The Pearson Series in Economics - 8th Edition

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 mate- rial, 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 dis- posal permits to resolve this externality? Any of these policies can help in the- ory, 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 materi- als. 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 MSC (dollars) MCR 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.

CHAPTER 18 • Externalities and Public Goods 677 $ Sr SrЈ P PЈ Sv FIGURE 18.10 M1 M* S REFUNDABLE DEPOSITS SЈ The supply of virgin glass containers is given by Sv and the supply D of recycled glass by Sr. The market supply S is the horizontal sum of Amount of glass these two curves. Initially, equilibrium in the market for glass contain- ers 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. REFUNDABLE DEPOSITS One policy solution that has been used with some suc- cess 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 addi- tional 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 down- ward-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 sup- ply 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 refund- able 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 pri- vate 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 X A M P L E 1 8 . 4 REGULATING MUNICIPAL SOLID WASTES By 1990, the average resident The potential effectiveness of Los Angeles was generating of each of these three policies is about 6.4 pounds of solid waste illustrated by a study that focused per day, and residents of other on the mix between glass and large American cities were not plastic. Consumers were assumed far behind. By contrast, residents to have varying preferences, with of Tokyo, Paris, Hong Kong, and half preferring glass and half pre- Rome generated 3 pounds, 2.4 ferring plastic, for products that pounds, 1.9 pounds, and 1.5 are otherwise identical in price, pounds, respectively.13 Some of these differences quantity, and quality. Without any incentive to are due to variations in consumption levels, but most recycle, a 50–50 division between glass and plastic are due to the efforts that many other countries have would result. From a social perspective, however, made to encourage recycling. In the United States, greater use of recyclable glass would be preferred. only about 25 percent of aluminum, 23 percent of Mandatory separation fails as a policy in this paper, and 8.5 percent of glass scrap are recycled. case: The cost of separation is so high that the percentage of glass container materials purchased A number of policy proposals have been introduced actually falls to 40 percent. A curbside charge, how- to encourage recycling in the United States. The first is ever, does much better: It leads to a 72.5 percent the refundable deposit described above. A second is use of recyclable glass. Finally, a refundable deposit a curbside charge, in which communities charge indi- system does best, with 78.9 percent of consumers viduals a fee for refuse disposal that is proportional to purchasing recyclable glass containers. the weight (or the volume) of the refuse. To encour- A recent case in Perkasie, Pennsylvania, shows that age separation of recyclable materials, all separable recycling programs can indeed be effective. Prior to glass materials are collected for free. Curbside charges implementation of a program combining all three encourage recycling, but they fail to discourage con- economic incentives just described, the total amount sumption of products that might require recycling. of unseparated solid waste was 2573 tons per year. When the program was implemented, this amount A third alternative is to require the mandatory fell to 1038 tons—a 59-percent reduction. As a result, separation of recyclable materials such as glass. the town saved $90,000 per year in disposal costs. Random spot checks with substantial penalties for Recycling efforts have expanded in the past violations are required to make the system effec- decade. By 2009, 50.7 percent of aluminum, 74.2 tive. Mandatory separation is perhaps the least percent of office paper, and 31.1 percent of glass desirable of the three alternatives, not only because containers were recycled. In total, Americans it is difficult to implement, but also because indi- created 4.34 pounds of solid waste per person per viduals, if the cost of separation is sufficiently high, day. 1.46 pounds of that total was either recycled or may be encouraged to shift to alternative contain- composted. ers such as plastic, which are environmentally dam- aging and cannot readily be recycled. 18.3 Stock Externalities We have studied the negative externalities that result directly from flows of harm- ful 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. • stock externality Recall that we compared the marginal cost of reducing the flow of emissions to Accumulated result of action by the marginal benefit in order to determine the socially optimal level of emissions. a producer or consumer which, though not accounted for in Sometimes, however, the damage to society comes not directly from the emis- the market price, affects other sions flow, but rather from the accumulated stock of the pollutant. A good example producers or consumers. is global warming. Global warming is thought to result from the accumulation of carbon dioxide and other greenhouse gasses (GHGs) in the atmosphere. (As Recall from §15.1 that a the GHG concentration grows, more sunlight is absorbed into the atmosphere firm’s capital is measured as rather than being reflected away, causing an increase in average temperatures.) a stock, while the investment GHG emissions do not cause the kind of immediate harm that sulfur dioxide that creates the capital is a emissions cause. Rather, it is the stock of accumulated GHGs in the atmosphere that flow. The firm’s output is also ultimately causes harm. Furthermore, the dissipation rate for accumulated GHGs measured as a flow. is very low: Once the GHG concentration in the atmosphere has increased sub- stantially, it will remain high for many years, even if further GHG emissions Recall from §15.2 that the were reduced to zero. That is why there is concern about reducing GHG emis- present discounted value sions now rather than waiting for concentrations to build up (and temperatures (PDV) of a series of expected to start rising) fifty or more years from now. future cash flows is the sum of those cash flows Stock externalities (like flow externalities) can also be positive. An example discounted by the appropri- is the stock of “knowledge” that accumulates as a result of investments in R&D. ate interest rate. Moreover, Over time, R&D leads to new ideas, new products, more efficient production we observe in §15.4 that, techniques, and other innovations that benefit society as a whole, and not just according to the net pres- those who undertake the R&D. Because of this positive externality, there is a ent value (NPV) rule, a firm strong argument for the government to subsidize R&D. Keep in mind, however, should invest if the PDV of that it is the stock of knowledge and innovations that benefits society, and not the expected future cash the flow of R&D that creates the stock. flow from an investment is greater than the cost. 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 dis- tinction 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 emis- sions 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

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 gener- ated 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 con- tinued 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 emis- sions 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 start- ing 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 = E, in the second year the stock is S2 = E + (1 - d)S1 = E + (1 - d)E, in the third year, the stock is S3 = E + (1 - d)S2 = E + (1 - d)E + (1 - d)2E, and so on. As N becomes infinitely large, the stock approaches E/d.

CHAPTER 18 • Externalities and Public Goods 681 TABLE 18.1 BUILDUP IN THE STOCK OF POLLUTANT YEAR E St DAMAGE Cost of E ϭ 0 NET BENEFIT 100 ($ BILLION) ($ BILLION) ($ BILLION) 2010 100 198 2011 100 296 0.100 1.5 - 1.400 2012 100 … 0.198 1.5 - 1.302 … 4,337 0.296 1.5 - 1.204 … 100 … … 2110 … 5,000 … 1.5 … 100 4.337 … 2.837 … 1.5 ϱ … … 5.000 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 avert- ing 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) + (-1.5 + .296) +c+ (-1.5 + 4.337) 1+R (1 + R)2 (1 + R)99 Is this NPV positive or negative? The answer depends on the discount rate, R. Recall from §15.1 that Table 18.2 shows the NPV as a function of the discount rate. (The middle row of the NPV of an investment Table 18.2, in which the dissipation rate d is 2 percent, corresponds to Table 18.1. declines as the discount rate Table 18.2 also shows NPVs for dissipation rates of 1 percent and 4 percent.) For becomes larger. Figure 15.3 discount rates of 4 percent or less, the NPV is clearly positive, but if the discount shows the NPV for an elec- rate is large, the NPV will be negative. tric motor factory; note the similarity to our environmen- Table 18.2 also shows how the NPV of a “zero emissions” policy depends on the tal policy problem. 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 emis- sions will be greater. Note from Table 18.2 that for any given discount rate, the NPV TABLE 18.2 NPV OF “ZERO EMISSIONS” POLICY Discount Rate, R .01 .02 .04 .06 .08 Dissipation .01 108.81 54.07 12.20 - 0.03 - 4.08 Rate, D .02 65.93 31.20 4.49 - 3.25 - 5.69 .04 15.48 - 7.82 - 8.11 3.26 - 5.70 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 of eliminating emissions is much larger if d = .01 and much smaller if d = .04. As Opportunity cost to society as a we will see, one of the reasons why there is so much concern over global warming whole of receiving an economic is the fact that the stock of GHGs dissipates very slowly; d is only about .005. benefit in the future rather than the present. Formulating environmental policy in the presence of stock externalities there- fore 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 cur- rent 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 X A M P L E 1 8 . 5 GLOBAL WARMING Emissions of carbon dioxide and increase in global mean tem- other greenhouse gases have peratures in 50 years or so and increased dramatically over the could have severe environmental past century as economic growth consequences—flooding of low- has been accompanied by the lying areas as the polar ice greater use of fossil fuels, which caps melt and sea levels rise, has in turn led to an increase in more extreme weather pat- atmospheric concentrations of terns, disruption of ecosys- GHGs. Even if worldwide GHG tems, and reduced agricultural emissions were to be stabilized output. GHG emissions could be at current levels, atmospheric GHG concentra- reduced from their current levels—governments, tions would continue to grow throughout the next for example, could impose stiff taxes on the use century. By trapping sunlight, these higher GHG of gasoline and other fossil fuels—but this solution concentrations are likely to cause a significant 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 for two scenarios. The first is a “business as usual” the benefits from reduced emissions would be real- scenario in which GHG emissions are projected ized only in some 50 or more years. Should the to more than double over the next century so world’s industrialized countries agree to adopt poli- that the average GHG concentration rises con- cies to dramatically reduce GHG emissions, or is siderably, and by 2110 the average temperature the present discounted value of the likely benefits is 4 degrees Celsius above its current level. The of such policies simply too small? resulting damage each year from this temperature increase is estimated to be 1.3 percent of world Many climate scientists and economists have GDP per degree Celsius of temperature increase. studied the probable build-up of GHG concentra- World GDP is in turn assumed to grow at 2.5 per- tions and resulting increases in global temperatures cent per year in real terms from its 2010 value of if no steps are taken to reduce emissions. Although $65 trillion, reaching $768 trillion in 2110. Thus the there is considerable uncertainty over the economic annual damage from global warming reaches about impact of higher temperatures, the consensus view (.01)(4)(768) = +40 trillion in 2110. is that the impact could be significant, so that there would be a future benefit from reducing emissions The second scenario shown in Table 18.3 is one today.16 The cost of reducing emissions (or prevent- in which the GHG concentration is stabilized at 550 ing them from growing above current levels) can be ppm so that the temperature increase is limited to assessed as well, although here too there is uncer- only 2 degrees Celsius, which is reached in 2060. tainty over the specific numbers. To achieve this, GHG emissions must be reduced by 1 percent per year starting in 2010. The annual cost Table 18.3 shows GHG emissions and average of this emissions reduction policy is estimated to be global temperature change at ten-year intervals TABLE 18.3 REDUCING GHG EMISSIONS “BUSINESS AS USUAL” EMISSIONS REDUCED BY 1% PER YEAR YEAR Et St ⌬Tt DAMAGE Et St ⌬Tt DAMAGE COST NET BENEFIT 2010 50 430 0° 0 50 430 0° 0 0.65 - 0.65 2020 55 460 0.5° 0.54 45 2030 62 490 1° 1.38 41 460 0.5° 0.43 0.83 - 0.72 2040 73 520 1.5° 2.66 37 2050 85 550 2° 4.54 33 485 1° 1.11 1.07 - 0.79 2060 90 580 2.3° 6.77 30 2070 95 610 2.7° 9.91 27 510 1.4° 2.13 1.36 - 0.83 2080 100 640 3° 14.28 25 2090 105 670 3.3° 20.31 22 530 1.8° 3.63 1.75 - 0.84 2100 110 700 3.7° 28.59 20 2110 115 730 4° 39.93 18 550 2° 5.81 2.23 - 1.27 550 2° 7.44 2.86 - 0.38 550 2° 9.52 3.66 1.10 550 2° 12.18 4.69 3.44 550 2° 15.60 6.00 7.00 550 2° 19.97 7.68 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 reduc- ing 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 which shows that the emissions-reduction policy assumed to increase each year, so too does the cost is clearly economical. The NPV is smaller but still of this policy.) Also shown in the table is the annual positive ($1.63 trillion) if we use a discount rate of net benefit from the policy, which equals the dam- 2 percent. But with a discount rate of 3 percent, the age under the “business as usual” scenario minus NPV is - +9.7 trillion; with a discount rate of 5 per- the (smaller) damage when emissions are reduced cent, the NPV is - +12.7 trillion. minus the cost of reducing emissions. We have examined a particular policy—and a rather Does this emissions-reduction policy make stringent one at that—to reduce GHG emissions. sense? To answer that question, we must calculate Whether that policy or any other policy to restrict GHG the present value of the flow of net benefits, which emissions makes economic sense clearly depends on depends critically on the discount rate. A review the rate used to discount future costs and benefits. conducted in the United Kingdom recommends Be warned, however, that economists disagree about a social rate of discount of 1.3 percent. With that what rate to use, and as a result, they disagree about discount rate, the NPV of the policy is $21.3 trillion, what should be done about global warming.18 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 exter- nal 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, inefficien- cies 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 Legal rules Property Rights stating what people or firms may do with their property. 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 esti- mate 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 exam- ple, 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) No filter, no treatment plant FACTORY’S PROFIT FISHERMEN’S PROFIT TOTAL PROFIT Filter, no treatment plant ($) ($) ($) No filter, treatment plant Filter, treatment plant 500 100 600 300 500 800 500 200 700 300 300 600 or pay the costs associated with the effluent. These costs would be internalized and an efficient allocation of resources achieved. Bargaining and Economic Efficiency • Coase theorem Principle that when parties can bargain Economic efficiency can be achieved without government intervention when without cost and to their the externality affects relatively few parties and when property rights are well mutual advantage, the resulting specified. To see how, let’s consider a numerical version of our effluent example. outcome will be efficient Suppose the steel factory’s effluent reduces the fishermen’s profit. As Table 18.4 regardless of how property rights shows, the factory can install a filter system to reduce its effluent, or the fisher- are specified. men can pay for the installation of a water treatment plant.19 The efficient solution maximizes the joint profit of the factory and the fisher- men. 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 treat- ment 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 coop- erating 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 proposi- tion 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.

686 PART 4 • Information, Market Failure, and the Role of Government TABLE 18.5 BARGAINING WITH ALTERNATIVE PROPERTY RIGHTS NO COOPERATION RIGHT TO DUMP ($) RIGHT TO CLEAN WATER ($) Profit of factory 500 300 Profit of fishermen 200 500 COOPERATION Profit of factory 550 300 Profit of fishermen 250 500 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 will- ing 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 differ- ent 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 fac- tory has the following options: 1. Do not install filter, pay damages: Profit = $100 ($500 - $400) 2. Install filter, avoid damages: 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 fish- ermen would have the legal right to require the factory to install the filter, but

CHAPTER 18 • Externalities and Public Goods 687 E X A M P L E 1 8 . 6 THE COASE THEOREM AT WORK As a September 1987 cooperative agreement But New Jersey wanted cleaner beaches, not between New York City and New Jersey illustrates, simply the recovery of damages. And New York the Coase theorem applies to governments as well wanted to be able to operate its trash facility. as to people and organizations. Consequently, there was room for mutually ben- eficial exchange. After two weeks of negotia- For many years, garbage spilling from waterfront tions, New York and New Jersey reached a settle- trash facilities along New York harbor had adversely ment. New Jersey agreed not to bring a lawsuit affected the quality of water along the New Jersey against the city. New York City agreed to use shore and occasionally littered the beaches. One of special boats and other flotation devices to con- the worst instances occurred in August 1987, when tain spills that might originate from Staten Island more than 200 tons of garbage formed a 50-mile- and Brooklyn. It also agreed to form a monitoring long slick off the New Jersey shore. team to survey all trash facilities and to shut down those failing to comply. At the same time, New New Jersey had the right to clean beaches and Jersey officials were allowed unlimited access to could have sued New York City to recover damages New York City trash facilities to monitor the pro- associated with garbage spills. New Jersey could gram’s effectiveness. have also asked the court to grant an injunction requiring New York City to stop using its trash facili- ties until the problem was removed. 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: Profit = $200 2. Have factory put in a filter Profit = $300 ($500 - $200) but pay damages: 3. Do not put in treatment Profit = $100 plant or require a filter: 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 bargain- ing 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 Common property resources are those to which anyone has free access. As a resource Resource to which result, they are likely to be overutilized. Air and water are the two most com- anyone has free access. mon 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.

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 rev- enue 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 fisher- man has the incentive to take into account how his fishing affects the oppor- tunities 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 avail- able for others. This leads to an inefficiency—too many fish are caught. Figure 18.11 illustrates this situation. Suppose that because the catch is suf- ficiently 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 prob- lem—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, Marginal Social Cost Costs Private Cost (dollars per Demand fish) 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). F* Fc Fish per month

CHAPTER 18 • Externalities and Public Goods 689 mines the annual total allowable catch and then allocates that catch to fisher- men through individual fishing quotas determined through an auction or other allocative process.21 E X A M P L E 1 8 . 7 CRAWFISH FISHING IN LOUISIANA In recent years, crawfish have to fishermen? The answer can be found become a popular restaurant item. by estimating the private cost of trapping In 1950, for example, the annual crawfish, the marginal social cost, and crawfish harvest in the Atchafalaya the demand for crawfish. Figure 18.12 River basin in Louisiana was just shows portions of the relevant curves. over 1 million pounds. By 1995, Private cost is upward-sloping: As the it had grown to over 30 million catch increases, so does the additional pounds. Because most crawfish effort that must be made to obtain it. The grow in ponds to which fishermen demand curve is downward sloping but have unlimited access, a common elastic because other shellfish are close property resource problem has substitutes. arisen: Too many crawfish have been trapped, causing the craw- We can find the efficient crawfish fish population to fall far below catch both graphically and algebraically. the efficient level.22 Let F represent the catch of crawfish in millions of pounds per year (shown on How serious is the problem? the horizontal axis), and let C represent Specifically, what is the social cost of unlimited access cost in dollars per pound (shown on the vertical C Marginal FIGURE 18.12 Cost Social (dollars per Cost CRAWFISH AS A COMMON PROPERTY pound) RESOURCE 2.10 Private Cost Because crawfish are bred in ponds to which fishermen 0.325 have unlimited access, they are a common property resource. The efficient level of fishing occurs when the Demand 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. 9.2 11.9 F Crawfish catch (millions of pounds) 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). 22This 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 inter- equating demand to private cost and is shown as the sect, the three curves in the graph are as follows: intersection of those two curves. The yellow-shaded triangle in the figure measures the social cost of free Demand C = 0.401 - 0.0064F access. This figure represents the excess of social cost above the private benefit of fishing summed from the Marginal efficient level (where demand is equal to marginal social cost C = -5.645 + 0.6509F social cost) to the actual level (where demand is equal to private cost). In this case, the social cost is approxi- Private cost: C = -0.357 + 0.0573F mated by the area of a triangle with a base of 2.7 million pounds (11.9 - 9.2) and a height of $1.775 The efficient crawfish catch of 9.2 million pounds, (+2.10 - +0.325), or $2,396,000. Note that by regu- which equates demand to marginal social cost, is lating the ponds—limiting either access or the size of shown as the intersection of the two curves. The the catch—this social cost could be avoided. actual catch, 11.9 million pounds, is determined by 18.6 Public Goods We have seen that externalities, including common-property resources, create mar- ket 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. • public good Nonexclusive NONRIVAL GOODS As we saw in Chapter 16, public goods have two charac- and nonrival good: The marginal teristics: They are nonrival and nonexclusive. A good is nonrival if for any given cost of provision to an additional level of production, the marginal cost of providing it to an additional consumer consumer is zero and people is zero. For most goods that are provided privately, the marginal cost of pro- cannot be excluded from ducing more of the good is positive. But for some goods, additional consumers consuming it. do not add to cost. Consider the use of a highway during a period of low traf- fic volume. Because the highway already exists and there is no congestion, the • nonrival good Good for additional cost of driving on it is zero. Or consider the use of a lighthouse by a which the marginal cost of ship. Once the lighthouse is built and functioning, its use by an additional ship its provision to an additional adds nothing to its running costs. Finally, consider public television. Clearly, the consumer is zero. 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 good Good NONEXCLUSIVE GOODS A good is nonexclusive if people cannot be excluded that people cannot be excluded from consuming it. As a consequence, it is difficult or impossible to charge peo- from consuming, so that it is ple for using nonexclusive goods; the goods can be enjoyed without direct pay- difficult or impossible to charge ment. One example of a nonexclusive good is national defense. Once a nation for its use. 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 eradi- cates an agricultural pest, all farmers and consumers benefit. It would be virtu- ally 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 author- ities 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 nonexclu- sive, 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 nonexclu- sive, as we have seen, but it is also nonrival because the marginal cost of provid- ing 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 govern- ments 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 posi- tive 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 rep- resents 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 Benefits (dollars) FIGURE 18.13 7.00 Marginal Cost EFFICIENT PUBLIC GOOD PROVISION 5.50 D D2 When a good is nonrival, the social marginal benefit of consumption, given by the demand 4.00 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. 1.50 D1 0 1 2 3 4 5 6 7 8 9 10 Output In §4.3, we show that a good, and $1.50 is the marginal benefit. Similarly, the second consumer has a market demand curve can marginal benefit of $4.00. be obtained by summing individual demand curves To calculate the sum of the marginal benefits to both people, we must add horizontally. 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 • free rider Consumer or system in which those households that value mosquito abatement most highly producer who does not pay pay the highest fees. for a nonexclusive good in the expectation that others will. Unfortunately, mosquito abatement is nonexclusive: There is no way to pro- vide 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 volun- tarily 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. EXAMPLE 18.8 THE DEMAND FOR CLEAN AIR In Example 4.6 (page 134), we used the value put on clean air depends on the demand curve for clean air to calculate level of nitrogen oxides and on income. the benefits of a cleaner environment. The horizontal axis measures the level of Now let’s examine the public-good air pollution in terms of parts per hun- characteristics of clean air. Many fac- dred million (pphm) of nitrogen oxide in tors, including the weather, driving pat- the air. The vertical axis measures each terns, and industrial emissions, deter- household’s willingness to pay for a one- mine a region’s air quality. Any effort to part-per-hundred-million reduction in clean up the air will generally improve the nitrogen oxide level. air quality throughout the region. As a result, clean air is nonexclusive: It is The demand curves are upward- difficult to stop any one person from sloping because we are measuring enjoying it. Clean air is also nonrival: pollution rather than clean air on the My enjoyment does not inhibit yours. horizontal axis. As we would expect, the cleaner the air, the lower the willingness to pay for Because clean air is a public good, there is no more of the good. These differences in the willing- market and no observable price at which people ness to pay for clean air vary substantially. In Boston, are willing to trade clean air for other commodi- for example, nitrogen oxide levels ranged from 3 to ties. Fortunately, we can infer people’s willingness to 9 pphm. A middle-income household would be pay for clean air from the housing market—house- willing to pay $800 for a 1 pphm reduction in nitro- holds will pay more for a home located in an area gen oxide levels when the level is 3 pphm, but the with good air quality than for an otherwise identical figure would jump to $2200 for a 1 pphm reduction home in an area with poor air quality. when the level is 9 pphm. Note that higher-income households are willing to Let’s look at the estimates of the demand for clean pay more than lower-income households to obtain air obtained from a statistical analysis of housing data a small improvement in air quality. At low nitrogen for the Boston metropolitan area.25 The analysis cor- oxide levels (3 pphm), the differential between low- relates housing prices with the quality of air and other and middle-income households is only $200, but it characteristics of the houses and their neighborhoods. increases to about $700 at high levels (9 pphm). Figure 18.14 shows three demand curves in which the 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 Willingness High Income to Pay Middle Income THE DEMAND FOR CLEAN AIR 3000 Low Income The three curves describe the willing- 2500 ness to pay for clean air (a reduction in the level of nitrogen oxides) for each of 2000 three different households (low income, middle income, and high income). In 1500 general, higher-income households have greater demands for clean air than low- 1000 er-income households. Moreover, each household is less willing to pay for clean 500 air as the level of air quality increases. 0 1 2 3 4 5 6 7 8 9 10 Nitrogen oxide (pphm) With quantitative information about the demand percent. The benefit of this 10-percent improvement for clean air and separate estimates of the costs of to all residents of the United States was calculated to improving air quality, we can determine whether the be approximately $2 billion. The study also estimated benefits of environmental regulations outweigh the that it would cost somewhat less than $2 billion to costs. A study by the National Academy of Sciences of install pollution control equipment in automobiles regulations on automobile emissions did just this. The to meet emissions standards. The study concluded, study found that controls would lower the level of pol- therefore, that the benefits of the regulations did out- lutants, such as nitrogen oxides, by approximately 10 weigh the costs. 18.7 Private Preferences for Public Goods Government production of a public good is advantageous because the govern- ment 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 peo- ple 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 oth- ers. 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 AW FIGURE 18.15 to pay W1 W2 W3 DETERMINING THE LEVEL OF 0 600 1200 1800 2400 EDUCATIONAL SPENDING Education spending per pupil (in dollars) The efficient level of educational spending is de- termined 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 spend- ing 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 spend- ing 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 effi- cient 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 citi- zens). 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 economi- cally efficient. Majority rule is inefficient because it weighs each citizen’s pref- erence equally: The efficient outcome weighs each citizen’s vote by his or her strength of preference. SUMMARY clearly specified, when transactions costs are zero, and when there is no strategic behavior. But bargaining is 1. An externality occurs when a producer or a consumer unlikely to generate an efficient outcome because par- affects the production or consumption activities of oth- ties frequently behave strategically. ers in a manner that is not directly reflected in the mar- 5. Common property resources are not controlled by a ket. Externalities cause market inefficiencies because single person and can be used without a price being they inhibit the ability of market prices to convey accu- paid. As a result of free usage, an externality is created rate information about how much to produce and how in which current overuse of the resource harms those much to buy. who might use it in the future. 6. Goods that private markets are not likely to produce 2. Pollution is a common example of an externality that efficiently are either nonrival or nonexclusive. A good leads to market failure. It can be corrected by emis- is nonrival if for any given level of production, the sions standards, emissions fees, marketable emissions marginal cost of providing it to an additional con- permits, or by encouraging recycling. When there is sumer is zero. A good is nonexclusive if it is expensive uncertainty about costs and benefits, any one of these or impossible to exclude people from consuming it. mechanisms can be preferable, depending on the Public goods are both nonrival and nonexclusive. shapes of the marginal social cost and marginal benefit 7. A public good is provided efficiently when the vertical curves. sum of the individual demands for the good is equal to the marginal cost of producing it. 3. Sometimes it is the accumulated stock of a pollutant, 8. Majority-rule voting is one way for citizens to voice rather than current level of emissions, that causes their preference for public goods. Under majority rule, damage. An example of such stock externality is the the level of spending provided will be that preferred buildup of greenhouse gases, which may lead to global by the median voter. This level need not be the effi- warming. cient outcome. 4. Inefficiencies due to market failure may be eliminated through private bargaining among the affected par- ties. According to the Coase theorem, the bargaining solution will be efficient when property rights are QUESTIONS FOR REVIEW 2. Compare and contrast the following three mechanisms for treating pollution externalities when the costs and 1. Which of the following describes an externality and benefits of abatement are uncertain: (a) an emissions which does not? Explain the difference. fee, (b) an emissions standard, and (c) a system of a. A policy of restricted coffee exports in Brazil causes transferable emissions permits. the U.S. price of coffee to rise—an increase which in turn also causes the price of tea to rise. 3. When do externalities require government intervention? b. An advertising blimp distracts a motorist who then When is such intervention unlikely to be necessary? hits a telephone pole.

CHAPTER 18 • Externalities and Public Goods 697 4. Consider a market in which a firm has monopoly 9. Why does free access to a common property resource power. Suppose in addition that the firm produces generate an inefficient outcome? under the presence of either a positive or a negative externality. Does the externality necessarily lead to a 10. Public goods are both nonrival and nonexclusive. greater misallocation of resources? Explain each of these terms and show clearly how they differ from each other. 5. Externalities arise solely because individuals are unaware of the consequences of their actions. Do you 11. A village is located next to 1000 acres of prime grazing agree or disagree? Explain. land. The village presently owns the land and allows all residents to graze cows freely. Some members of 6. To encourage an industry to produce at the socially the village council have suggested that the land is optimal level, the government should impose a unit being overgrazed. Is this likely to be true? These same tax on output equal to the marginal cost of production. members have also suggested that the village should True or false? Explain. either require grazers to purchase an annual permit or sell off the land to the grazers. Would either of these 7. George and Stan live next door to each other. George be a good idea? likes to plant flowers in his garden, but every time he does, Stan’s dog comes over and digs them up. Stan’s 12. Public television is funded in part by private dona- dog is causing the damage, so if economic efficiency is tions, even though anyone with a television set can to be achieved, it is necessary that Stan pay to put up a watch for free. Can you explain this phenomenon in fence around his yard to confine the dog. Do you agree light of the free rider problem? or disagree? Explain. 13. Explain why the median voter outcome need not be 8. An emissions fee is paid to the government, whereas efficient when majority-rule voting determines the an injurer who is sued and held liable pays damages level of public spending. directly to the party harmed by an externality. What differences in the behavior of victims might you expect 14. Would you consider Wikipedia a public good? Does it to arise under these two arrangements? provide any positive or negative externalities? EXERCISES a. What is the socially efficient level of emissions abatement? 1. A number of firms have located in the western portion of a town after single-family residences took up the b. What are the marginal benefit and marginal cost eastern portion. Each firm produces the same product of abatement at the socially efficient level of abate- and in the process emits noxious fumes that adversely ment? affect the residents of the community. a. Why is there an externality created by the firms? c. What happens to net social benefits (benefits minus b. Do you think that private bargaining can resolve costs) if you abate one million more tons than the the problem? Explain. efficient level? One million fewer? c. How might the community determine the efficient level of air quality? d. Why is it socially efficient to set marginal benefits equal to marginal costs rather than abating until 2. A computer programmer lobbies against copyrighting total benefits equal total costs? software, arguing that everyone should benefit from innovative programs written for personal computers 4. Four firms located at different points on a river dump and that exposure to a wide variety of computer pro- various quantities of effluent into it. The effluent grams will inspire young programmers to create even adversely affects the quality of swimming for home- more innovative programs. Considering the marginal owners who live downstream. These people can build social benefits possibly gained by this proposal, do swimming pools to avoid swimming in the river, and you agree with this position? the firms can purchase filters that eliminate harmful chemicals dumped in the river. As a policy adviser 3. Assume that scientific studies provide you with the for a regional planning organization, how would you following information concerning the benefits and compare and contrast the following options for deal- costs of sulfur dioxide emissions: ing with the harmful effect of the effluent: a. An equal-rate effluent fee on firms located on the Benefits of abating (reduc- MB = 500 - 20A river. ing) emissions: MC = 200 + 5A b. An equal standard per firm on the level of effluent that each can dump. Costs of abating emissions: c. A transferable effluent permit system in which the aggregate level of effluent is fixed and all firms where A is the quantity abated in millions of tons and receive identical permits. the benefits and costs are given in dollars per ton.

698 PART 4 • Information, Market Failure, and the Role of Government 5. Medical research has shown the negative health effects f. Assuming that no attempt is made to monitor or of “secondhand” smoke. Recent social trends point regulate the pollution, which market structure to growing intolerance of smoking in public areas. If yields higher social welfare? Discuss. you are a smoker and you wish to continue smoking despite tougher anti-smoking laws, describe the effect 8. Refer back to Example 18.5 on global warming. of the following legislative proposals on your behav- Table 18.3 (page 683) shows the annual net benefits ior. As a result of these programs, do you, the individ- from a policy that reduces GHG emissions by 1 per- ual smoker, benefit? Does society benefit as a whole? cent per year. At what discount rate is the NPV of a. A bill is proposed that would lower tar and nicotine this policy just equal to zero? levels in all cigarettes. b. A tax is levied on each pack of cigarettes. 9. A beekeeper lives adjacent to an apple orchard. The c. A tax is levied on each pack of cigarettes sold. orchard owner benefits from the bees because each d. Smokers would be required to carry government- hive pollinates about one acre of apple trees. The issued smoking permits at all times. orchard owner pays nothing for this service, however, because the bees come to the orchard without his hav- 6. The market for paper in a particular region in the ing to do anything. Because there are not enough bees United States is characterized by the following to pollinate the entire orchard, the orchard owner must demand and supply curves: complete the pollination by artificial means, at a cost of $10 per acre of trees. QD = 160,000 - 2000P and QS = 40,000 + 2000P Beekeeping has a marginal cost MC = 10 + 5Q, where Q is the number of beehives. Each hive yields where QD is the quantity demanded in 100-pound $40 worth of honey. lots, QS is the quantity supplied in 100-pound lots, a. How many beehives will the beekeeper maintain? and P is the price per 100-pound lot. Currently there b. Is this the economically efficient number of hives? is no attempt to regulate the dumping of effluent into c. What changes would lead to a more efficient streams and rivers by the paper mills. As a result, operation? dumping is widespread. The marginal external cost (MEC) associated with the production of paper is 10. There are three groups in a community. Their demand given by the curve MEC = 0.0006QS. curves for public television in hours of programming, a. Calculate the output and price of paper if it is T, are given respectively by produced under competitive conditions and no W1 = +200 - T attempt is made to monitor or regulate the dump- ing of effluent. W2 = +240 - 2T b. Determine the socially efficient price and output of paper. W3 = +320 - 2T c. Explain why the answers you calculated in parts (a) and (b) differ. Suppose public television is a pure public good that 7. In a market for dry cleaning, the inverse market can be produced at a constant marginal cost of $200 demand function is given by P = 100 - Q, and the per hour. (private) marginal cost of production for the aggrega- a. What is the efficient number of hours of public tel- tion of all dry-cleaning firms is given by MC = 10 + Q. Finally, the pollution generated by the dry cleaning evision? process creates external damages given by the mar- b. How much public television would a competitive ginal external cost curve MEC = Q. a. Calculate the output and price of dry cleaning if it private market provide? is produced under competitive conditions without 11. Reconsider the common resource problem given in regulation. b. Determine the socially efficient price and output of Example 18.7. Suppose that crawfish popularity con- dry cleaning. tinues to increase, and that the demand curve shifts c. Determine the tax that would result in a competi- from C = 0.401 - 0.0064F to C = 0.50 - 0.0064F. tive market producing the socially efficient output. How does this shift in demand affect the actual craw- d. Calculate the output and price of dry cleaning if it fish catch, the efficient catch, and the social cost of is produced under monopolistic conditions without common access? (Hint: Use the marginal social cost regulation. and private cost curves given in the example.) e. Determine the tax that would result in a monopolis- 12. The Georges Bank, a highly productive fishing area off tic market producing the socially efficient output. 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 $100 per ton. Total cost (capital and operating) per has fewer fish per mile but is larger, and diminishing boat is constant at $1000 per day. Answer the follow- returns are less of a problem. Its daily fish catch is ing questions about this situation: a. If the boats are allowed to fish where they want, F2 = 100(X2) - (X2)2 with no government restriction, how many will where X2 is the number of boats fishing in Zone 2. The fish in each zone? What will be the gross value of marginal fish catch MFC in each zone can be repre- the catch? sented as b. If the U.S. government can restrict the number and distribution of the boats, how many should be allo- MFC1 = 200 - 4(X1) cated to each zone? What will be the gross value MFC2 = 100 - 2(X2) of the catch? Assume the total number of boats remains at 100. There are 100 boats now licensed by the U.S. govern- c. If additional fishermen want to buy boats and join ment to fish in these two zones. The fish are sold at the fishing fleet, should a government wishing to maximize the net value of the catch grant them licenses? Why or why not?

APPENDIX The Basics of Regression • multiple regression analysis This appendix explains the basics of multiple regression analysis, using an Statistical procedure for example to illustrate its application in economics.1 Multiple regression is a quantifying economic statistical procedure for quantifying economic relationships and testing hypoth- relationships and testing eses about them. hypotheses about them. In a linear regression, the relationships are of the following form: • linear regression Model specifying a linear relationship Y = b0 + b1X1 + b2X2 + g + bkXk + e (A.1) between a dependent variable and several independent (or Equation (A.1) relates a dependent variable Y to several independent (or explan- explanatory) variables and an atory) variables, X1, X2,…For example, in an equation with two independent error term. 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). 700

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 • least-squares criterion “best fit.” The criterion most often used is to minimize the sum of squared residuals Criterion of “best fit” used to between the actual values of Y and the fitted values for Y obtained after equation choose values for regression (A.1) has been estimated. This is called the least-squares criterion. If we denote parameters, usually by the estimated parameters (or coefficients) for the model in (A.1) by nb0, nb1, c, bnk, minimizing the sum of squared then the fitted values for Y are given by residuals between the actual values of the dependent variable Yn = nb0 + nb1X1 + g + nbkXk (A.4) and the fitted values. Figure A.1 illustrates this for our example, in which there is a single inde- pendent 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 value for the price values Pi is given by Sni = nb0 + nb1Pi (at point B). For each data point, the regression residual is the difference between the actual and fitted value of the dependent variable. -ThSnei.rTehsiedpuaarl,anemi,eatsesrovcaialuteeds with data point A in the figure, is given by nei = Si 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. Sales (S) Residual (Si – Si) Si = b0 + b1Pi FIGURE A.1 (billions A of dollars) LEAST SQUARES B 60 The regression line is chosen to minimize the Si sum of squared residuals. The residual associ- ated with price Pi is given by line AB. 50 Si 40 100 110 120 Pi Price index ( P)

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 least- squares criterion is Sn = -25.5 + 0.57P (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 Sn = 51.1 - 0.42P + 0.046I - 0.84R (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 vari- ables are added. Note that the coefficient of the P variable has changed sub- stantially, 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. • sample Set of observations Statistical Tests for study, drawn from a larger universe. 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 sum- marized 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 dif- ferent 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.

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 we construct an interval around nb 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 nb { 1.96 (standard error of nb) (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 coeffi- cients 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 cor- responding 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= nb (A.8) Standard error ofnb If the t-statistic is less than 1.96 in magnitude, the 95-percent confidence interval around nb 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: Sn = 51.1 - 0.42P + 0.046I - 0.84R (A.9) (9.4) (0.13) (0.006) (0.32) - 3.23 7.67 - 2.63 t = 5.44 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 some- what larger than 1.96.

704 APPENDIX • The Basics of Regression Note that the income and interest rate variables are also significantly differ- ent 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 • standard error of the Reported regression results usually contain information that tells us how closely the regression Estimate of regression line fits the data. One statistic, the standard error of the regression (SER), the standard deviation of the is an estimate of the standard deviation of the regression error term e. Whenever all regression error. 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 • R-squared (R2) Percentage regression line. To decide whether the SER is large or small, we compare it in mag- of the variation in the dependent nitude with the mean of the dependent variable. This comparison provides a mea- variable that is accounted for by sure of the relative size of the SER, a more meaningful statistic than its absolute size. all the explanatory variables. 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 depen- dent 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 Sn = nb0 + nb1P + nb2I + nb3R + ne (A.10) where ne is our prediction for the error term. Without additional information, we usually take ne to be zero. Then, to calculate the forecast, we use the estimated sales equation: Sn = 51.1 - 0.42P + 0.046I - 0.84R (A.11) We can use (A.11) to predict sales when, for example, P = 100, I = $1 trillion, and R = 8 percent. Then, Sn = 51.1 - 0.42(100) + 0.046(1000 billion) - 0.84(8) = $48.4 billion 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 cer- tainty. Two sources of error are implicit in the SEF. The first is the error term itself, because ne 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 bil- lion, 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 pre- dict the values for the independent variables before calculating the forecast for automobile sales. Assume, for example, that our predictions of these variables are as follows: Pn = 200, In = $5 trillion, and Rn = 10 percent. Then, the forecast is given by Pn = 51.1 - 0.42(200) + 0.046(5000 billion) - 0.84(10) = $188.7 billion . Here $188.7 billion is an ex ante conditional forecast. 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 elec- tricity, 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 produc- tion 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 forecast- ing period into the estimated equation. We also estimate the standard error of forecast (the estimate is 0.17 million tons) and use it to calcu- late 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) FORECAST CONFIDENCE INTERVAL 6-month forecast (tons) 12-month forecast (tons) 5.2 million 4.9–5.5 million 4.7 million 4.4–5.0 million 5.0 million 4.7–5.3 million SUMMARY holding the effects of all other independent variables constant. 1. Multiple regression is a statistical procedure for quan- 4. A t-test can be used to test the hypothesis that a par- tifying economic relationships and testing hypotheses ticular slope coefficient is different from zero. about them. 5. The overall fit of the regression equation can be evalu- ated using the standard error of the regression (SER) 2. The linear regression model, which relates one depen- (a value close to zero means a good fit) or R2 (a value dent variable to one or more independent variables, is close to one means a good fit). usually estimated by choosing the intercept and slope 6. Regression models can be used to forecast future parameters that minimize the sum of the squared values of the dependent variable. The standard residuals between the actual and predicted values of error of forecast (SEF) measures the accuracy of the the dependent variable. forecast. 3. In a multiple-regression model, each slope coefficient measures the effect on the dependent variable of a change in the corresponding independent variable,

Glossary A asymmetric information (page 632) Situation in which a buyer and a seller possess different information absolute advantage (page 618) Situation in which about a transaction. Country 1 has an advantage over Country 2 in pro- ducing a good because the cost of producing the auction market (page 503) Market in which prod- good in 1 is lower than the cost of producing it in 2. ucts are bought and sold through formal bidding processes. accounting cost (page 230) Actual expenses plus depre- ciation charges for capital equipment. average expenditure curve (page 537) Supply curve representing the price per unit that a firm pays for actual return (page 178) Return that an asset earns. a good. actuarially fair (page 173) Characterizing a situation in average expenditure (page 383) Price paid per unit of which an insurance premium is equal to the expected a good. payout. average fixed cost (AFC) (page 237) Fixed cost divided adverse selection (page 634) Form of market failure by the level of output. resulting when products of different qualities are sold at a single price because of asymmetric information, average product (page 206) Output per unit of a par- so that too much of the low-quality product and too ticular input. little of the high-quality product are sold. average total cost (ATC) (page 237) Firm’s total cost advertising elasticity of demand (page 431) Percentage divided by its level of output. change in quantity demanded resulting from a 1-percent increase in advertising expenditures. average variable cost (AVC) (page 237) Variable cost divided by the level of output. advertising-to-sales ratio (page 431) Ratio of a firm’s advertising expenditures to its sales. B agent (page 646) Individual employed by a principal to 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 bandwagon effect (page 136) Positive network exter- expenditure as an annual cost spread out over some nality in which a consumer wishes to possess a good number of years. in part because others do. anchoring (page 194) Tendency to rely heavily on one barrier to entry (page 376) Condition that impedes prior (suggested) piece of information when making entry by new competitors. a decision. Bertrand model (page 464) Oligopoly model in which antitrust laws (page 390) Rules and regulations prohib- firms produce a homogeneous good, each firm treats iting actions that restrain, or are likely to restrain, the price of its competitors as fixed, and all firms competition. decide simultaneously what price to charge. arbitrage (page 8) Practice of buying at a low price at bilateral monopoly (page 388) Market with only one one location and selling at a higher price in another. seller and one buyer. arc elasticity of demand (page 36) Price elasticity calcu- block pricing (page 404) Practice of charging different lated over a range of prices. prices for different quantities or “blocks” of a good. asset (page 176) Something that provides a flow of bond (page 564) Contract in which a borrower agrees to money or services to its owner. pay the bondholder (the lender) a stream of money. asset beta (page 575) A constant that measures the sen- bubble (page 185) An increase in the price of a good based sitivity of an asset’s return to market movements not on the fundamentals of demand or value, but and, therefore, the asset’s nondiversifiable risk. instead on a belief that the price will keep going up. 708

budget constraints (page 82) Constraints that consum- GLOSSARY • 709 ers face as a result of limited incomes. completely inelastic demand (page 34) Principle budget line (page 82) All combinations of goods for that consumers will buy a fixed quantity of a good which the total amount of money spent is equal to regardless of its price. income. condominium (page 283) A housing unit that is individ- bundling (page 419) Practice of selling two or more ually owned but provides access to common facilities products as a package. that are paid for and controlled jointly by an associa- tion of owners. C constant returns to scale (page 223) Situation in which Capital Asset Pricing Model (CAPM) (page 575) Model output doubles when all inputs are doubled. in which the risk premium for a capital investment depends on the correlation of the investment’s return constant-cost industry (page 307) Industry whose long- with the return on the entire stock market. run supply curve is horizontal. cardinal utility function (page 80) Utility function Consumer Price Index (page 12) Measure of the aggre- describing by how much one market basket is pre- gate price level. ferred to another. consumer surplus (page 132) Difference between what cartel (page 452) Market in which some or all firms a consumer is willing to pay for a good and the explicitly collude, coordinating prices and output amount actually paid. levels to maximize joint profits. contract curve (page 606) Curve showing all efficient chain-weighted price index (page 104) Cost-of-living allocations of goods between two consumers, or of index that accounts for changes in quantities of two inputs between two production functions. goods and services. cooperative (page 283) Association of businesses or Coase theorem (page 685) Principle that when parties people jointly owned and operated by members for can bargain without cost and to their mutual advan- mutual benefit. tage, the resulting outcome will be efficient regard- less of how property rights are specified. cooperative game (page 488) Game in which partici- pants can negotiate binding contracts that allow Cobb-Douglas production function (page them to plan joint strategies. 276) Production function of the form q = AKaLb, where q is the rate of output, K is the quantity of capi- corner solution (page 89) Situation in which the mar- tal, and L is the quantity of labor, and where A, a, ginal rate of substitution of one good for another in a and b are constants. chosen market basket is not equal to the slope of the budget line. Cobb-Douglas utility function (page 153) Utility func- tion U(X,Y) = XaY1-a, where X and Y are two goods cost function (page 265) Function relating cost of pro- and a is a constant. duction to level of output and other variables that the firm can control. common property resource (page 687) Resource to which anyone has free access. cost-of-living index (page 100) Ratio of the present cost of a typical bundle of consumer goods and common-value auction (page 518) Auction in which the services compared with the cost during a base item has the same value to all bidders, but bidders do period. not know that value precisely and their estimates of it vary. Cournot equilibrium (page 460) Equilibrium in the Cournot model, in which each firm correctly assumes company cost of capital (page 576) Weighted average how much its competitor will produce and sets its of the expected return on a company’s stock and the own production level accordingly. interest rate that it pays for debt. Cournot model (page 458) Oligopoly model in which comparative advantage (page 618) Situation in which firms produce a homogeneous good, each firm treats Country 1 has an advantage over Country 2 in pro- the output of its competitors as fixed, and all firms ducing a good because the cost of producing the good decide simultaneously how much to produce. in 1, relative to the cost of producing other goods in 1, is lower than the cost of producing the good in 2, cross-price elasticity of demand (page 35) Percentage relative to the cost of producing other goods in 2. change in the quantity demanded of one good resulting from a 1-percent increase in the price of complements (page 24) Two goods for which an another. increase in the price of one leads to a decrease in the quantity demanded of the other. cyclical industries (page 41) Industries in which sales tend to magnify cyclical changes in gross domestic product and national income.

710 • GLOSSARY than choosing the highest indifference curve, given a budget constraint, the consumer chooses the low- D est budget line that touches a given indifference curve. deadweight loss (page 321) Net loss of total (consumer plus producer) surplus. duopoly (page 458) Market in which two firms compete with each other. decreasing returns to scale (page 223) Situation in which output less than doubles when all inputs are Dutch auction (page 517) Auction in which a seller doubled. begins by offering an item at a relatively high price, then reduces it by fixed amounts until the item is decreasing-cost industry (page 309) Industry whose sold. long-run supply curve is downward sloping. E degree of economies of scope (SC) (page 260) Percentage of cost savings resulting when two or economic cost (page 230) Cost to a firm of utilizing eco- more products are produced jointly rather than nomic resources in production. individually. economic efficiency (page 323) Maximization of aggre- demand curve (page 23) Relationship between the gate consumer and producer surplus. quantity of a good that consumers are willing to buy and the price of the good. economic rent (page 302) Amount that firms are willing to pay for an input less the minimum amount neces- derived demand (page 530) Demand for an input that sary to obtain it. depends on, and is derived from, both the firm’s level of output and the cost of inputs. economies of scale (page 256) Situation in which output can be doubled for less than a doubling of cost. deviation (page 162) Difference between expected pay- off and actual payoff. economies of scope (page 259) Situation in which joint output of a single firm is greater than output that diminishing marginal utility (page 95) Principle that could be achieved by two different firms when each as more of a good is consumed, the consumption of produces a single product. additional amounts will yield smaller additions to utility. Edgeworth box (page 603) Diagram showing all possible allocations of either two goods between two discount rate (page 569) Rate used to determine the people or of two inputs between two production value today of a dollar received in the future. processes. diseconomies of scale (page 256) Situation in which a effective yield (or rate of return) (page 566) Percentage doubling of output requires more than a doubling return that one receives by investing in a bond. of cost. efficiency wage (page 655) Wage that a firm will pay to diseconomies of scope (page 259) Situation in which an employee as an incentive not to shirk. joint output of a single firm is less than could be achieved by separate firms when each produces a efficiency wage theory (page 654) Explanation for the single product. presence of unemployment and wage discrimina- tion which recognizes that labor productivity may be diversifiable risk (page 574) Risk that can be eliminated affected by the wage rate. either by investing in many projects or by holding the stocks of many companies. elasticity (page 33) Percentage change in one variable resulting from a 1-percent increase in another. diversification (page 170) Practice of reducing risk by allocating resources to a variety of activities whose emissions fee (page 668) Charge levied on each unit of outcomes are not closely related. a firm’s emissions. dominant firm (page 476) Firm with a large share emissions standard (page 668) Legal limit on the of total sales that sets price to maximize profits, amount of pollutants that a firm can emit. taking into account the supply response of smaller firms. endowment effect (page 190) Tendency of individuals to value an item more when they own it than when dominant strategy (page 490) Strategy that is optimal they do not. no matter what an opponent does. Engel curve (page 116) Curve relating the quantity of a double marginalization (page 442) When each firm good consumed to income. in a vertical chain marks up its price above its mar- ginal cost, thereby increasing the price of the final English (or oral) auction (page 517) Auction in which a product. seller actively solicits progressively higher bids from a group of potential buyers. duality (page 154) Alternative way of looking at the consumer’s utility maximization decision: Rather

equal marginal principle (page 96) Principle that utility is GLOSSARY • 711 maximized when the consumer has equalized the mar- ginal utility per dollar of expenditure across all goods. fixed-weight index (page 103) Cost-of-living index in which the quantities of goods and services remain equilibrium (or market-clearing) price (page 25) Price unchanged. that equates the quantity supplied to the quantity demanded. framing (page 191) Tendency to rely on the context in which a choice is described when making a decision. equilibrium in dominant strategies (page 491) Outcome of a game in which each firm is doing the best it can free entry (or exit) (page 280) Condition under which regardless of what its competitors are doing. there are no special costs that make it difficult for a firm to enter (or exit) an industry. excess demand (page 608) When the quantity demanded of a good exceeds the quantity supplied. free rider (page 693) Consumer or producer who does not pay for a nonexclusive good in the expectation excess supply (page 608) When the quantity supplied of that others will. a good exceeds the quantity demanded. G exchange economy (page 602) Market in which two or more consumers trade two goods among game (page 488) Situation in which players (partici- themselves. pants) make strategic decisions that take into account each other’s actions and responses. expansion path (page 249) Curve passing through points of tangency between a firm’s isocost lines and general equilibrium analysis (page 596) Simultaneous its isoquants. determination of the prices and quantities in all rel- evant markets, taking feedback effects into account. expected return (page 178) Return that an asset should earn on average. Giffen good (page 122) Good whose demand curve slopes upward because the (negative) income effect expected utility (page 165) Sum of the utilities associ- is larger than the substitution effect. ated with all possible outcomes, weighted by the probability that each outcome will occur. H expected value (page 161) Probability-weighted average Hicksian substitution effect (page 157) Alternative to of the payoffs associated with all possible outcomes. the Slutsky equation for decomposing price changes without recourse to indifference curves. extensive form of a game (page 503) Representation of possible moves in a game in the form of a decision tree. horizontal integration (pages 439, 651) Organizational form in which several plants produce the same or extent of a market (page 9) Boundaries of a market, related products for a firm. both geographical and in terms of range of products produced and sold within it. human capital (page 580) Knowledge, skills, and expe- rience that make an individual more productive and externality (pages 324, 662) Action by either a producer thereby able to earn a higher income over a lifetime. or a consumer which affects other producers or con- sumers, but is not accounted for in the market price. I F ideal cost-of-living index (page 102) Cost of attaining a given level of utility at current prices relative to the factors of production (page 204) Inputs into the produc- cost of attaining the same utility at base-year prices. tion process (e.g., labor, capital, and materials). import quota (page 340) Limit on the quantity of a good first-degree price discrimination (page 401) Practice of that can be imported. charging each customer her reservation price. income effect (page 121) Change in consumption of first-price auction (page 517) Auction in which the sales a good resulting from an increase in purchasing price is equal to the highest bid. power, with relative prices held constant. fixed cost (FC) (page 233) Cost that does not vary with income elasticity of demand (page 35) Percentage the level of output and that can be eliminated only by change in the quantity demanded resulting from a shutting down. 1-percent increase in income. fixed input (page 205) Production factor that cannot be income-consumption curve (page 114) Curve tracing varied. the utility-maximizing combinations of two goods as a consumer’s income changes. fixed-proportions production function (page 219) Production function with L-shaped isoquants, so increasing returns to scale (page 223) Situation in which that only one combination of labor and capital can be output more than doubles when all inputs are doubled. used to produce each level of output.

712 • GLOSSARY Laspeyres price index (page 102) Amount of money at current year prices that an individual requires to increasing-cost industry (page 308) Industry whose purchase a bundle of goods and services chosen in a long-run supply curve is upward sloping. base year divided by the cost of purchasing the same bundle at base-year prices. indifference curve (page 71) Curve representing all combinations of market baskets that provide a con- law of diminishing marginal returns (page 209) sumer with the same level of satisfaction. Principle that as the use of an input increases with other inputs fixed, the resulting additions to output indifference map (page 72) Graph containing a set will eventually decrease. of indifference curves showing the market baskets among which a consumer is indifferent. law of small numbers (page 195) Tendency to overstate the probability that a certain event will occur when individual demand curve (page 113) Curve relating the faced with relatively little information. quantity of a good that a single consumer will buy to its price. learning curve (page 261) Graph relating amount of inputs needed by a firm to produce each unit of out- inferior good (page 121) A good that has a negative put to its cumulative output. income effect. least-squares criterion (page 701) Criterion of “best infinitely elastic demand (page 34) Principle that con- fit” used to choose values for regression parameters, sumers will buy as much of a good as they can get at usually by minimizing the sum of squared residuals a single price, but for any higher price the quantity between the actual values of the dependent variable demanded drops to zero, while for any lower price and the fitted values. the quantity demanded increases without limit. Lerner Index of Monopoly Power (page 371) Measure informational cascade (page 189) An assessment (e.g., of monopoly power calculated as excess of price over of an investment opportunity) based in part on the marginal cost as a fraction of price. actions of others, which in turn were based on the actions of others. linear demand curve (page 34) Demand curve that is a straight line. interest rate (page 561) Rate at which one can borrow or lend money. linear regression (page 700) Model specifying a linear relationship between a dependent variable and sev- intertemporal price discrimination (page 410) Practice eral independent (or explanatory) variables and an of separating consumers with different demand error term. functions into different groups by charging different prices at different points in time. long run (page 205) Amount of time needed to make all production inputs variable. isocost line (page 245) Graph showing all possible com- binations of labor and capital that can be purchased long-run average cost curve (LAC) (page 254) Curve for a given total cost. relating average cost of production to output when all inputs, including capital, are variable. isoelastic demand curve (page 127) Demand curve with a constant price elasticity. long-run competitive equilibrium (page 303) All firms in an industry are maximizing profit, no firm has an isoquant (page 216) Curve showing all possible combi- incentive to enter or exit, and price is such that quan- nations of inputs that yield the same output. tity supplied equals quantity demanded. isoquant map (page 217) Graph combining a number of long-run marginal cost curve (LMC) (page 254) Curve isoquants, used to describe a production function. showing the change in long-run total cost as output is increased incrementally by 1 unit. K loss aversion (page 191) Tendency for individuals to kinked demand curve model (page 473) Oligopoly prefer avoiding losses over acquiring gains. model in which each firm faces a demand curve kinked at the currently prevailing price: at higher M prices demand is very elastic, whereas at lower prices it is inelastic. macroeconomics (page 4) Branch of economics that deals with aggregate economic variables, such as L the level and growth rate of national output, interest rates, unemployment, and inflation. labor productivity (page 214) Average product of labor for an entire industry or for the economy as a whole. marginal benefit (page 87) Benefit from the consump- tion of one additional unit of a good. Lagrangian (page 150) Function to be maximized or minimized, plus a variable (the Lagrange multiplier) multiplied by the constraint.

marginal cost (pages 87, 236) Cost of one additional unit GLOSSARY • 713 of a good. market failure (page 324) Situation in which an unregu- marginal expenditure (page 383) Additional cost of lated competitive market is inefficient because prices buying one more unit of a good. fail to provide proper signals to consumers and producers. marginal expenditure curve (page 537) Curve describ- ing the additional cost of purchasing one additional market mechanism (page 25) Tendency in a free market unit of a good. for price to change until the market clears. marginal external benefit (page 664) Increased benefit market power (page 358) Ability of a seller or buyer to that accrues to other parties as a firm increases out- affect the price of a good. put by one unit. market price (page 8) Price prevailing in a competitive marginal external cost (page 663) Increase in cost market. 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 marginal product (page 207) Additional output pro- product quality. duced as an input is increased by one unit. maximin strategy (page 495) Strategy that maximizes marginal rate of substitution (MRS) (page 74) the minimum gain that can be earned. Maximum amount of a good that a consumer is will- ing to give up in order to obtain one additional unit method of Lagrange multipliers (page 150) Technique of another good. to maximize or minimize a function subject to one or more constraints. marginal rate of technical substitution (MRTS) (page 218) Amount by which the quantity of one input can microeconomics (page 4) Branch of economics that be reduced when one extra unit of another input is deals with the behavior of individual economic used, so that output remains constant. units—consumers, firms, workers, and investors—as well as the markets that these units comprise. marginal rate of transformation (page 614) Amount of one good that must be given up to produce one addi- mixed bundling (page 423) Selling two or more goods tional unit of a second good. both as a package and individually. marginal revenue (pages 284, 358) Change in revenue mixed strategy (page 496) Strategy in which a player resulting from a one-unit increase in output. makes a random choice among two or more possible actions, based on a set of chosen probabilities. marginal revenue product (page 530) Additional rev- enue resulting from the sale of output created by the monopolistic competition (page 452) Market in which use of one additional unit of an input. firms can enter freely, each producing its own brand or version of a differentiated product. marginal social benefit (page 664) Sum of the marginal private benefit plus the marginal external benefit. monopoly (page 358) Market with only one seller. marginal social cost (page 663) Sum of the marginal monopsony (page 358) Market with only one buyer. cost of production and the marginal external cost. monopsony power (page 382) Buyer’s ability to affect marginal utility (MU) (page 95) Additional satisfaction the price of a good. obtained from consuming one additional unit of a good. moral hazard (page 643) When a party whose actions are unobserved can affect the probability or magni- marginal value (page 382) Additional benefit derived tude of a payment associated with an event. from purchasing one more unit of a good. multiple regression analysis (page 700) Statistical pro- market (page 7) Collection of buyers and sellers that, cedure for quantifying economic relationships and through their actual or potential interactions, deter- testing hypotheses about them. mine the price of a product or set of products. mutual fund (page 171) Organization that pools funds market basket (or bundle) (page 68) List with specific of individual investors to buy a large number of dif- quantities of one or more goods. ferent stocks or other financial assets. market definition (page 8) Determination of the buy- N ers, sellers, and range of products that should be included in a particular market. Nash equilibrium (page 458) Set of strategies or actions in which each firm does the best it can given its com- market demand curve (page 124) Curve relating the petitors’ actions. quantity of a good that all consumers in a market will buy to its price. natural monopoly (page 380) Firm that can produce the entire output of the market at a cost lower than what it would be if there were several firms.

714 • GLOSSARY parallel conduct (page 390) Form of implicit collusion in which one firm consistently follows actions of negatively correlated variables (page 171) Variables another. having a tendency to move in opposite directions. partial equilibrium analysis (page 596) Determination net present value (NPV) criterion (page 569) Rule hold- of equilibrium prices and quantities in a market inde- ing that one should invest if the present value of pendent of effects from other markets. the expected future cash flow from an investment is larger than the cost of the investment. payoff (pages 161, 488) Value associated with a possible outcome. network externality (page 135) Situation in which each individual’s demand depends on the purchases of payoff matrix (page 470) Table showing profit (or pay- other individuals. off) to each firm given its decision and the decision of its competitor. nominal price (page 12) Absolute price of a good, unad- justed for inflation. peak-load pricing (page 410) Practice of charging higher prices during peak periods when capacity noncooperative game (pages 470, 488) Game in which constraints cause marginal costs to be high. negotiation and enforcement of binding contracts are not possible. perfect complements (page 76) Two goods for which the MRS is zero or infinite; the indifference curves nondiversifiable risk (page 574) Risk that cannot be are shaped as right angles. eliminated by investing in many projects or by hold- ing the stocks of many companies. perfect substitutes (page 76) Two goods for which the marginal rate of substitution of one for the other is a nonexclusive good (page 690) Good that people cannot constant. be excluded from consuming, so that it is difficult or impossible to charge for its use. perfectly competitive market (page 8) Market with many buyers and sellers, so that no single buyer or nonrival good (page 690) Good for which the marginal seller has a significant impact on price. cost of its provision to an additional consumer is zero. perpetuity (page 565) Bond paying out a fixed amount of money each year, forever. normative analysis (page 7) Analysis examining ques- tions of what ought to be. point elasticity of demand (page 36) Price elasticity at a particular point on the demand curve. O positive analysis (page 6) Analysis describing relation- oligopoly (page 452) Market in which only a few firms ships of cause and effect. compete with one another, and entry by new firms is impeded. positively correlated variables (page 171) Variables having a tendency to move in the same direction. oligopsony (page 382) Market with only a few buyers. predatory pricing (page 390) Practice of pricing to drive opportunity cost (page 230) Cost associated with oppor- current competitors out of business and to discour- tunities forgone when a firm’s resources are not put age new entrants in a market so that a firm can enjoy to their best alternative use. higher future profits. opportunity cost of capital (page 570) Rate of return present discounted value (PDV) (page 561) The current that one could earn by investing in an alternate proj- value of an expected future cash flow. ect with similar risk. price discrimination (page 401) Practice of charging optimal strategy (page 488) Strategy that maximizes a different prices to different consumers for similar player’s expected payoff. goods. ordinal utility function (page 80) Utility function that price elasticity of demand (page 33) Percentage change generates a ranking of market baskets in order of in quantity demanded of a good resulting from a most to least preferred. 1-percent increase in its price. P price elasticity of supply (page 36) Percentage change in quantity supplied resulting from a 1-percent Paasche index (page 103) Amount of money at current- increase in price. year prices that an individual requires to purchase a current bundle of goods and services divided by the price leadership (page 474) Pattern of pricing in which cost of purchasing the same bundle in a base year. one firm regularly announces price changes that other firms then match. Pareto efficient allocation (page 602) Allocation of goods in which no one can be made better off unless price of risk (page 180) Extra risk that an investor must someone else is made worse off. incur to enjoy a higher expected return.

price rigidity (page 473) Characteristic of oligopolis- GLOSSARY • 715 tic markets by which firms are reluctant to change prices even if costs or demands change. public good (pages 626, 690) Nonexclusive and nonrival good: the marginal cost of provision to an additional price signaling (page 474) Form of implicit collusion in consumer is zero and people cannot be excluded which a firm announces a price increase in the hope from consuming it. that other firms will follow suit. pure bundling (page 423) Selling products only as a price support (page 332) Price set by government above package. free-market level and maintained by governmental purchases of excess supply. pure strategy (page 496) Strategy in which a player makes a specific choice or takes a specific action. price taker (page 280) Firm that has no influence over market price and thus takes the price as given. Q price-consumption curve (page 112) Curve tracing the quantity forcing (page 443) Use of a sales quota or other utility-maximizing combinations of two goods as the incentives to make downstream firms sell as much as price of one changes. possible. principal (page 646) Individual who employs one or R more agents to achieve an objective. rate-of-return regulation (page 381) Maximum price principal–agent problem (page 645) Problem arising allowed by a regulatory agency is based on the when agents (e.g., a firm’s managers) pursue their (expected) rate of return that a firm will earn. own goals rather than the goals of principals (e.g., the firm’s owners). reaction curve (page 459) Relationship between a firm’s profit-maximizing output and the amount it thinks prisoners’ dilemma (page 470) Game theory exam- its competitor will produce. ple in which two prisoners must decide separately whether to confess to a crime; if a prisoner confesses, real price (page 12) Price of a good relative to an aggre- he will receive a lighter sentence and his accomplice gate measure of prices; price adjusted for inflation. will receive a heavier one, but if neither confesses, sentences will be lighter than if both confess. real return (page 178) Simple (or nominal) return on an asset, less the rate of inflation. private-value auction (page 517) Auction in which each bidder knows his or her individual valuation of the reference point (page 190) The point from which an object up for bid, with valuations differing from bid- individual makes a consumption decision. der to bidder. rent seeking (page 378) Spending money in socially probability (page 160) Likelihood that a given outcome unproductive efforts to acquire, maintain, or exercise will occur. monopoly. Producer Price Index (page 12) Measure of the aggre- rental rate (page 244) Cost per year of renting one unit gate price level for intermediate products and whole- of capital. sale goods. repeated game (page 498) Game in which actions are producer surplus (page 298) Sum over all units pro- taken and payoffs received over and over again. duced by a firm of differences between the market price of a good and the marginal cost of production. reservation price (page 401) Maximum price that a cus- tomer is willing to pay for a good. product transformation curve (page 258) Curve show- ing the various combinations of two different out- return (page 177) Total monetary flow of an asset as a puts (products) that can be produced with a given set fraction of its price. of inputs. returns to scale (page 223) Rate at which output production function (page 204) Function showing the increases as inputs are increased proportionately. highest output that a firm can produce for every specified combination of inputs. risk averse (page 166) Condition of preferring a certain income to a risky income with the same expected value. production possibilities frontier (page 614) Curve showing the combinations of two goods that can be risk loving (page 166) Condition of preferring a risky produced with fixed quantities of inputs. income to a certain income with the same expected value. profit (page 284) Difference between total revenue and total cost. risk neutral (page 166) Condition of being indifferent between a certain income and an uncertain income property rights (page 684) Legal rules stating what peo- with the same expected value. ple or firms may do with their property. risk premium (pages 166, 573) Maximum amount of money that a risk-averse individual will pay to avoid taking a risk.

716 • GLOSSARY speculative demand (page 129) Demand driven not by the direct benefits one obtains from owning or riskless (or risk-free) asset (page 177) Asset that pro- consuming a good but instead by an expectation that vides a flow of money or services that is known with the price of the good will increase. certainty. Stackelberg model (page 463) Oligopoly model risky asset (page 177) Asset that provides an uncertain in which one firm sets its output before other flow of money or services to its owner. firms do. R-squared (R2) (page 704) Percentage of the variation standard deviation (page 162) Square root of the in the dependent variable that is accounted for by all weighted average of the squares of the deviations of the explanatory variables. the payoffs associated with each outcome from their expected values. S standard error of the regression (page 704) Estimate of sample (page 702) Set of observations for study, drawn the standard deviation of the regression error. from a larger universe. stock of capital (page 214) Total amount of capital avail- sealed-bid auction (page 517) Auction in which all bids able for use in production. are made simultaneously in sealed envelopes, the winning bidder being the individual who has sub- stock externality (page 679) Accumulated result of mitted the highest bid. action by a producer or consumer which, though not accounted for in the market price, affects other pro- second-degree price discrimination (page 404) Practice ducers or consumers. of charging different prices per unit for different quantities of the same good or service. strategy (page 488) Rule or plan of action for playing a game. second-price auction (page 517) Auction in which the sales price is equal to the second-highest bid. subsidy (page 348) Payment reducing the buyer’s price below the seller’s price; i.e., a negative tax. sequential game (page 502) Game in which players move in turn, responding to each other’s actions and substitutes (page 24) Two goods for which an increase reactions. in the price of one leads to an increase in the quantity demanded of the other. shirking model (page 655) Principle that workers still have an incentive to shirk if a firm pays them a substitution effect (page 120) Change in consumption market-clearing wage, because fired workers can be of a good associated with a change in its price, with hired somewhere else for the same wage. the level of utility held constant. short run (page 205) Period of time in which quanti- sunk cost (page 230) Expenditure that has been made ties of one or more production factors cannot be and cannot be recovered. changed. supply curve (page 22) Relationship between the quan- short-run average cost curve (SAC) (page 254) Curve tity of a good that producers are willing to sell and relating average cost of production to output when the price of the good. level of capital is fixed. surplus (page 25) Situation in which the quantity sup- shortage (page 25) Situation in which the quantity plied exceeds the quantity demanded. demanded exceeds the quantity supplied. T Slutsky equation (page 156) Formula for decompos- ing the effects of a price change into substitution and tariff (page 340) Tax on an imported good. income effects. technical efficiency (page 613) Condition under which snob effect (page 137) Negative network externality firms combine inputs to produce a given output as in which a consumer wishes to own an exclusive or inexpensively as possible. unique good. technological change (page 214) Development of new social rate of discount (page 682) Opportunity cost to technologies allowing factors of production to be society as a whole of receiving an economic benefit in used more effectively. the future rather than the present. theory of consumer behavior (page 68) Description social welfare function (page 611) Measure describing of how consumers allocate incomes among the well-being of society as a whole in terms of the different goods and services to maximize their utilities of individual members. well-being. specific tax (page 345) Tax of a certain amount of money per unit sold.

theory of the firm (page 202) Explanation of how a firm GLOSSARY • 717 makes cost-minimizing production decisions and how its cost varies with its output. utility possibilities frontier (page 610) Curve show- ing all efficient allocations of resources measured in third-degree price discrimination (page 404) Practice terms of the utility levels of two individuals. of dividing consumers into two or more groups with separate demand curves and charging different V prices to each group. value of complete information (page 174) Difference tit-for-tat strategy (page 499) Repeated-game strategy between the expected value of a choice when there is in which a player responds in kind to an opponent’s complete information and the expected value when previous play, cooperating with cooperative oppo- information is incomplete. nents and retaliating against uncooperative ones. variability (page 161) Extent to which possible out- total cost (TC or C) (page 233) Total economic cost of comes of an uncertain event differ. production, consisting of fixed and variable costs. variable cost (VC) (page 233) Cost that varies as output transfer prices (page 439) Internal prices at which parts varies. and components from upstream divisions are “sold” to downstream divisions within a firm. variable profit (page 401) Sum of profits on each incre- mental unit produced by a firm; i.e., profit ignoring tradeable emissions permits (page 672) System of mar- fixed costs. ketable permits, allocated among firms, specifying the maximum level of emissions that can be generated. vertical integration (pages 439, 651) Organizational form in which a firm contains several divisions, with two-part tariff (page 414) Form of pricing in which con- some producing parts and components that others sumers are charged both an entry and a usage fee. use to produce finished products. tying (page 428) Practice of requiring a customer to pur- W chase one good in order to purchase another. welfare economics (page 609) Normative evaluation of U markets and economic policy. user cost of capital (page 243) The annual cost of own- welfare effects (page 319) Gains and losses to consum- ing and using a capital asset, equal to economic ers and producers. depreciation plus forgone interest. winner’s curse (page 520) Situation in which the winner user cost of production (page 585) Opportunity cost of of a common-value auction is worse off as a conse- producing and selling a unit today and so making it quence of overestimating the value of the item and unavailable for production and sale in the future. thereby overbidding. utility (page 78) Numerical score representing the satisfac- Z tion that a consumer gets from a given market basket. zero economic profit (page 302) A firm is earning a nor- utility function (page 79) Formula that assigns a level of mal return on its investment—i.e., it is doing as well utility to individual market baskets. as it could by investing its money elsewhere.

Answers to Selected Exercises CHAPTER 1 3. If Brazil and Indonesia add 200 million bushels of wheat to U.S. wheat demand, the new demand curve 1. a. False. There is little or no substitutability across geo- will be Q + 200, or QD = (3244 - 283P) + 200 = graphical regions of the United States. A consumer in 3444 - 283P. Los Angeles, for example, will not travel to Houston, Atlanta, or New York for lunch just because ham- Equate supply and the new demand to find the burger prices are lower in those cities. Likewise, a new equilibrium price. 1944 + 207P = 3444 - 283P, McDonald’s or Burger King in New York cannot sup- or 490P = 1500, and thus P ϭ $3.06 per bushel. To ply hamburgers in Los Angeles, even if prices were find the equilibrium quantity, substitute the price into higher in Los Angeles. In other words, a fast-food either the supply or demand equation. Using demand, price increase in New York will affect neither the QD = 3444 - 283(3.06) = 2578 million bushels. quantity demanded nor the quantity supplied in Los Angeles or other parts of the country. 5. a. Total demand is Q = 3244 - 283P; domestic demand is QD = 1700 - 107P; subtracting domestic b. False. Although consumers are unlikely to travel demand from total demand gives export demand across the country to buy clothing, suppliers can QE = 1544 - 176P. The initial market equilibrium easily move clothing from one part of the country price (as given in example) is P* = $2.65. With a to another. Thus if clothing prices were substantially 40-percent decrease in export demand, total higher in Atlanta than Los Angeles, clothing com- demand becomes Q = QD + 0.6QE = 1700 - 107P panies could shift supplies to Atlanta, which would + 0.6(1544 - 176P) = 2626.4 - 212.6P. Demand is reduce the price there. equal to supply. Therefore: c. False. Although some consumers might be die-hard 2626.4 - 212.6P = 1944 + 207P Coke or Pepsi loyalists, there are many consumers 682.4 = 419.6P who will substitute one for the other based on price differences. Thus there is a single market for colas. So P= 682.4 = $1.626 or $1.63. At this price, 419.6 CHAPTER 2 Q = 2281. Yes, farmers should be worried. With this 2. a. With each price increase of $20, the quantity drop in quantity and price, revenue goes from $6609 demanded decreases by 2. Therefore, (⌬QD/⌬P) = million to $3718 million. - 2/20 = - 0.1. At P = 80, quantity demanded equals 20 and ED = (8/20)( - 0.1) = - 0.40. Similarly, b. If the U.S. government supports a price of $3.50, the at P = 100, quantity demanded equals 18 and market is not in equilibrium. At this support price, ED = (100/18)( - 0.1) = - 0.56. demand is equal to 2626.4 - 212.6(3.5) = 1882.3 and supply is 1944 + 207(3.5) = 2668.5. There is b. With each price increase of $20, quantity supplied excess supply (2668.5 - 1882.3 = 786.2) which increases by 2. Therefore, (⌬QS/⌬P) = 2/20 = 0.1. the government must buy, costing $3.50(786.2) = At P = 80, quantity supplied equals 16 and ES = $2751.7 million. (80/16)(0.1) = 0.5. Similarly, at P = 100, quantity supplied equals 18 and ES = (100/18)(0.1) = 0.56. 8. a. To derive the new demand curve, we follow the same procedure as in Section 2.6. We know that c. The equilibrium price and quantity are found where ED = - b(P*/Q*); substituting ED = - 0.75, P* = $3, the quantity supplied equals the quantity demanded and Q* = 18 gives - 0.75 = - b(3/18) so that b = at the same price. From the table, the P* = $100 and 4.5. Substituting this value into the equation for the Q* = 18 million. the linear demand curve, QD = a - bP, we have 18 = a - 4.5(3). So a = 31.5. The new demand d. With a price ceiling of $80, consumers want curve is QD = 31.5 - 4.5P. 20 million, but producers supply only 16 million, for a shortage of 4 million. 718

b. To determine the effect of a 20-percent decline in cop- ANSWERS TO SELECTED EXERCISES • 719 per demand, we note that the quantity demanded is 80 percent of what it would be otherwise for every J1 J2 price. Multiplying the right-hand side of the demand R curve by 0.8, QD = (0.8)(31.5 - 4.5P) = 25.2 - 3.6P. Supply is still QS = - 9 + 9P and demand is equal S2 to supply. Solving, P* = $2.71 per pound. A decline S1 in demand of 20 percent, therefore, entails a drop in price of 29 cents per pound, or 9.7 percent. H 10. a. First, considering non-OPEC supply: SC = Q* = 19. FIGURE 3(a) With ES = 0.05 and P* = $80, ES = d(P*/Q) implies d = 0.012. Substituting for d, SC = 19, and P = 80 in G 50 Slope ϭ Ϫ1.00 the supply equation gives 19 = c + (0.012)(80), 45 so that c = 18.05. Hence, the supply curve is 40 Slope ϭ Ϫ0.75 SC = 18.05 + 0.012P. Similarly, since QD = 32, 35 Slope ϭ Ϫ0.50 ED = - b(P*/Q*) = - 0.05andb = 0.020. Substituting 30 for b, QD = 32, and P = 80 in the demand equation 25 gives 32 = a - (0.020)(80), so that a = 33.6. Hence 20 QD = 33.6 - 0.020P. 15 10 b. The long-run elasticities are: ES = 0.30 and 5 ED = - 0.30. As above, ES = d(P*/Q*) and ED = - b(P*/Q*) , i m p l y i n g 0.30 = d(80/19) a n d 0 25 50 75 - 0.30 = - b(80/32). So d = 0.07 and b = –0.12. Next M solve for c and a: SC = c + dP and QD = a - bP, which implies that 19 = c + (0.07)(80) and FIGURE 3(b) 32 = a - (0.12)(80). Therefore, c = 13.3 and a = 41.6. Jones has a higher MRS of R for H than Smith has. c. The discovery of new oil fields will increase OPEC Jones’ indifference curves are steeper than Smith’s supply by 2bb/yr, so SC = 19, SO = 15, and D = 34. at any point on the graph. The new short-run total supply curve is ST = 33.05 + 0.012P. Demand is unchanged: 8. In Figure 3(b) we plot miles flown, M, against all other D = 33.6 - .020P. Since supply equals demand, goods, G, in dollars. The slope of the budget line is 33.05 + 0.012P = 33.6 - .020P. Solving, P = $17.19 - PM/PG. The price of miles flown changes as number per barrel. An increase in OPEC supply entails a of miles flown changes, so the budget curve is kinked drop in price of $62.81, or 79% in the short-run. at 25,000 and 50,000 miles. Suppose PM is $1 per mile for … 25,000 miles, then PM = $0.75 for 25,000 6 M To analyze the long-run, use the new long- … 50,000, and PM = $.50 for M > 50,000. Also, let PG = run supply curve, ST = 28.3 + 0.071P. Setting $1. Then the slope of the first segment is - 1, the slope this equal to long-run demand gives: 28.3 + of the second segment is - 0.75, and the slope of the 0.071 P = 41.6 - 0.120P, so that P = $69.63 per last segment is - 0.5. barrel, only $10.37 per barrel (13%) less than the original long-run price. CHAPTER 3 3. Not necessarily true. Suppose that she has convex preferences (a diminishing marginal rate of substi- tution), and has a lot of movie tickets. Even though she would give up movie tickets to get another basketball ticket, she does not necessarily like basketball better. 6. a. See Figure 3(a), where R is the number of rock con- certs, and H is the number of hockey games. b. At any combination of R and H, Jones is willing to give up more of R to get some H than Smith is. Thus

720 • ANSWERS TO SELECTED EXERCISES CHAPTER 4 However, she did not choose to return to her original bundle. We can therefore infer that she found a better 9. a. For computer chips, EP = - 2, so - 2 = %⌬Q/10, bundle that gave her a higher level of utility. and therefore %⌬Q = - 20. For disk drives, EP = - 1, so a 10 percent increase in price will reduce sales 13. a. The demand curve is a straight line with a vertical intercept of P = 15 and a horizontal intercept of Q = 30. by 10 percent. Sales revenue will decrease for com- b. If there were no toll, the price P would be 0, so that puter chips because demand is elastic and price Q = 30. has increased. To estimate the change in rev- c. If the toll is $5, Q = 20. The consumer surplus lost is the difference between consumer surplus when P = 0 enue, let TR1 = P1Q1 be revenue before the price and consumer surplus when P = 5, or $125. change and TR2 = P2Q2 be revenue after the price change. Therefore ⌬TR = P2Q2 - P1Q1, and thus CHAPTER 4—APPENDIX ⌬TR = (1.1P1)(0.8Q1) - P1Q1 = - 0.12P1Q1, or a 12 percent decline. Sales revenue for disk drives will 1. The first utility function can be represented as a series of straight lines; the second as a series of hyperbolas in remain unchanged because demand elasticity is -1. the positive quadrant; and the third as a series of “L”s. Only the second utility function meets the definition b. Although we know the responsiveness of demand of a strictly convex shape. to change in price, we need to know the quantities and the prices of the products to determine total 3. The Slutsky equation is dX/dPX = 0X/0P*|U=U* sales revenues. - X(⌬X/⌬I), where the first term represents the substitution effect and the second term represents 11. a. With small changes in price, the point elastic- the income effect. With this type of utility function the consumer does not substitute one good for the ity formula would be appropriate. But here, the other when the price changes, so the substitution effect is zero. price of food increases from $2 to $2.50, so arc elas- CHAPTER 5 ticity should be used: Ep = (⌬Q/⌬P)(P/Q). We know that Ep = - 1, P = 2, ⌬P = .50, and Q = 5000. 2. The four mutually exclusive states are given in Table 5 So, if there is no change in income, we can solve for below. ⌬=Q(⌬: -Q1# = (⌬Q/.50) [((2 + .50)/2)/(5000 + ⌬Q/2)] 4. The expected value is EV = (0.4)(100) + (0.3)(30) 2.50)/(10,000 + ⌬Q). We find that ⌬Q = + (0.3)( - 30) = $40. The variance is s2 = (0.4)(100 - 40)2 + (0.3)(30 - 40)2 + (0.3)(- 30 - 40)2 = 2,940. - 1000: she decreases her consumption of food from 8. Initially, total wealth is $450,000. We calculate 5000 to 4000 units. expected wealth under three options. Under the safe option, E(U) = (450,000 + 1.05*200,000).5 = 678. b. A tax rebate of $2500 implies an income increase of With the summer corn crop, E(U) = .7(250,000 + $2500. To calculate the response of demand to the 500,000).5 + .3(250,000 + 50,000).5 = 770. Finally, tax rebate, we use the definition of the arc income with the drought resistant summer corn crop, E(U) = elasticity: EI = (⌬Q/⌬I)(I/Q). We know that .7(250,000 + 450,000).5 + .3(250,000 + 350,000).5 = EI = 0.5, I = 25,000, ⌬I = 2500, and Q = 4000. We solve for 818. The option with the highest expected utility is ⌬Q:0.5 = (⌬Q/2500)[((25,000 + 27,500)/2)/(4000 + planting the drought resistant crop. (⌬Q/2)]. Since ⌬Q = 195, she increases her consump- tion of food from 4000 to 4195 units. c. Felicia is better off after the rebate. The amount of the rebate is enough to allow her to purchase her original bundle of food and other goods. Recall that originally she consumed 5000 units of food. When the price went up by fifty cents per unit, she needed an extra (5000)($0.50) = $2500 to afford the same quantity of food without reducing the quantity of the other goods consumed. This is the exact amount of the rebate. TABLE 5 CONGRESS PASSES TARIFF CONGRESS DOES NOT PASS TARIFF Slow growth rate State 1: State 2: Fast growth rate Slow growth with tariff Slow growth without tariff State 3: State 4: Fast growth with tariff Fast growth without tariff

Total Demand ANSWERS TO SELECTED EXERCISES • 721 20 isoquant, and hence the MRTS, we need to know 15 the rate at which one input may be substituted for the other. Without the marginal product of each input, we Price 10 cannot calculate the MRTS. 5 9. a. Let Q1 be the output of DISK, Inc., Q2 be the output of FLOPPY, Inc., and X be equal amounts of capital and 0 1000 1500 2000 2500 3000 labor for the two firms. Then, Q1 = 10X0.5X0.5 = 0 500 Quantity 10X(0.5 + 0.5) = 10X and Q2 = 10X0.6X0.4 = 10X(0.6 + 0.4) = 10X. Because Q1 = Q2, they both generate the same FIGURE 5 output with the same inputs. b. With capital fixed at 9 machine units, the production functions become Q1 = 30L0.5 and Q2 = 37.37L0.4. Consider the following table: Q MP Q MP L FIRM 1 FIRM 1 FIRM 2 FIRM 2 12. To determine the total demand curve, we add 0 0 —0 — up 100 standard demand curves and 100 rule of thumb demand curves: Q = 100*(20 - P) + 100* 1 30.00 30.00 37.37 37.37 (10 if P 6 10 or 0 if P Ú 10) = 3000 - 100P if P < 10 and 2000 - 100P if P Ú 10. The resulting total 2 42.43 12.43 49.31 11.94 demand curve is given below. 3 51.96 9.53 57.99 8.69 4 60.00 8.04 65.07 7.07 CHAPTER 6 For each unit of labor above 1 unit, the marginal prod- uct of labor is greater for DISK, Inc. 2. a. The average product of labor, AP, is equal to Q/L. The marginal product of labor, MP, is equal to CHAPTER 7 ⌬Q/⌬L. The relevant calculations are given in the following table. 4. a. Total cost, TC, is equal to fixed cost, FC, plus vari- able cost, VC. Since the franchise fee, FF, is a fixed L Q AP MP sum, the firm’s fixed costs increase by the fee. Then average cost, equal to (FC + VC)/Q, and average 0 0— — fixed cost, equal to (FC/Q), increase by the average franchise fee (FF/Q). Average variable cost is unaf- 1 10 10 10 fected by the fee, as is marginal cost. 2 18 9 8 b. When a tax t is imposed, variable costs increase by tQ. Average variable cost increases by t (fixed cost is 3 24 8 6 constant), as does average (total) cost. Because total cost increases by t with each additional unit, mar- 4 28 7 4 ginal cost increases by t. 5 30 6 2 5. It is probably referring to accounting profit; this is the standard concept used in most discussions of 6 28 4.7 Ϫ2 how firms are doing financially. In this case, the 7 25 3.6 Ϫ3 article points to a substantial difference between accounting and economic profits. It claims that, b. This production process exhibits diminish- under the current labor contract, automakers must ing returns to labor, which is characteristic of all pay many workers even if they are not working. production functions with one fixed input. Each This implies that their wages are sunk for the life additional unit of labor yields a smaller increase in of the contract. Accounting profits would subtract output than the last unit of labor. wages paid; economic profits would not, since they are sunk costs. Therefore automakers may be earn- c. Labor’s negative marginal product can arise from con- ing economic profits on these sales, even if they gestion in the chair manufacturer’s factory. As more have accounting losses. laborers are using a fixed amount of capital, they get in each other’s way, decreasing output. 6. No. If the inputs are perfect substitutes, the isoquants will be linear. However, to calculate the slope of the

722 • ANSWERS TO SELECTED EXERCISES b. Because the firm is a price taker, the imposition of the tax on only one firm does not change the market price. 10. If the firm can produce one chair with either 4 hours Given that the firm’s short-run supply curve is its of labor or 4 hours of machinery or any combination, marginal cost curve (above average variable cost), and then the isoquant is a straight line with a slope of -1 that the marginal cost curve has shifted up (or inward), and intercepts at K = 4 and L = 4. The isocost line, the firm supplies less to the market at every price. TC = 30L + 15K, has a slope of -2 and intercepts at K = TC/15 and L = TC/30. The cost-minimizing c. If the tax is placed on a single firm, that firm will go point is a corner solution, where L = 0 and K = 4, and out of business unless it was earning a positive eco- TC = $60. nomic profit before the tax. CHAPTER 7—APPENDIX CHAPTER 9 1. a. Returns to scale refers to the relationship between out- 1. a. In free-market equilibrium, LS = LD. Solving, w = $4 put and proportional increases in all inputs. If and LS = LD = 40. If the minimum wage is $5, then F(lL,lK) 7 lF(L,K), there are increasing returns to LS = 50 and LD = 30. The number of people employed scale; if F(lL,lK) = lF(L,K), there are constant will be given by the labor demand. So employers returns to scale; if F(lL,lK) 6 lF(L,K), there are will hire 30 million workers. decreasing returns to scale. Applying this to F(L,K) = K2L, F(lL,lK) = (lK)2(lL) = l3K2L = b. With the subsidy, only w - 1 is paid by the firm. The l3F(L,K) 7 lF(L,K). So, this production function labor demand becomes LD* = 80 - 10(w - 1). So exhibits increasing returns to scale. w = $4.50 and L = 45. b. F(lL,lK) = 10lK + 5lL = lF(L,K). The production function exhibits constant returns to scale. 4. a. E4Pqu# Pa*tin=g demand and supply, 28 - 2P = 4 + and Q* = 20. c. F(lL,lK) = (lKlL)0.5 = (l2)0.5 = (KL)0.5 = l(KL)0.5 = 4 lF(L,K). The production function exhibits constant returns to scale. b. The 25-percent reduction would imply that farmers produce 15 billion bushels. To encourage farmers to 2. The marginal product of labor is 100K. The withdraw their land from cultivation, the government marginal product of capital is 100L. The marginal must give them 5 billion bushels that they can sell on rate of technical substitution is K/L. Set this equal the market. Since the total supply to the market is still to the ratio of the wage rate to the rental rate of 20 billion bushels, the market price remains at $4 per capital: K/L = 30/120 or L = 4K. Then sub- bushel. Farmers gain because they incur no costs for stitute for L in the production function and the 5 billion bushels received from the government. solve for a K that yields an output of 1000 We calculate these cost savings by taking the area under the supply curve between 15 and 20 billion #u n i t s : 1000 = 100K 4K . S o , K = 2.50.5 , bushels. The prices when Q = 15 and when Q = 20 #L = 4 2.50.5, and total cost is equal to $379.20. are P = $2.75 and P = $4.00. The total cost of produc- ing the last 5 billion bushels is therefore the area of CHAPTER 8 a trapezoid with a base of 20 - 15 = 5 billion and an average height of (2.75 + 4.00)/2 = 3.375. The area is 4. a. Profit is maximized where marginal cost (MC) is equal 5(3.375) = $16.875 billion. to marginal revenue (MR). Here, MR is equal to $100. Setting MC equal to 100 yields a profit-maximizing c. Taxpayers gain because the government does not quantity of 25. have to pay to store the wheat for a year and then ship it to an underdeveloped country. The PIK Program b. Profit is equal to total revenue (PQ) minus total cost. can last only as long as wheat reserves last. But PIK So profit = PQ - 200 - 2Q2. At P = 100 and Q = 25, assumes that the land removed from production can profit = $1050. be restored to production at such time as the stock- piles are exhausted. If this cannot be done, consumers c. The firm produces in the short run if its revenues are may eventually pay more for wheat-based products. greater than its variable costs. The firm’s short-run Finally, farmers enjoy a windfall profit because they supply curve is its MC curve above minimum AVC. have no production costs. Here, AVC is equal to variable cost, 2Q2, divided by quantity, Q. So, AVC = 2Q. Also, MC is equal to 4Q. 10. a. To find the price of natural gas when the price of So, MC is greater than AVC for any quantity greater than 0. This means that the firm produces in the short oil is $60 per barrel, equate the quantity demanded run as long as price is positive. and quantity supplied of natural gas, and solve 11. The firm should produce where price is equal to marginal cost so that: P = 115 = 15 + 4q = MC for PG. The relevant equations are: Supply: and q = 25. Profit is $800. Producer surplus is profit Q = 15.90 + 0.72PG + 0.05PO, Demand: Q = 0.02 - plus fixed cost, which is $1250. 1.8PG + 0.69PO. Using PO = $60, we get: 15.90 + 0.72PG + 0.05(60) = 0.02 - 1.8PG + 0.69(60), so the 14. a. With the imposition of a $1 tax on a single firm, all its price of natural gas is PG = $8.94. Substituting into cost curves shift up by $1. the supply or the demand curve gives a free-market quantity of 25.34 Tcf. If a maximum price of natural

ANSWERS TO SELECTED EXERCISES • 723 gas were set at $3, the quantity supplied would be b. Substituting the new price of 32.56 cents into the 21.06 Tcf and the quantity demanded would be 36.02 Tcf. To calculate the deadweight loss, we mea- supply and demand equations, we find that the U.S. sure the area of triangles B and C (see Figure 9.4). To find area B we must first determine the price on the production of sugar would decrease to 13.54 billion demand curve when quantity equals 21.1. From the demand equation, 21.1 = 41.42 - 1.8PG. Therefore, pounds, while demand would increase to 23.54 bil- PG = $11.29. Area B equals (0.5)(25.3 - 21.1)(11.29 - 8.94) = $4.9 billion, and area C is (0.5)(25.3 - 21.1) lion pounds, with the additional 10 billion pounds (8.94 - 3) = $12.5 billion. The deadweight loss is 4.9 + 12.5 = $17.4 billion. supplied by imports. In order to find the change b. To find the price of oil that would yield a free in the consumer and producer surpluses, it might market price of natural gas of $3, we set the quan- tity demanded equal to the quantity supplied, use help to redraw the graph as Figure 9(a). The gain PG = $3, and solve for PO. Therefore, QS = 15.90 + 0.72(3) + 0.05PO = 0.02 - 1.8(3) + 0.69PO = QD, or to producers is given by the area of trapezoid 18.06 + 0.05PG = -5.38 + 0.69PO, so that 0.64PO = 23.44 1 1 * (32.56 - 24)(8.2)2 + (13.54 - 8.2) and PO = $36.63. This yields a free market price of A: A = 2 natural gas of $3. (32.56 - 24) = $930 million, which is $500 million 11. a. To find the new domestic price, we set the quantity demanded minus the quantity supplied equal to 10. less than the producer gain when imports were lim- Therefore, QD - QS = (29.73 - 0.19P) - ( - 7.95 + 0.66P) = 10. 0.85P = 27.68, meaning that P = ited to 6.9 billion pounds. 32.56 cents. If imports had been expanded to 10 billion pounds, the U.S. price would have fallen by 3.44 cents. To find the gain to consumers, we must find the change in the lost consumer surplus, given by the sum of trapezoid A, triangles B and C, and rectangle D. We’ve already found the area of trapezoid A. Triangle tBria=ng12 l(e32C.56=-21 24)(13.54 - 8.2) = $228.52 million, (32.56 - 24)(25.4 - 23.54) = $79.47 m i l l i o n , a n d r e c t a n g l e D = (32.56 - 24) (23.54 - 13.54) = $856.34 million. The sum of A, B, C, and D is $2.09 billion. When imports were limited to 6.9 billion pounds, the loss in consumer surplus is $2.88 billion, meaning that consumers gain about $790 million when imports are raised to 10 billion pounds. 50 45 40 Price (cents per pound) 35 PUS ϭ 32.56 30 D A C B Pw ϭ 24 25 20 15 10 5 0 0 5 10 15 20 25 30 35 Qs ϭ 8.2 QЈs ϭ 13.54 QЈd ϭ 23.5 Qd ϭ 25.4 Quantity (billions of pounds) FIGURE 9(a)

724 • ANSWERS TO SELECTED EXERCISES c. The deadweight loss is given by the sum of the areas of triangles B and C: MCm MCc' MCc 1 B= 2 (32.56 - 24)(13.54 - 8.2) = $228.52 million and 1 C = 2 (32.56 - 24)(25.4 - 23.54) = $79.47 mil- lion. B + C = $228.52 + $79.47 = $308 million. To find the change in deadweight loss from Example 9.6, we subtract this from the original deadweight loss of $614.22 million. $614.22 million – $308 million P ϭ MR ϭ AR = $306.22 million. In other words, raising the import quota to 10 billion pounds per year reduces the dead- weight loss by $306.22 million. The gain to foreign producers is given by the area of rectangle D. When imports are lim- ited to 6.9 billion pounds, D = $836.4 million; when imports are raised to 10 billion pounds, D = (32.56 - 24)(23.54 - 13.54) = $856.34 million. Qm Qc' Qc Because the U.S. price of sugar has increased, for- FIGURE 10 eign producers are able to earn higher profits – about $19.94 million, to be exact. 12. First, equate supply and demand to determine equilib- area a, or (0.5)(200 - 100)(50) = $25 million, a loss of rium quantity: 50 + Q = 200 - 2Q, or QEQ = 50 (million $24 million. Producer surplus increases by area b, pounds). Substitute QEQ = 50 into either the supply or or (100 - 60)(10) + (0.5)(100 - 60)(50 - 10) = $12 mil- demand equation to determine price: PS = 50 + 50 = lion. Finally, because domestic production is equal to 100 and PD = 200 - (2)(50) = 100. Thus, the equilibrium domestic demand at $1, no hula beans are imported price P is $1 (100 cents). However, the world market and the government receives no revenue. The differ- price is 60 cents. At this price, the domestic quantity ence between the loss of consumer surplus and the supplied is 60 = 50 - QS or QS = 10, and domestic increase in producer surplus is deadweight loss which demand is 60 = 200 - 2QD or QD = 70. Imports equal is $12 million. the difference between domestic demand and supply, or 60 million pounds. If Congress imposes a tariff of 13. No, they would not. The clearest case is where labor 40 cents, the effective price of imports increases to $1. markets are competitive. With either design of the tax, At $1, domestic producers satisfy domestic demand the wedge between supply and demand must total 12.4 and imports fall to zero. percent of the wage paid. It does not matter whether As shown in Figure 9(b), consumer surplus before the tax is imposed entirely on the workers (shifting the the tariff is equal to area a + b + c, or (0.5)(200 + 60) effective supply curve up by 12.4 percent) or entirely (70) = 4,900 million cents or $49 million. After the tariff, on the employers (shifting the effective demand curve the price rises to $1.00 and consumer surplus falls to down by 12.4 percent). The same applies to any com- bination of the two that sums to 12.4 percent. P CHAPTER 10 S 2. There are three important factors: (1) How similar 200 are the products offered by Caterpillar’s competi- tors? If they are close substitutes, a small increase a c in price could induce customers to switch to the competition. (2) What is the age of the existing stock 100 D of tractors? A 5-percent price increase induces a b 100 smaller drop in demand with an older population of tractors. (3) As a capital input in agricultural produc- 60 tion, what is the expected profitability of the agricul- tural sector? If expected farm incomes are falling, an 50 increase in tractor prices induces a greater decline in demand than one would estimate with information 10 50 70 Q on past sales and prices. FIGURE 9(b) 4. a. Optimal production is found by setting marginal rev- enue equal to marginal cost. If the demand function is linear, P = a - bQ (here, a = 120 and b = 0.02), so that MR = a Ϫ 2bQ = 100 Ϫ 2(0.02)Q.

Total cost = 25,000 + 60Q, so MC = 60. Setting ANSWERS TO SELECTED EXERCISES • 725 MR = MC implies 120 Ϫ 0.04Q = 60, so Q = 1500. Substituting into the demand function, P = 120 Ϫ average revenue, which is equal to marginal revenue. (0.02)(1500) = 90 cents. Total profit is (90)(1500) Ϫ If Connecticut’s marginal cost increases, price will still (60)(1500) Ϫ 25,000, or $200 per week. be equal to Massachusetts’s marginal cost, total mar- ginal cost, and marginal revenue. Only Connecticut’s b. Suppose initially that the consumers must pay the quantity is reduced (which, in turn, reduces overall tax. Since the price (including the tax) that consum- quantity), as shown in Figure 10. ers would be willing to pay remains unchanged, the demand function can be written P + t = 120 Ϫ CHAPTER 11 0.02Q Ϫ t. Because the tax increases the price of each unit, total revenue for the monopolist increases 1. a. The Saturday-night requirement separates business by t, so MR = 120 Ϫ 0.04Q Ϫ t, where t = 14 cents. travelers, who prefer to return home for the weekend, To determine the profit-maximizing output with from tourists, who travel on the weekend. tax, equate marginal revenue and marginal cost: 120 Ϫ 0.04Q - 14 = 60, or Q = 1150 units. b. By basing prices on the buyer’s location, sorting is From the demand function, average revenue = done by geography. Then prices can reflect trans- 120 Ϫ (0.02)(1150) Ϫ 14 = 83 cents. Total profit is 1450 portation charges, which the customer pays for cents or $14.50 per week. whether delivery is received at the buyer’s location or at the cement plant. 7. a. The monopolist’s pricing rule is: (P Ϫ MC)/P = Ϫ1/ED, using Ϫ2 for the elasticity and 40 for price, c. Rebate coupons with food processors separate con- solve to find MC = 20. sumers into two groups: (1) customers who are less price sensitive (those who have a lower elasticity of b. In percentage terms, the mark-up is 50%, since mar- demand) do not request the rebate; and (2) custom- ginal cost is 50% of price. ers who are more price sensitive (those who have a higher demand elasticity) request the rebate. c. Total revenue is price times quantity, or ($40) (800) = $32,000. Total cost is equal to average cost d. A temporary price cut on bathroom tissue is a form times quantity, or ($15)(800) = $12,000, so profit is of intertemporal price discrimination. Price-sensitive $20,000. Producer surplus is profit plus fixed cost, customers buy more tissue than they would other- or $22,000. wise during the price cut, while non-price-sensitive consumers buy the same amount. 10. a. Pro: Although Alcoa controlled about 90 percent of primary aluminum production in the United e. The plastic surgeon can distinguish a high-income States, secondary aluminum production by recyclers patient from a low-income patient by negotiation. accounted for 30 percent of the total aluminum sup- Arbitrage is no problem because plastic surgery ply. It should be possible for a much larger proportion cannot be transferred from low-income patients to of aluminum supply to come from secondary sources. high-income patients. Therefore the price elasticity of demand for Alcoa’s primary aluminum is much higher than we would 8. a. A monopolist with two markets should pick quantities expect. In many applications, other metals, such as in each market so that the marginal revenues in both copper and steel, are feasible substitutes for alumi- markets are equal to one another and equal to marginal num. Here, the demand elasticity Alcoa faces may be cost. Marginal cost is the slope of the total cost curve, 40. lower than we would otherwise expect. To determine marginal revenues in each market, we solve for price as a function of quantity. Then we substi- b. Con: The stock of potential supply is limited. tute this expression for price into the equation for Therefore, by keeping a stable high price, Alcoa could t o t a l r e v e n u e . PNY = 240 - 4QNY, a n d reap monopoly profits. Furthermore, since Alcoa had PLA = 200 - 2QLA. Then total revenues are originally produced the metal reappearing as recycled TRNY = QNYPNY = QNY(240 - 4QNY), and TRLA = scrap, it would have taken into account in its output QLAPLA = QLA(200 - 2QLA). The marginal revenues decisions the effect of scrap reclamation on future are the slopes of the total revenue curves: MRNY= prices. Hence, it exerted effective monopolistic control 240 - 8QNY and MRLA = 200 - 4QLA. Next, we set over the secondary metal supply. each marginal revenue to marginal cost (= 40), imply- ing QNY = 25 and QLA = 40. With these quantities, we c. Alcoa was not ordered to sell any of its U.S. produc- solve for price in each market: PNY = 240 - (4)(25) = tion facilities. Rather, (1) it was barred from bidding $140 and PLA = 200 - (2)(40) = $120. for two primary aluminum plants constructed by the government during World War II; and (2) it was b. With the new satellite, Sal can no longer separate ordered to divest itself of its Canadian subsidiary, the two markets. The total demand function is the which became Alcan. horizontal summation of the two markets. Above a price of $200, the total demand is just the New York 13. No, you should not. In a competitive market, a demand function. Below a price of $200, we add the firm views price as being horizontal and equal to two demands: QT = 60 - 0.25P + 100 - 0.50P = 160 - 0.75P. Sal maximizes profit by choosing a quantity