line fits the data. One statistic, the standard error of the regression (SER), is an estimate of the standard deviation of the regression error term e. Whenever all the data points lie on the regression line, the SER is zero. Other things being equal, the larger the standard error of the regression, the poorer the fit of the data to the regression line. To decide whether the SER is large or small, we compare it in magnitude with the mean of the dependent variable. This comparison provides a measure of the relative size of the SER, a more meaningful statistic than its absolute size. R-squared (R2), the percentage of the variation in the dependent variable that is accounted for by all the explanatory variables, measures the overall goodness-of-fit of the multiple regression equation.4 Its value ranges from 0 to 1. An R2 of 0 means that the independent variables explain none of the variation of the dependent variable; an R2 of 1 means that the independent variables explain the variation perfectly. The R2 for the sales equation (A.9) is 0.94. This tells us that the three independent variables explain 94 percent of the variation in sales. Note that a high R2 does not by itself mean that the variables actually included in the model are the appropriate ones. First, the R2 varies with the types of data being studied. Time series data with substantial upward growth usually generate much higher R2s than do cross-section data. Second, the underlying economic theory provides a vital check. If a regression of auto sales on the price of wheat happened to yield a high R2, we would question the model
’s reliability. Why? Because our theory tells us that changes in the price of wheat have little or no effect on automobile sales. The overall reliability of a regression result depends on the formulation of the model. When studying an estimated regression, we should consider things that might make the reported results suspicious. First, have variables that should appear in the relationship been omitted? That is, is the specification of the equation wrong? Second, is the functional form of the equation correct? For instance, should variables be in logarithms? Third, is there another relationship that relates one of the explanatory variables (say X) to the dependent variable Y? If so, X and Y are jointly determined, and we must deal with a two-equation model, not one with a single equation. Finally, does adding or removing one or two data points result in a major change in the estimated coefficients—i.e., is the equation robust? If not, we should be very careful not to overstate the importance or reliability of the results. Economic Forecasting A forecast is a prediction about the values of the dependent variable, given information about the explanatory variables. Often, we use regression models to generate ex ante forecasts, in which we predict values of the dependent 4The variation in Y is the sum of the squared deviations of Y from its mean. R2 and SER provide similar information about goodness of fit, because R2 = 1 - SER2/Variance (Y). APPENDIX • The Basics of Regression 705 variable beyond the time period over which the model has been estimated. If we know the values of the explanatory variables, the forecast is unconditional; if they must be predicted as well, the forecast is conditional on these predictions. Sometimes ex post forecasts, in which we predict what the value of the dependent variable would have been if the values of the independent variables had been different, can be useful. An ex post forecast has a forecast period such that all values of the dependent and explanatory variables are known. Thus ex post forecasts can be checked against existing data and provide a direct means of evaluating a model. For example, reconsider the auto sales regression discussed above. In gen- eral, the forecasted value for auto sales is given by 1P + b n 2I + b 3R + en (A.10) where en is our prediction for the error term. Without additional information, we usually take en to be zero. Then, to calculate the forecast, we use the estimated sales equation: n = 51
.1 - 0.42P + 0.046I - 0.84R S (A.11) We can use (A.11) to predict sales when, for example, P = 100, I = $1 trillion, and R = 8 percent. Then, n = 51.1 - 0.42(100) + 0.046(1000 billion) - 0.84(8) = $48.4 billion S Note that $48.4 billion is an ex post forecast for a time when P = 100, I = $1 trillion, and R = 8 percent. To determine the reliability of ex ante and ex post forecasts, we use the standard error of forecast (SEF). The SEF measures the standard deviation of the forecast error within a sample in which the explanatory variables are known with certainty. Two sources of error are implicit in the SEF. The first is the error term itself, because en may not equal 0 in the forecast period. The second source arises because the estimated parameters of the regression model may not be exactly equal to the true parameters. As an application, consider the SEF of $7.0 billion associated with equation (A.11). If the sample size is large enough, the probability is roughly 95 percent that the predicted sales will be within 1.96 standard errors of the forecasted value. In this case, the 95-percent confidence interval is $48.4 billion ± $14.0 billion, i.e., from $34.4 billion to $62.4 billion. Now suppose we wish to forecast automobile sales for some date in the future, such as 2007. To do so, the forecast must be conditional because we need to predict the values for the independent variables before calculating the forecast for automobile sales. Assume, for example, that our predictions of these variables n = 10 percent. Then, the forecast is are as follows: P n = 51.1 - 0.42(200) + 0.046(5000 billion) - 0.84(10) = $188.7 billion given by P. Here $188.7 billion is an ex ante conditional forecast. n = $5 trillion, and R n = 200, I Because we are predicting the future, and because the explanatory variables do not lie close to the means of the variables throughout our period of study, the SEF is equal to $8.2 billion, which is somewhat greater than the SEF that we calculated previously.5 The 95-percent
confidence interval associated with our forecast is the interval from $172.3 billion to $205.1 billion. 5For more on SEF, see Pindyck and Rubinfeld, Econometric Models and Economic Forecasts, ch. 8. 706 APPENDIX • The Basics of Regression EXAMPLE A.1 THE DEMAND FOR COAL Suppose we want to estimate the demand for bituminous coal (given by sales in tons per year, COAL) and then use the relationship to forecast future coal sales. We would expect the quantity demanded to depend on the price of coal (given by the Producer Price Index for coal, PCOAL) and on the price of a close substitute for coal (given by the Producer Price Index for natural gas, PGAS). Because coal is used to produce steel and electricity, we would also expect the level of steel production (given by the Federal Reserve Board Index of iron and steel production, FIS) and electricity production (given by the Federal Reserve Board Index of electric utility production, FEU) to be important demand determinants. Our model of coal demand is therefore given by the following equation: COAL = b0 + b1 PCOAL + b2 PGAS + b3 FIS + b4 FEU + e From our theory, we would expect b1 to be negative because the demand curve for coal is downward sloping. We would also expect b2 to be positive because a higher price of natural gas should lead industrial consumers of energy to substitute coal for natural gas. Finally, we would expect both b3 and b4 to be positive because the greater the production of steel and electricity, the greater the demand for coal. This model was estimated using monthly time-series data covering eight years. The results (with t-statistics in parentheses) are COAL = 12,262 + 92.34 FIS + 118.57 FEU - 48.90 PCOAL + 118.91 PGAS (3.51) (6.46) (7.14) ( -3.82) (3.18) R2 = 0.692 SER = 120,000 All the estimated coefficients have the signs that economic theory would predict. Each coefficient is also statistically significantly different from zero because the t-statistics are all greater than 1.96 in absolute value. The R2 of 0.692 says that the model explains more than two-thirds of the variation in coal sales. The standard error of the regression SER is
equal to 120,000 tons of coal. Because the mean level of coal production was 3.9 million tons, SER represents approximately 3 percent of the mean value of the dependent variable. This suggests a reasonably good model fit. Now suppose we want to use the estimated coal demand equation to forecast coal sales up to one year into the future. To do so, we substitute values for each of the explanatory variables for the 12-month forecasting period into the estimated equation. We also estimate the standard error of forecast (the estimate is 0.17 million tons) and use it to calculate 95-percent confidence intervals for the forecasted values of coal demand. Some representative forecasts and confidence intervals are given in Table A.1. APPENDIX • The Basics of Regression 707 TABLE A.1 FORECASTING COAL DEMAND 1-month forecast (tons) 6-month forecast (tons) 12-month forecast (tons) FORECAST 5.2 million 4.7 million 5.0 million CONFIDENCE INTERVAL 4.9–5.5 million 4.4–5.0 million 4.7–5.3 million SUMMARY 1. Multiple regression is a statistical procedure for quantifying economic relationships and testing hypotheses about them. 2. The linear regression model, which relates one dependent variable to one or more independent variables, is usually estimated by choosing the intercept and slope parameters that minimize the sum of the squared residuals between the actual and predicted values of the dependent variable. 3. In a multiple-regression model, each slope coefficient measures the effect on the dependent variable of a change in the corresponding independent variable, holding the effects of all other independent variables constant. 4. A t-test can be used to test the hypothesis that a par- ticular slope coefficient is different from zero. 5. The overall fit of the regression equation can be evaluated using the standard error of the regression (SER) (a value close to zero means a good fit) or R2 (a value close to one means a good fit). 6. Regression models can be used to forecast future values of the dependent variable. The standard error of forecast (SEF) measures the accuracy of the forecast. Glossary A absolute advantage (page 618) Situation in which Country 1 has an advantage over Country 2 in producing a good because the cost of producing the good in 1 is lower than the cost of producing it in 2. accounting cost (page 230) Actual expenses plus depre- ciation charges for capital
equipment. actual return (page 178) Return that an asset earns. actuarially fair (page 173) Characterizing a situation in which an insurance premium is equal to the expected payout. adverse selection (page 634) Form of market failure resulting when products of different qualities are sold at a single price because of asymmetric information, so that too much of the low-quality product and too little of the high-quality product are sold. advertising elasticity of demand (page 431) Percentage change in quantity demanded resulting from a 1-percent increase in advertising expenditures. advertising-to-sales ratio (page 431) Ratio of a firm’s advertising expenditures to its sales. agent (page 646) Individual employed by a principal to asymmetric information (page 632) Situation in which a buyer and a seller possess different information about a transaction. auction market (page 503) Market in which products are bought and sold through formal bidding processes. average expenditure curve (page 537) Supply curve representing the price per unit that a firm pays for a good. average expenditure (page 383) Price paid per unit of a good. average fixed cost (AFC) (page 237) Fixed cost divided by the level of output. average product (page 206) Output per unit of a par- ticular input. average total cost (ATC) (page 237) Firm’s total cost divided by its level of output. average variable cost (AVC) (page 237) Variable cost divided by the level of output. B bad (page 76) Good for which less is preferred rather achieve the principal’s objective. than more. amortization (page 235) Policy of treating a one-time expenditure as an annual cost spread out over some number of years. bandwagon effect (page 136) Positive network externality in which a consumer wishes to possess a good in part because others do. anchoring (page 194) Tendency to rely heavily on one prior (suggested) piece of information when making a decision. antitrust laws (page 390) Rules and regulations prohibiting actions that restrain, or are likely to restrain, competition. arbitrage (page 8) Practice of buying at a low price at one location and selling at a higher price in another. arc elasticity of demand (page 36) Price elasticity calcu- lated over a range of prices. asset (page 176) Something that provides a flow of money or services to its owner. asset beta (page 575) A
constant that measures the sensitivity of an asset’s return to market movements and, therefore, the asset’s nondiversifiable risk. barrier to entry (page 376) Condition that impedes entry by new competitors. Bertrand model (page 464) Oligopoly model in which firms produce a homogeneous good, each firm treats the price of its competitors as fixed, and all firms decide simultaneously what price to charge. bilateral monopoly (page 388) Market with only one seller and one buyer. block pricing (page 404) Practice of charging different prices for different quantities or “blocks” of a good. bond (page 564) Contract in which a borrower agrees to pay the bondholder (the lender) a stream of money. bubble (page 185) An increase in the price of a good based not on the fundamentals of demand or value, but instead on a belief that the price will keep going up. 708 budget constraints (page 82) Constraints that consum- ers face as a result of limited incomes. budget line (page 82) All combinations of goods for which the total amount of money spent is equal to income. bundling (page 419) Practice of selling two or more products as a package. C Capital Asset Pricing Model (CAPM) (page 575) Model in which the risk premium for a capital investment depends on the correlation of the investment’s return with the return on the entire stock market. cardinal utility function (page 80) Utility function describing by how much one market basket is preferred to another. cartel (page 452) Market in which some or all firms explicitly collude, coordinating prices and output levels to maximize joint profits. chain-weighted price index (page 104) Cost-of-living index that accounts for changes in quantities of goods and services. Coase theorem (page 685) Principle that when parties can bargain without cost and to their mutual advantage, the resulting outcome will be efficient regardless of how property rights are specified 276) Production function of the form q = AK, L where q is the rate of output, K is the quantity of capital, and L is the quantity of labor, and where A, a, and b are constants. f u n c t i o n Cobb-Douglas utility function (page 153) Utility function U(X,Y) = XaY1 - a, where X and Y are two goods and a is a constant. common property resource (page 687) Resource to which anyone
has free access. common-value auction (page 518) Auction in which the item has the same value to all bidders, but bidders do not know that value precisely and their estimates of it vary. company cost of capital (page 576) Weighted average of the expected return on a company’s stock and the interest rate that it pays for debt. comparative advantage (page 618) Situation in which Country 1 has an advantage over Country 2 in producing a good because the cost of producing the good in 1, relative to the cost of producing other goods in 1, is lower than the cost of producing the good in 2, relative to the cost of producing other goods in 2. complements (page 24) Two goods for which an increase in the price of one leads to a decrease in the quantity demanded of the other. GLOSSARY • 709 completely inelastic demand (page 34) Principle that consumers will buy a fixed quantity of a good regardless of its price. condominium (page 283) A housing unit that is individually owned but provides access to common facilities that are paid for and controlled jointly by an association of owners. constant returns to scale (page 223) Situation in which output doubles when all inputs are doubled. constant-cost industry (page 307) Industry whose long- run supply curve is horizontal. Consumer Price Index (page 12) Measure of the aggre- gate price level. consumer surplus (page 132) Difference between what a consumer is willing to pay for a good and the amount actually paid. contract curve (page 606) Curve showing all efficient allocations of goods between two consumers, or of two inputs between two production functions. cooperative (page 283) Association of businesses or people jointly owned and operated by members for mutual benefit. cooperative game (page 488) Game in which participants can negotiate binding contracts that allow them to plan joint strategies. corner solution (page 89) Situation in which the marginal rate of substitution of one good for another in a chosen market basket is not equal to the slope of the budget line. cost function (page 265) Function relating cost of production to level of output and other variables that the firm can control. cost-of-living index (page 100) Ratio of the present cost of a typical bundle of consumer goods and services compared with the cost during a base period. Cournot equilibrium (page 460) Equilibrium in the Cournot model, in which each firm correctly assumes how much its competitor will produce and sets its own production level accordingly.
Cournot model (page 458) Oligopoly model in which firms produce a homogeneous good, each firm treats the output of its competitors as fixed, and all firms decide simultaneously how much to produce. cross-price elasticity of demand (page 35) Percentage change in the quantity demanded of one good resulting from a 1-percent increase in the price of another. cyclical industries (page 41) Industries in which sales tend to magnify cyclical changes in gross domestic product and national income. 710 • GLOSSARY D deadweight loss (page 321) Net loss of total (consumer plus producer) surplus. decreasing returns to scale (page 223) Situation in which output less than doubles when all inputs are doubled. decreasing-cost industry (page 309) Industry whose long-run supply curve is downward sloping. degree of economies of scope (SC) (page 260) Percentage of cost savings resulting when two or more products are produced jointly rather than individually. demand curve (page 23) Relationship between the quantity of a good that consumers are willing to buy and the price of the good. derived demand (page 530) Demand for an input that depends on, and is derived from, both the firm’s level of output and the cost of inputs. deviation (page 162) Difference between expected pay- off and actual payoff. diminishing marginal utility (page 95) Principle that as more of a good is consumed, the consumption of additional amounts will yield smaller additions to utility. discount rate (page 569) Rate used to determine the value today of a dollar received in the future. diseconomies of scale (page 256) Situation in which a doubling of output requires more than a doubling of cost. diseconomies of scope (page 259) Situation in which joint output of a single firm is less than could be achieved by separate firms when each produces a single product. diversifiable risk (page 574) Risk that can be eliminated either by investing in many projects or by holding the stocks of many companies. diversification (page 170) Practice of reducing risk by allocating resources to a variety of activities whose outcomes are not closely related. dominant firm (page 476) Firm with a large share of total sales that sets price to maximize profits, taking into account the supply response of smaller firms. dominant strategy (page 490) Strategy that is optimal no matter what an opponent does. double marginalization (page 442) When each firm in a vertical chain marks up its price above its marginal cost, thereby increasing the price of
the final product. duality (page 154) Alternative way of looking at the consumer’s utility maximization decision: Rather than choosing the highest indifference curve, given a budget constraint, the consumer chooses the lowest budget line that touches a given indifference curve. duopoly (page 458) Market in which two firms compete with each other. Dutch auction (page 517) Auction in which a seller begins by offering an item at a relatively high price, then reduces it by fixed amounts until the item is sold. E economic cost (page 230) Cost to a firm of utilizing eco- nomic resources in production. economic efficiency (page 323) Maximization of aggre- gate consumer and producer surplus. economic rent (page 302) Amount that firms are willing to pay for an input less the minimum amount necessary to obtain it. economies of scale (page 256) Situation in which output can be doubled for less than a doubling of cost. economies of scope (page 259) Situation in which joint output of a single firm is greater than output that could be achieved by two different firms when each produces a single product. Edgeworth box (page 603) Diagram showing all possible allocations of either two goods between two people or of two inputs between two production processes. effective yield (or rate of return) (page 566) Percentage return that one receives by investing in a bond. efficiency wage (page 655) Wage that a firm will pay to an employee as an incentive not to shirk. efficiency wage theory (page 654) Explanation for the presence of unemployment and wage discrimination which recognizes that labor productivity may be affected by the wage rate. elasticity (page 33) Percentage change in one variable resulting from a 1-percent increase in another. emissions fee (page 668) Charge levied on each unit of a firm’s emissions. emissions standard (page 668) Legal limit on the amount of pollutants that a firm can emit. endowment effect (page 190) Tendency of individuals to value an item more when they own it than when they do not. Engel curve (page 116) Curve relating the quantity of a good consumed to income. English (or oral) auction (page 517) Auction in which a seller actively solicits progressively higher bids from a group of potential buyers. equal marginal principle (page 96) Principle that utility is maximized when the consumer has equalized the marginal utility per dollar of expenditure across all goods. equilibrium (or market-clearing) price (page 25) Price that
equates the quantity supplied to the quantity demanded. equilibrium in dominant strategies (page 491) Outcome of a game in which each firm is doing the best it can regardless of what its competitors are doing. excess demand (page 608) When the quantity demanded of a good exceeds the quantity supplied. excess supply (page 608) When the quantity supplied of a good exceeds the quantity demanded. exchange economy (page 602) Market in which two or more consumers trade two goods among themselves. expansion path (page 249) Curve passing through points of tangency between a firm’s isocost lines and its isoquants. expected return (page 178) Return that an asset should earn on average. expected utility (page 165) Sum of the utilities associated with all possible outcomes, weighted by the probability that each outcome will occur. expected value (page 161) Probability-weighted average of the payoffs associated with all possible outcomes. extensive form of a game (page 503) Representation of possible moves in a game in the form of a decision tree. extent of a market (page 9) Boundaries of a market, both geographical and in terms of range of products produced and sold within it. externality (pages 324, 662) Action by either a producer or a consumer which affects other producers or consumers, but is not accounted for in the market price. F factors of production (page 204) Inputs into the produc- tion process (e.g., labor, capital, and materials). first-degree price discrimination (page 401) Practice of GLOSSARY • 711 fixed-weight index (page 103) Cost-of-living index in which the quantities of goods and services remain unchanged. framing (page 191) Tendency to rely on the context in which a choice is described when making a decision. free entry (or exit) (page 280) Condition under which there are no special costs that make it difficult for a firm to enter (or exit) an industry. free rider (page 693) Consumer or producer who does not pay for a nonexclusive good in the expectation that others will. G game (page 488) Situation in which players (participants) make strategic decisions that take into account each other’s actions and responses. general equilibrium analysis (page 596) Simultaneous determination of the prices and quantities in all relevant markets, taking feedback effects into account. Giffen good (page 122) Good whose demand curve slopes upward because the (negative)
income effect is larger than the substitution effect. H Hicksian substitution effect (page 157) Alternative to the Slutsky equation for decomposing price changes without recourse to indifference curves. horizontal integration (pages 439, 651) Organizational form in which several plants produce the same or related products for a firm. human capital (page 580) Knowledge, skills, and experience that make an individual more productive and thereby able to earn a higher income over a lifetime. I ideal cost-of-living index (page 102) Cost of attaining a given level of utility at current prices relative to the cost of attaining the same utility at base-year prices. import quota (page 340) Limit on the quantity of a good charging each customer her reservation price. that can be imported. first-price auction (page 517) Auction in which the sales price is equal to the highest bid. fixed cost (FC) (page 233) Cost that does not vary with the level of output and that can be eliminated only by shutting down. fixed input (page 205) Production factor that cannot be varied. fixed-proportions production function (page 219) Production function with L-shaped isoquants, so that only one combination of labor and capital can be used to produce each level of output. income effect (page 121) Change in consumption of a good resulting from an increase in purchasing power, with relative prices held constant. income elasticity of demand (page 35) Percentage change in the quantity demanded resulting from a 1-percent increase in income. income-consumption curve (page 114) Curve tracing the utility-maximizing combinations of two goods as a consumer’s income changes. increasing returns to scale (page 223) Situation in which output more than doubles when all inputs are doubled. 712 • GLOSSARY increasing-cost industry (page 308) Industry whose long-run supply curve is upward sloping. indifference curve (page 71) Curve representing all combinations of market baskets that provide a consumer with the same level of satisfaction. indifference map (page 72) Graph containing a set of indifference curves showing the market baskets among which a consumer is indifferent. individual demand curve (page 113) Curve relating the quantity of a good that a single consumer will buy to its price. inferior good (page 121) A good that has a negative income effect. infinitely elastic demand (page 34) Principle that consumers will buy as much of a good as they can get at a single price, but for any higher price the quantity demanded
drops to zero, while for any lower price the quantity demanded increases without limit. informational cascade (page 189) An assessment (e.g., of an investment opportunity) based in part on the actions of others, which in turn were based on the actions of others. interest rate (page 561) Rate at which one can borrow or lend money. intertemporal price discrimination (page 410) Practice of separating consumers with different demand functions into different groups by charging different prices at different points in time. isocost line (page 245) Graph showing all possible combinations of labor and capital that can be purchased for a given total cost. isoelastic demand curve (page 127) Demand curve with a constant price elasticity. isoquant (page 216) Curve showing all possible combi- nations of inputs that yield the same output. isoquant map (page 217) Graph combining a number of isoquants, used to describe a production function. K kinked demand curve model (page 473) Oligopoly model in which each firm faces a demand curve kinked at the currently prevailing price: at higher prices demand is very elastic, whereas at lower prices it is inelastic. L labor productivity (page 214) Average product of labor for an entire industry or for the economy as a whole. Lagrangian (page 150) Function to be maximized or minimized, plus a variable (the Lagrange multiplier) multiplied by the constraint. Laspeyres price index (page 102) Amount of money at current year prices that an individual requires to purchase a bundle of goods and services chosen in a base year divided by the cost of purchasing the same bundle at base-year prices. law of diminishing marginal returns (page 209) Principle that as the use of an input increases with other inputs fixed, the resulting additions to output will eventually decrease. law of small numbers (page 195) Tendency to overstate the probability that a certain event will occur when faced with relatively little information. learning curve (page 261) Graph relating amount of inputs needed by a firm to produce each unit of output to its cumulative output. least-squares criterion (page 701) Criterion of “best fit” used to choose values for regression parameters, usually by minimizing the sum of squared residuals between the actual values of the dependent variable and the fitted values. Lerner Index of Monopoly Power (page 371) Measure of monopoly power calculated as excess of price over marginal cost as a fraction of price. linear demand
curve (page 34) Demand curve that is a straight line. linear regression (page 700) Model specifying a linear relationship between a dependent variable and several independent (or explanatory) variables and an error term. long run (page 205) Amount of time needed to make all production inputs variable. long-run average cost curve (LAC) (page 254) Curve relating average cost of production to output when all inputs, including capital, are variable. long-run competitive equilibrium (page 303) All firms in an industry are maximizing profit, no firm has an incentive to enter or exit, and price is such that quantity supplied equals quantity demanded. long-run marginal cost curve (LMC) (page 254) Curve showing the change in long-run total cost as output is increased incrementally by 1 unit. loss aversion (page 191) Tendency for individuals to prefer avoiding losses over acquiring gains. M macroeconomics (page 4) Branch of economics that deals with aggregate economic variables, such as the level and growth rate of national output, interest rates, unemployment, and inflation. marginal benefit (page 87) Benefit from the consump- tion of one additional unit of a good. GLOSSARY • 713 marginal cost (pages 87, 236) Cost of one additional unit of a good. marginal expenditure (page 383) Additional cost of buying one more unit of a good. marginal expenditure curve (page 537) Curve describing the additional cost of purchasing one additional unit of a good. marginal external benefit (page 664) Increased benefit that accrues to other parties as a firm increases output by one unit. market failure (page 324) Situation in which an unregulated competitive market is inefficient because prices fail to provide proper signals to consumers and producers. market mechanism (page 25) Tendency in a free market for price to change until the market clears. market power (page 358) Ability of a seller or buyer to affect the price of a good. market price (page 8) Price prevailing in a competitive market. marginal external cost (page 663) Increase in cost imposed externally as one or more firms increase output by one unit. market signaling (page 638) Process by which sellers send signals to buyers conveying information about product quality. marginal product (page 207) Additional output pro- maximin strategy (page 495) Strategy that maximizes duced as an input is increased by one unit. the minimum gain that can be earned. marginal rate of substitution (MRS) (page 74) Maximum amount of a

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