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Solutions and Activities for CHAPTER 1 WHY STUDY PUBLIC FINANCE? Questions and Problems 1. Many states have language in their constitutions that requires the state to provide for an “adequate” level of education spending. What is the economic rationale for such arequirement? There are two economic rationales for government provision of a good or service: mar- ket failure and redistribution. A market failure argument for state provision of educationwould be that an educated population benefits society generally because, for example, well-educated individuals have better job prospects and are therefore less likely to commit crimes.Each person who receives an education receives a private benefit (e.g., higher wage rate) andalso confers a positive externality on the community (e.g., lower crime rate). In the absenceof public provision of education, self-interested people would acquire less-than-optimal lev-els of education because they would not take into account its external benefit. Public educa-tion can correct this market failure. An argument can also be made that public education isredistributive because it increases the human capital of all students regardless of their indi-vidual economic status. 2. How has the composition of federal and state and local government spending changed over the past 40 years? What social and economic factors might have con-tributed to this change in how governments spend their funds? Since 1960, there has been a marked shift of federal spending away from defense spend- ing and toward spending on Social Security and health care. In 1960, defense spending ac-counted for approximately half of the federal budget, while Social Security and health carecombined accounted for about 15% of the budget. In 2001, Social Security and health carespending each exceeded defense spending, which accounted for less than 20% of total fed-eral spending. Health spending has also increased as a fraction of state and local spending, more than doubling over the last 40 years. Otherwise, the composition of the state and local spendinghas been relatively stable over that time. The increases in expenditures on Social Security and health care reflect the aging of the population. As the baby boom generation has aged, it has had a greater need for these kindsof spending. Furthermore, this generation has played an increasingly important role in thepolitical process, which has allowed them to win increases in spending directed toward theirinterests. The relative decrease in defense spending may have been influenced by the collapse of the Soviet Union and the end of the cold war. 13. Some goods and services are provided directly by the government, while others are funded publicly but provided privately. What is the difference between these twomechanisms of public financing? Why do you think the same government would useone approach sometimes and the other approach at other times? Direct public provision of a good or service occurs when the government itself produces the good or service. Police forces and military are examples of direct provision. Public fi-nancing of private provision of goods and services occurs when the government wishes toincrease the provision of a good or service, but it does not want to directly involve itself inits provision. An example is when the government hires private companies to build or repairroads, or when the government purchases military aircraft from private companies instead ofbuilding them itself. Public funding for private provision is appealing relative to direct public provision whenever the private market can produce the goods or services more efficiently than thegovernment. This is likely to be the case where there is an existing market or industry for thegood or service, especially when that market is competitive. When there is no existing mar-ket for a good or service provided by the government, or when that market is characterizedby an imperfectly competitive industry, there may be a stronger case for direct provision (although it is important to recognize that direct provision can also suffer from efficiencyfailures). There may be national security concerns related to private provision of certaingoods and services, especially those performed by the military and police forces. The gov-ernment is more likely to provide these goods and services directly. 4. Why does redistribution cause efficiency losses? Why might society choose to redis- tribute resources from one group to another when doing so reduces the overall sizeof the economic pie? Redistribution can cause efficiency losses if there are behavioral responses to the redistribution system. The government might raise money to fund redistribution by im-posing a tax on labor income, and this might cause a reduction in the labor supply.Similarly, generous unemployment benefits might induce some who are out of work toremain unemployed. Despite these possible efficiency losses, we (collectively) choose toredistribute wealth. Some reasons for redistribution are that people have a taste or pref-erence for a certain degree of economic equity; that the existence of a large or visibleunderclass is somewhat discomforting or threatening; that people are risk averse and soare willing to pay for a “safety net” in case they or their families ever need assistance;and that humans are naturally empathetic. In a country with many very poor people,redistribution from the few rich to the many poor may make the majority of peoplebetter off, even if it reduces the overall size of the pie. A democratic process maytherefore lead to the occurrence of this sort of redistribution. 5. Consider the four basic questions of public finance listed in the chapter. Which of these questions are positive—questions that can be proved or disproved—and whichare normative—questions of opinion? Explain your answer. The four basic questions of public finance: 1.When should the government intervene in the economy? The word “should” suggests that this is a question about which opinion will vary, so it is normative. 2.How might the government intervene? This question is positive. It asks: How does the government actually intervene now, and how might it intervene in the future? Onecan check whether a government might intervene in a particular way directly by ex-amining the behavior of existing and future governments. 3.What is the effect of those interventions on economic outcomes? Economic effects can be measured and thus are not a matter of opinion, so this question is positive.CHAPTER 1 / Why Study Public Finance? - 2 -4.Why do governments choose to intervene in the way they do? This is a factual (posi- tive) question. It may be difficult to directly observe the answer, but one can poten-tially learn about the motivations behind a government’s interventions by looking atpatterns of behavior over time. 6. One rationale for imposing taxes on alcohol consumption is that people who drink al- cohol impose negative spillovers on the rest of society—for example through loudand unruly behavior or intoxicated driving. If this rationale is correct, in the absenceof governmental taxation, will people tend to consume too much, too little, or the rightamount of alcohol? People demand goods primarily on the basis of their own enjoyment of that good. They tend to underweight the impact of their consumption on the well-being of others. In the ab-sence of taxes on alcohol, people will tend to consume too much of it. That is, they will tendto consume more than they would if they took the harm they cause others into account. 7. What is the role of the Congressional Budget Office? Why is independence and impar- tiality important when conducting empirical analyses? The CBO provides economic analyses of proposed legislation, particularly estimates of the cost of proposed projects. To do this accurately and to provide the best possible advice toCongress, the CBO must carefully consider all the economic effects of a proposal. A politi-cally motivated CBO might be tempted to understate some costs or overstate others in orderto influence legislation. 8. In order to make college more affordable for students from families with fewer resources, a government has proposed allowing the student of any family with less than $50,000in savings to attend public universities for free. Discuss the direct and possible indi-rect effects of such a policy. This policy would make college cheaper for students from families with less than $50,000 in savings. There would be two direct effects of this policy. First, it would make thefamilies of students who already intended to attend college better off if the families that weresaving had less then $50,000 in savings. Second, it would probably encourage additional stu-dents from low-savings families to attend college. A potential indirect effect of this policywould be to reduce the savings of other families—families that were saving money for a col- lege education but would stop doing so when they could anticipate getting a free ride if theydon’t save. 9. The country of Adventureland has two citizens, Bill and Ted. Bill has a private legal busi- ness. He earns $50 per hour. At a tax rate of 0%, Bill works 20 hours. At a 25% tax rate heworks only 16 hours, and at a 40% tax rate he works only 8 hours per week. Ted works amanufacturing job. He works 20 hours per week and earns $6 per hour, regardless of thetax rate. The government is considering imposing an income tax of either 25% or 40% onBill and using the revenues to make transfer payments to Ted. The accompanying tablesummarizes the three possible policies. Does either tax policy raise social welfare? Areeither of the policies obviously less than optimal? Explain your answers. Effects of Redistributive Policies in Adventureland 0% 25% 40% Bill’s Pre-Tax Income $1,000 $800 $400 Bill’s Taxes 0 $200 $160 Bill’s Net Income $1,000 $600 $240 Ted’s Pre-Tax Income $120 $120 $120 Ted’s Transfer Payment 0 $200 $160 Ted’s Net Income $120 $320 $280CHAPTER 1 / Why Study Public Finance? - 3 -Whether or not the policies raise social welfare depends on the society’s taste for redis- tribution. Indeed, either of the policies makes Ted better off and makes Bill worse off thanthe status quo of no taxes, so if society deems it sufficiently important to redistribute to Ted,then either policy would raise social welfare. If society cares about only the “size of the pie,”however, then both policies would lower social welfare. Whenever society deems that im-proving Ted’s income by $200 improves social welfare more than reducing Bill’s income by$400 harms social welfare, the 25% tax policy raises social welfare and is the optimal policy.The 40% tax policy can never be optimal, since the 25% tax policy makes both Bill and Tedbetter off than the 40% tax policy. Advanced Questions 10. In the United States, the federal government pays for a considerably larger share of social welfare spending (that is, spending on social insurance programs to help low-income, disabled, or elderly people) than it does for K–12 education spending. Simi-larly, state and local governments provide a larger share of education spending and asmaller share of welfare spending. Is this a coincidence, or can you think of a reasonfor why this might be so? Local control is often considered more important for education than for other services because there may be regional variations in curriculum preferences—whether to teach thetheory of evolution, for example. There may be fewer regional variations in preferences re-lated to social programs, however, so people may be more willing to give up local controlover these programs. Another possible explanation for federal control of social welfare pro-grams is jurisdiction “shopping.” If social insurance benefits varied substantially amongstates, people might move from one to another to avail themselves of more generous benefits. 11. The urban African-American community is decidedly split on the subject of school vouchers, with their leaders comprising some of the most vocal proponents and op-ponents of increased school competition. Why do you think this split exists? This community contains a disproportionate number of poor families, with many stu- dents attending substandard schools. Proponents of the voucher system may believe that itwill allow them to send their children to better schools or that competition will encouragetheir local schools to improve in order to retain students who would have a choice of schoolsunder the voucher system. Opponents may view it as a threat to neighborhood schools, fear-ing that if students take their vouchers and leave, inner-city schools may become even moreimpoverished. Philosophically, some proponents believe that market competition can solve awide variety of problems, while some opponents are suspicious of the market system—atleast as applied in the context of education—possibly viewing it as an institution that favorsthose with more money to spend in the marketplace. 12. Many states have constitutional requirements that their budgets be in balance (or in surplus) in any given year, but this is not true for the U.S. federal government. Whymight it make sense to allow for deficits in some years and surpluses in others? Time-series graphs illustrate one striking reason to allow for deficits: during World War II the federal government spent far more than it took in. Like a family, a government some-times faces unforeseen emergencies that require it to borrow. Had the United States beenconstrained by a balanced budget requirement at the time of World War II, the outcome ofthe war might have been very different. The family metaphor is relevant for a second reason:CHAPTER 1 / Why Study Public Finance - 4 -borrowing allows an entity to pay over time for a durable good that is being consumed over time. It makes sense for most families to take out a mortgage to purchase a home, becausethat purchase delivers benefits over many years. Similarly, many government investmentsyield long-term benefits. Surpluses and deficits may also have beneficial macroeconomic ef-fects, such as helping to stabilize a volatile economy. 13. Proper hygiene, such as regular hand-washing, can greatly limit the spread of many diseases. How might this suggest a role for public interventions? What kinds of pub-lic interventions might be possible? Suggest three distinct types of possible interven-tions. Individuals tend to ignore the external costs they impose on others by failing to wash their hands frequently enough (or by failing to employ other sorts of hygienic practices).This suggests that they tend to wash their hands less than optimally and that there may there-fore be a role for public interventions. One possible intervention would be a requirement thatindividuals wash their hands after using restrooms. (Such regulations are imposed for em-ployees at businesses, for example.) A second possible intervention is public provision ofhand-washing facilities. This would reduce the cost of hand-washing, thereby encouragingindividuals to engage in that activity more frequently. A third possibility would be an adver-tising campaign to encourage hand-washing. In-class Projects or Demonstrations Federal Budget Shares and Positive vs. Normative Questions 1. How does the federal government allocate its budget? On the first day of class (before most students have read the text), ask students individu- ally or in small teams to allocate 100 “points” among the federal budget categories, showingthe proportion of the budget they think is actually spent on each category. This is a positive question; initial guesses can be verified against the data in the text. 2. How “should” federal government dollars be spent? After the first exercise, ask small groups of students to set an “ideal” budget (again based on 100 points so that their allocations can be easily translated into percentages), thenrequire each team to justify its allocations. Part of this exercise forces students with differingpriorities to negotiate over the 100 points. The exercise also encourages them to use eco-nomic theory to justify their allocations. Students can investigate the effects of these decisions at www.budgetsim.org/nbs/ shortbudget06.html. CHAPTER 1 / Why Study Public Finance - 5 -1Solutions and Activities for CHAPTER 2 THEORETICAL TOOLS OF PUBLIC FINANCE Questions and Problems 1. The price of a bus trip is $1 and the price of a gallon of gas (at the time of this writ- ing!) is $3. What is the relative price of a gallon of gas, in terms of bus trips? Whathappens when the price of a bus trip falls to 75¢? A commuter could exchange 3 bus trips for 1 gallon of gas (both will cost $3), so the relative price of a gallon of gas is 3 bus trips. At 75¢ per bus trip, the relative price of a gal-lon of gas has increased to 3 ÷ 0.75 = 4 bus trips. 2. Draw the demand curve Q = 200 – 10 P. Calculate the price elasticity of demand at prices of $5, $10, and $15 to show how it changes as you move along this linear de-mand curve. One way to sketch a linear demand function is to find the x (Q) and y (P) intercepts. Q = 0 when P= $20. When P= 0, Q = 200. Solving for P= $5, Q = 200 – 10(5) = 200 – 50 = 150. Similarly, solving for P= $10, Q = 200 – 10(10) = 100. And solving for P= $15, Q = 200 – 150 = 50. Price elasticity is the percent change in the quantity purchased divided by the percent change in price. To calculate these percentage changes, divide the change in each variable byits original value. Moving in $5 increments: As Pincreases from $5 to $10, Q falls from 150 to 100. Therefore, Pincreases by 100% (5/5) as Q falls by 33% (50/150). Elasticity = –0.33/1.00 = –0.33. As Pincreases from $10 to $15, Q falls from 100 to 50. Pincreases by 50% (5/10) as Q falls by 50% (50/100). Elasticity = –0.5/0.5 = –1.0.0Price 200 50 100 150$20 $15$10 $5 QuantityAs Pincreases from $15 to $20, Q falls from 50 to 0. Pincreases by 33% (5/15) and Q increases by 100% (50/50). Elasticity is –1.0/0.33 = –3.03. Even though the magnitude of the change remains the same (for every $5 increase in price, the quantity purchased falls by 50), in terms of percentage change elasticity of demandincreases in magnitude as price increases. 3. You have $100 to spend on food and clothing. The price of food is $5 and the price of clothing is $10. a. Graph your budget constraint. The food intercept ( y in the accompanying figure) is 20 units. If you spend the entire $100 on food, at $5 per unit you can afford to purchase 100/5 = 20 units. Similarly, theclothing intercept ( x) is 100/10 = 10. The slope, when food is graphed on the vertical axis, will be –2. b. Suppose that the government subsidizes clothing such that each unit of clothing is half-price, up to the first 5 units of clothing. Graph your budget constraint in thiscircumstance. This budget constraint will have two different slopes. At quantities of clothing less than or equal to 5, the slope will be –1 because 1 unit of food costs the same as 1 unitof clothing ($5). At quantities of clothing greater than 5, the slope will be –2 (ifgraphed with food on the y-axis), parallel to the budget constraint in a. The point where the line kinks, (5,15), is now feasible. The new x-intercept (clothing intercept) is 12.5: if you purchase 5 units at $5 per unit, you are left with $75 to spend. If you spend it allon clothing at $10 per unit, you can purchase 7.5 units, for a total of 12.5 units. New budget constraint (bold) and original (dashed):CHAPTER 2 / Theoretical Tools of Public Finance - 2 - 0Food (units) 10 468 220 1510 5 Clothing (units) 0Food (units) 10 12.5 520 1510 5 Clothing (units)4. Use utility theory to explain why people ever leave all-you-can-eat buffets. The theory of diminishing marginal utility predicts that the more people eat the less util- ity they gain from each additional unit consumed. The marginal price of an additional unit offood at an all-you-can-eat buffet is zero; rational consumers will eat only until their marginalutility gain from an additional bite is exactly zero. The marginal cost of remaining at the buf-fet is the value of the time spent on the best alternative activity. When the marginal benefitof that activity is greater than the marginal benefit of remaining at the buffet, diners willleave. 5. Explain why a consumer’s optimal choice is the point at which her budget constraint is tangent to an indifference curve. Consumers optimize their choice when they are on the highest possible indifference curve given their budget constraint. Suppose a consumer’s choice is feasible (on the budgetconstraint) but not at a tangency, as at point Ain the accompanying figure. Under these cir- cumstances, the budget constraint must pass through the indifference curve where it inter-sects the chosen point. There must then be at least a segment of the budget constraint thatlies above (up and to the right of) the indifference curve associated with that choice. Anychoice on that segment would yield higher utility. Only when no part of the budget constraintlies above the indifference curve associated with a consumer’s choice are no feasible im-provements in utility possible. The single tangency point ( C in the figure) is the only point at which this occurs. 6. Consider the utilitarian social welfare function and the Rawlsian social welfare func- tion, the two social welfare functions described in Chapter 2. a. Which one is more consistent with a government that redistributes from rich to poor? Which is more consistent with a government that does not do any redistribu-tion from rich to poor? The Rawlsian social welfare function is consistent with redistribution from the rich to the poor whenever utility is increasing in wealth (or income). The utilitarian social wel-fare function can also be consistent with a government that redistributes from the rich tothe poor, for example, if utility depends only on wealth and exhibits diminishing marginalutility. However, the Rawlsian social welfare function weights the least-well-off moreheavily, so it will generally prescribe more redistribution than the utilitarian social welfarefunction. b. Think about your answer to a. Show that government redistribution from rich to poor can still be consistent with either of the two social welfare functions. If utility depends only on wealth and exhibits diminishing marginal utility, and if effi- ciency losses from redistribution are small, then both the utilitarian and Rawlsian socialwelfare functions can be consistent with government redistribution. A simple example can CHAPTER 2 / Theoretical Tools of Public Finance - 3 - Good y Good xA Cillustrate this point. Suppose that utility as a function of wealth is expressed as v= √w, and that a rich person has wealth of $100 (yielding utility of 10) and a poor person haswealth of $25 (yielding utility of 5). The sum of utilities is 10 + 5 = 15. Tax the wealthy person $19; their remaining wealth is $81, yielding utility of 9. Give $12 of the $19 to the poor person; this yields wealth of 25 + 12 = $37. The square root(utility) of 37 is greater than 6, so total utility is now greater than 15, even with the effi-ciency loss of $7 ($19 – $12). Under the Rawlsian function, which considers only theleast-well-off person’s utility, social welfare has increased from 5 to greater than 6. 7. Since the free market (competitive) equilibrium maximizes social efficiency, why would the government ever intervene in an economy? Efficiency is not the only goal of government policy. Equity concerns induce govern- ment to intervene to help people living in poverty, even when there are efficiency losses. Ineconomic terms, a society that willingly redistributes resources has determined that it is will-ing to pay for or give up some efficiency in exchange for the benefit of living in a societythat cares for those who have fewer resources. Social welfare functions that reflect this will-ingness to pay for equity or preference for equity may be maximized when the governmentintervenes to redistribute resources. 8. Consider an income guarantee program with an income guarantee of $6,000 and a benefit reduction rate of 50%. A person can work up to 2,000 hours per year at $8 perhour. a. Draw the person’s budget constraint with the income guarantee. A person will no longer be eligible for benefits when he or she works 1,500 hours and earns $12,000 (guarantee of $6,000/50%). b. Suppose that the income guarantee rises to $9,000 but with a 75% reduction rate. Draw the new budget constraint. Benefits will end under these conditions when earned income is $9,000/.75 = $12,000, just as shown in a. The difference is that the all-leisure income is higher, but theslope of the line segment from 500 hours of leisure to 2,000 hours of leisure is flatter.CHAPTER 2 / Theoretical Tools of Public Finance - 4 - 0Consumption (dollars) 500 2,000$6,000$16,000 $12,000 Leisure (hours/year) 0Consumption (dollars) 500 2,000$16,000 $12,000 $9,000 Leisure (hours/year)c. Which of these two income guarantee programs is more likely to discourage work? Explain. A higher income guarantee with a higher reduction rate is more likely to discourage work for two reasons. First, not working at all yields a higher income. Second, a personwho works less than 1,500 hours will be allowed to keep much less of his or her earnedincome when the effective tax rate is 75%. With a 75% benefit reduction rate, the effec-tive hourly wage is only $2 per hour (25% of $8). 9. A good is called normal if a person consumes more of it when her income rises (for example, she might see movies in theaters more often as her income rises). It iscalled inferior if a person consumes less of it when her income rises (for example, she might be less inclined to buy a used car as her income rises). Sally eats out at thelocal burger joint quite frequently. The burger joint suddenly lowers its prices. a. Suppose that, in response to the lower burger prices, Sally goes to the local pizza restaurant less often. Can you tell from this whether or not pizza is an inferior goodfor Sally? You cannot. Since Sally eats at the burger joint quite a bit, falling burger prices imply that she is richer. If this was the only effect, you could indeed conclude that pizza is an in-ferior good—Sally gets richer and buys less pizza. But there is also a substitution effecthere: the relative price of pizza has gone up. This leads her to substitute away from pizza.If the substitution effect is bigger than the income effect for Sally, then she could respondin this way, even if pizza is a normal good. b. Suppose instead that, in response to the lower burger prices, Sally goes to the burger joint less often. Explain how this could happen in terms of the income andsubstitution effects by using the concepts of normal and/or inferior goods. The substitution effect says that when the relative price of burgers falls, Sally should consume more of them. Since she actually consumes less of them, the income effect mustbe working in the opposite direction, leading her to consume fewer burgers (and it mustbe stronger than the substitution effect). Since the fall of burger prices made Sally richer,burgers must be an inferior good for Sally. (Note: A good for which falling prices leads toreduced consumption is known as a Giffen good.) Advanced Questions 10. Consider an income guarantee program with an income guarantee of $3,000 and a benefit reduction rate of 50%. A person can work up to 2,000 hours per year at $6 perhour. Alice, Bob, Calvin, and Deborah work for 100, 333¹/ 3, 400, and 600 hours, respec- tively, under this program. The government is considering altering the program to improve work incentives. Its proposal has two pieces. First, it will lower the guarantee to $2,000. Second, it willnot reduce benefits for the first $3,000 earned by the workers. After this, it will reducebenefits at a reduction rate of 50%. a. Draw the budget constraint facing any worker under the original program. The budget constraint for the original program is depicted in the graph that follows. With zero hours worked (2,000 hours leisure), a worker gets to consume $3,000—theguaranteed income level. After 1,000 hours of work, the benefits have been reduced tozero (50% of $6,000 in income).CHAPTER 2 / Theoretical Tools of Public Finance - 5 -b. Draw the budget constraint facing any worker under the proposed new program. The budget constraint for the proposed program is depicted in the following graph. At zero hours of work (2,000 hours of leisure), the worker now only gets to consume thelower $2,000 guarantee. She can work for up to 500 hours without any benefit reductions,so if she works for 500 hours, she gets to consume $5,000 (= $2,000 + $6/hr ×500 hrs) and has 1,500 hours of leisure. After working an additional 2,000/3 ≈666.67 hours, for a total of about 1,133.33 hours of work or 833.33 hours of leisure, she will be receiving nobenefits. (Her benefits have been reduced by 50% ×$6/hr ×2,000/3 hrs = 50% ×$4,000 = $2,000.) The dashed line also depicts the original budget constraint. c. Which of the four workers do you expect to work more under the new program? Who do you expect work less? Are there any workers for whom you cannot tell ifthey will work more or less? Workers working fewer than 500 hours see their hourly wage effectively doubled under the plan. The substitution effect therefore tends to make Alice, Bob, and Calvin allwork more. One can calculate that the two budget constraints cross at 333 ¹/3hours ofCHAPTER 2 / Theoretical Tools of Public Finance - 6 - 0$3,000$6,000$12,000 2,000 1,000 Leisure (hours)Consumption (dollars) 0$2,000$7,000$12,000 2,000 833.33 Leisure (hours) 1,500Consumption (dollars) $5,000 1,666.67work, or 1,666.67 hours of leisure. The income effect is thus different for these three workers. Alice was working less than 333 ¹/3hours under the old policy, so the policy change effectively makes her poorer. She consumes less of all normal goods, includingleisure, so this also makes her work more. We can unambiguously conclude that she willwork more. Bob was working exactly 333 ¹/3hours, so he feels no income effect. We can conclude from the substitution effect alone that he too will work more. Calvin was work-ing more than 333 ¹/3hours before, so this policy change effectively makes him richer. He will therefore tend to work less due to the income effect. We cannot tell if the substitutioneffect or the income effect is stronger, so we cannot tell if Calvin will work more or less.Finally, Deborah was working 600 hours before. Under both policies, the effective wageof someone working this many hours is $3/hr (since 50% of income is offset by reducedbenefits). There is no substitution effect for her. As the graph shows, however, she experi-ences an increase in income. We conclude that she will work less. 11. Consider a free market with demand equal to Q= 1,200 – 10 Pand supply equal to Q= 20P. a. What is the value of consumer surplus? What is the value of producer surplus? The first step is to find the equilibrium price and quantity by setting quantity demanded equal to quantity supplied. Recall that the condition for equilibrium is that it is the price atwhich these quantities are equal. From Q = 1,200 – 10 Pand Q = 20P, substitute: 1,200 – 10 P= 20P. Adding 10 Pto each side of the equation yields 1,200 = 30 P. Dividing both sides by 30 yields P= 40. If Q = 20P, then in equilibrium Q = 20(40) = 800. Consumer and producer surplus are determined by finding the areas of triangles; area is equal to ½ the base times the height. The vertical intercept is the price at which quantity demanded is zero: 0 = 1,200 – 10 P. This solves to 120. Consumer surplus = ½ (800)(120 – 40) = ½ (800)(80) = 32,000. Producer surplus = ½ (800)(40) = 16,000.Total surplus = 48,000.CHAPTER 2 / Theoretical Tools of Public Finance - 7 - 0Price 800$120 $40Supply Demandb. Now the government imposes a $10 per unit subsidy on the production of the good. What is the consumer surplus now? The producer surplus? Why is there adeadweight loss associated with the subsidy, and what is the size of this loss? A subsidy in effect lowers the cost of producing a good, yielding the bold supply line. The new supply function is Q = 20( P+ 10) because the producer receives the price plus $10 when it produces. Solving for a new equilibrium, 20P+ 200 = 1,200 – 10 P. 30P = 1,000.P= $100/3 ≈$33.33; Q = 20 (100/3 + 10) = 2,600/3 ≈866.67. Consumer surplus = ½ (2600/3)(120-100/3) ≈37,555.56. Producer surplus = ½ (100/3 + 10)(2,600/3) ≈18,777.78. Cost of subsidy = 10(2600/3) ≈8,666.67. Total surplus = consumer surplus + producer surplus – cost of subsidy ≈47,666.67, less than the original 48,000. There is efficiency loss because trades are induced for which the actual resource cost (without the subsidy) is greater than consumer willingness to pay. The deadweight loss is thearea of the triangle that encompasses these new trades (the shaded area in the graph, pointingto the original equilibrium): ½ (2,600/3 – 800)(10) ≈333.33. 12. Governments offer both cash assistance and in-kind benefits, such as payments that must be spent on food or housing. Will recipients be indifferent between receivingcash versus in-kind benefits with the same monetary values? Use indifference curveanalysis to show the circumstances in which individuals would be indifferent and sit-uations in which the form of the benefits would make a difference to them. Generally recipients can attain a higher level of utility (they can choose a consumption bundle on a higher indifference curve) when they are given cash rather than a specific good.People who would purchase the same amount of food or housing as the in-kind grant pro-vides would be indifferent between in-kind and cash benefits because they would use thecash to purchase the same items. However, people whose preferences would lead them topurchase less food or housing than the in-kind grant provides would prefer to receive cash.That way they could spend some of the cash on food or housing and the rest on the othergoods they prefer. Suppose the government provides the first ten units of food at no cost.The person represented in panel (a) of the following graph would prefer cash. The indiffer-ence curve tangent to the extension of the new budget constraint identifies a consumptionbundle that includes less than ten units of food. The person represented in panel (b) wouldchoose the same point given cash or food. The optimal consumption bundle includes morethan ten units of food.CHAPTER 2 / Theoretical Tools of Public Finance - 8 - 0Price 800 867$120.00 $40.00$43.33 $33.33Suppl y Demand13. Consider Bill and Ted, the two citizens in the country of Adventureland described in Problem 9 from Chapter 1. Suppose that Bill and Ted have the same utility functionU(Y) = Y 1/2,where Yis consumption (which is equal to net income). a. Rank the three tax policies discussed in Problem 9 from Chapter 1 for a utilitarian social welfare function. Rank the three for a Rawlsian social welfare function. The utility function is increasing in income. Rawlsian social welfare is therefore equal to the utility of the individual with lower income. For 0% and 25% tax rates, Ted has thelower incomes ($120 and $320, respectively). For a 40% tax rate, Bill has the lower in-come ($240). Since $320 > $240 > $120, Rawlsian social welfare is highest under the25% tax rate and lowest under the 40% tax rate. To compute utilitarian social welfare, wecompare: Utilitarian social welfare with a 0% tax = 1,000 1/2 + 1201/2≈42.58 Utilitarian social welfare with a 25% tax = 6001/2 + 3201/2 ≈42.38 Utilitarian social welfare with a 40% tax = 2401/2 + 2801/2≈32.33 We see that the 0% tax rate is best. b. How would your answer change if the utility function was instead U(Y) = Y1/5? This change does not affect the order of tax rates according to the Rawlsian social welfare function. To compute social welfare for the utilitarian social welfare function wecompare: utilitarian social welfare with 0% tax = (1000) 1/5 + 1201/5≈6.59. utilitarian social welfare with 25% tax = 6001/5 + 3201/5 ≈6.76. utilitarian social welfare with 40% tax = 2401/5 + 2801/5≈6.08. We see that the 25% tax rate is best and the 40% tax rate is the worst. c. Suppose that Bill and Ted instead have different utility functions: Bill’s utility is given by UB(Y) = ¼ Y1/2, and Ted’s is given by UT(Y) = Y1/2. (This might happen, for example, because Bill has significant disabilities and therefore needs more incometo get the same level of utility.) How would a Rawlsian rank the three tax policiesnow? Since the two have different utility functions, it is no longer easy to see who is better off under each situation. Under the 0% tax policy, we see that Ted has utility 1201/2≈ 10.95 and Bill has utility ¼ 1,0001/2≈7.91. We see that Bill is worse off under this policy.CHAPTER 2 / Theoretical Tools of Public Finance - 9 - Other goods 10 FoodOther goods 10 Food(a) (b)Since the other two tax policies make Bill worse off and Ted better off than the 0% policy, Bill’s utility will be used to compute Rawlsian social welfare. Rawlsian social welfare ishighest with 0% taxes and lowest with 50% taxes, the policies that make Bill the best andworst off, respectively. 14. You have $3,000 to spend on entertainment this year (lucky you!). The price of a day trip ( T) is $40 and the price of a pizza and a movie ( M)is $20. Suppose that your utility function is U(T,M) = T1/3M2/3. a. What combination of Tand Mwill you choose? This question can be solved by students who have taken calculus, following the ap- proach described in the appendix to the chapter. The constrained optimization problem can be written as Max T1/3(M)2/3subject to $3,000 = 40 T+ 20M. Rewriting the budget constraint as M = 150 – 2 Tand substituting into the utility function gives Max T1/3(150–2 T)2/3. Taking the derivative with respect to Tand setting equal to zero gives 1/3 T–2/3(150 – 2 T)2/3– 4/3 T1/3(150 – 2 T)–1/3 = 0. Rearranging gives (150 – 2 T) = 4 T, or T= 150/6 = 25. Plugging back into the budget constraint gives M= 150–2 (25) = 100. You take 25 trips and go on 100 movie-and-a-pizza outings. b. Suppose that the price of day trips rises to $50. How will this change your decision? The new constrained optimization problem can be writtenMax T 1/3(M)2/3subject to $3,000 = 50 T+ 20M. Rewriting the budget constraint as M = 150 – 2.5 Tand substituting into the utility func- tion gives Max T1/3(150 – 2.5 T)2/3 Taking the derivative with respect to Tand setting equal to zero gives 1/3 T–-2/3(150 – 2.5 T)2/3– 5/3 T1/3(150 – 2.5 T)–1/3 = 0. Rearranging givesCHAPTER 2 / Theoretical Tools of Public Finance - 10 - Effects of Redistributive Policies in Adventureland 0% 25% 40% Bill’s Pre-Tax Income $1,000 $800 $400 Bill’s Taxes 0 $200 $160 Bill’s Net Income $1,000 $600 $240 Ted’s Pre-Tax Income $120 $120 $120 Ted’s Transfer Payment 0 $200 $160 Ted’s Net Income $120 $320 $280(150 – 2.5 T) = 5 T, or T= 150/7.5 = 20. Plugging back into the budget constraint gives: M= 150 – 2.5(20) = 100. You now take 20 trips and go on 100 movie-and-a-pizza outings.CHAPTER 2 / Theoretical Tools of Public Finance - 11 -1Solutions and Activities for CHAPTER 3 EMPIRICAL TOOLS OF PUBLIC FINANCE Questions and Problems 1. Suppose you are running a randomized experiment and you randomly assign study participants into control and treatment groups. After making the assignments, youstudy the characteristics of the two groups and find that the treatment group has alower average age than the control group. How could this arise? Random draws do not guarantee that the average of all demographic and other variables will be exactly the same for groups, although if the size of the groups is large, they shouldconverge to the same value. One reason the average ages might differ in this experiment isthat the samples are too small. Imagine tossing a coin 10 times. You would expect to get ap-proximately 5 heads and 5 tails, but you would not assume that your coin was biased if youinstead got 6 or 7 heads. However, if you tossed the coin a very large number of times andgot heads in 60% or 70% of the tosses, you would tend to conclude that the coin was biased.The law of large numbers says that the more times a fair coin is tossed, the closer the per-centage of heads will tend to be toward 50%. Similarly with the groups from the randomizedexperiment: it is possible for the average age of the treatment and control groups to be quitedifferent if the sample size is small, but as the sample size gets larger, these differencesshould disappear. 2. Why is a randomized trial the “gold standard” for solving the identification problem? If participant assignment to the treatment group and the control group is truly random and the groups are large enough, it is statistically unlikely that membership in one group orthe other will be biased in a way that is related to the question being studied. On average, thetwo groups will have the same characteristics. This would not be true if subjects were al-lowed to choose their own groups, because people with certain traits in common may bemore or less likely to select a given group. 3. What do we mean when we say that correlation does not imply causality? What are some of the ways in which an empirical analyst attempts to disentangle the two? Correlation merely means that two events tend to occur together; causality means that one event causes the other. Correlation can occur when a third event causes both of the otherevents. For example, ice cream consumption and air-conditioning use tend to happen to-gether. They are correlated, but their relationship is not causal. A third event, hot weather,causes the other two events. The point of much empirical work is to control for possiblevariables that might cause other events (that are not causally related) to occur together. Ran-domized trials, regression analysis of data that include control variables, and quasi-ex-peri-ments are all ways to investigate causal relationships by controlling for other possiblemechanisms that might influence the variables of interest.4. A researcher conducted a cross-sectional analysis of children and found that average test performance of children with divorced parents was lower than average test per-formance of children of intact families. This researcher then concluded that divorce isbad for children’s test outcomes. What is wrong with this analysis? This is a clear example of using correlation to infer causality. Perhaps the causality is re- versed: it could be that parents of children who perform poorly on tests feel stressed, whichleads to higher divorce rates, or a third variable might explain both events: perhaps residencein a close-knit community both enhances scholastic performance and deters divorce. In ei-ther case, we would observe lower scores among children with divorced parents, but in nei-ther case would the divorced parents be the cause of the lower scores. In assessing the results of any study, researchers should consider all possible explanations for what was ob-served and then control for alternative explanations. 5. A study in the Annals of Improbable Research once reported that counties with large numbers of mobile home parks had higher rates of tornadoes than did other counties.The authors conclude that mobile home parks cause tornado occurrences. What is analternative explanation for this fact? This conclusion illustrates another obvious confusion of correlation with causation. Per- haps tornadoes are more frequently reported for neighborhoods with mobile home parks be-cause even a very small tornado will damage a mobile home, but tornadoes may not dodamage (and thus go unreported) in a neighborhood with masonry or wood homes (the ThreeLittle Pigs theory). Perhaps people who have more resources are better able to choose saferlocations to live in, leaving “tornado alley” neighborhoods to mobile home residents. Torna-does occur much more frequently in some parts of the country than in others; perhaps theseareas also have a higher share of mobile home parks. 6. What are some of the concerns with conducting randomized trials? How can quasi- experiments potentially help here? Randomized trials are expensive: the validity of each study relies on the law of large numbers, and the greater the number of participants needed, the more expensivethe data. It may be possible to run trials only by recruiting voluntary participants forthem. If the people who respond to recruiting efforts differ in some way from the restof the population, the results of the experiments may be unrepresentative of effects onthe population at large. Attrition can also pose problems. It may be impossible to pre-vent some participants in a study from leaving town or otherwise ceasing to participate.If this attrition is nonrandom, it can undermine the initial randomization of the experi-ment and lead to biased results. Human subject approval is required to subject peopleto experimental practices, since subjecting individuals to intrusive or dangerous proce-dures can raise serious ethical concerns. Quasi-experiments allow researchers to takeadvantage of naturally occurring changes. For example, tax laws change periodically.Researchers can observe behavior before and after a tax-law change to investigate itseffects. In some instances, where every taxpayer in a jurisdiction is affected by achange, there are sufficient numbers of participants to create a valid experimental pool.And there is no need to divide the participants into control and treatment groups be-cause the date of the change divides the sample. Similarly, some changes in laws affectone group of people but not another group; thus, the legal distinction may create acontrol (unaffected) group and a treatment (affected) group. 7. You are hired by the government to evaluate the impact of a policy change that affects one group of individuals but not another. Suppose that before the policy change,members of a group affected by the policy averaged $17,000 in earnings and mem-bers of a group unaffected by the policy averaged $16,400. After the policy change,CHAPTER 3 / Empirical Tools of Public Finance - 2 -members of the affected group averaged $18,200 in earnings while members of the unaffected group averaged $17,700 in earnings. a. How can you estimate the impact of the policy change? What is the name for this type of estimation? The question here is one of differences in changes: both groups experienced a change in earnings, but it is not immediately obvious whether either group experienced a biggerchange. The appropriate approach to estimate the impact on each group is called a differ-ence-in-differences approach. Treatment group difference: $18,200 – $17,000 = $1,200 Control group difference: $17,700 – $16,400 = $1,300 Thus, we estimate that the impact of the policy change was to lower earnings by $100. b. What are the assumptions you have to make for this to be a valid estimate of the impact of the policy change? The essential assumption you have to make is that trends in earnings would have been the same for the two groups had there been no policy change. If, for some reason, onegroup would have experienced larger income growth than the other in the absence of thepolicy change, then the difference in difference estimate will be biased. 8. Consider the example presented in the appendix to this chapter. Which coefficient es- timates would be considered “statistically significant” or distinct from zero? There are two ways to determine at a glance whether a coefficient is statistically distinct from zero. The first way is to consider whether zero falls in the range bounded by two standarderrors less than the estimate and two standard errors greater than the estimate. The second wayis to divide the coefficient estimate by the standard error. If the quotient is approximately two orgreater, the estimate can be considered statistically significant. By these standards, the estimatedcoefficient for the indicator, or dummy, variable “Black” is not distinct from zero; neither are theestimated coefficients for living in a central city, another urban area, or a rural area. All of theother variables pass this test of statistical significance: White, High School Dropout, HighSchool Graduate, Some College, Age, TANF, and the constant term. 9. A researcher wants to investigate the effects of education spending on housing prices, but she only has cross-sectional data. When she performs her regressionanalysis, she controls for average January and July temperatures. Why is she doingthis? What other variables would you control for, and why? This researcher has access to very limited data and would like to control for the charac- teristics of the location of the housing stock. Housing prices reflect, among other things, thedesirability of house location, and the researcher thinks that climate must affect desirability.She is unable to use historical prices to look at changes in price for a single location overtime because she has only cross-sectional data, so she must use the data she has to controlfor systematic differences. Examples of other variables she could include are: local unem-ployment rates, average population age, number of school-age children, etc. 10. It is commonly taught in introductory microeconomics courses that minimum wages cause unemployment. The federally mandated minimum wage is $5.15, but approxi-mately 1/3 of states have higher state-mandated minimum wages. Why can’t you testthe “minimum wages cause unemployment” theory by simply comparing unemploy-ment rates across states with different minimum wages? Can you think of a betterway to test it? The problem with this test is that all states are not the same. Different states have popu- lations with different characteristics and different preferences. Some of these characteristicsCHAPTER 3 / Empirical Tools of Public Finance - 3 -may be related to both the choice of the state-level minimum wage and the unemployment level. For example, consider states with a large number of people who have taken an eco-nomics course. People in these states may be inclined to favor low minimum wages (basedon what they were taught in their introductory micro class) and also may find it very easy toget a job (they have studied economics, after all!). This would lead us to observe a relation-ship between unemployment rates and minimum wages across states even without any of thedirect causation suggested by economic theory. A better way to test this would be to look at how unemployment rates changed after a new minimum wage law was passed in one state compared with the change in unemploy-ment rates in a nearby state that did not change its law. This is the approach taken, for exam-ple, in Card and Krueger (1994). Advanced Questions 11. Suppose that your friend Oscar has collected data and determined that towns with newly constructed high schools tend to have higher SAT scores than other towns. Hetells you that he has proved that new high schools cause higher SAT scores. Whenyou object that “correlation does not imply causation,” he is ready with more data. Heshows you convincing evidence that SAT scores tend to increase shortly after townsbuild new high schools, but that there is no tendency for new high schools to be builtin towns that have recently seen large increases in SAT scores. Is this enough evi-dence to prove that new high schools cause higher SAT scores, or can you think ofan alternative explanation for Oscar’s data? The timing evidence is certainly more convincing than simple correlations—and it strongly suggests that SAT scores do not cause new schools to be built. However, there arealternative explanations to the conclusion that new schools cause higher SAT scores. For ex-ample, consider a town that has recently experienced a wave of “yuppification”—a numberof young, well-educated couples have recently moved to what was traditionally a more blue-collar town. As these new couples have children who begin to approach high school age,they may vote to raise taxes to build a new school for their children. Their children—thechildren of well educated parents—are likely to do well on their SATs. This story would thuslead to the pattern Oscar found in these towns: a new high school gets built shortly beforethe children of better-educated parents begin to take their SATs. But in this story, the newschool does notcause better SAT scores. 12. Researchers often use panel data (multiple observations over time of the same peo- ple) to conduct regression analysis. With these data, researchers are able to comparethe same person over time in order to assess the impacts of policies on individual be-havior. How could this provide an improvement over cross-sectional regressionanalysis of the type described in the text? Panel data sets allow researchers to control for attributes of a person that do not change over time. For example, it is particularly hard to obtain data about attitudes, preferences forleisure, familial or cultural values, and the like, but these traits are likely to be fairly stable inadults. Therefore a researcher can control for these unobservable, or unmeasurable, influ-ences on behavior by using panel data. In effect, the researcher can hold the person’s under-lying preferences and attitudes constant while observing their responses to policy over time. 13. Suppose that your state announced that it would provide free tuition to high- achieving students graduating from high school starting in 2007. You decide to seewhether this new program induces families with high-achieving children graduating in2007 or later to purchase new cars. To test your findings, you use a “falsification CHAPTER 3 / Empirical Tools of Public Finance - 4 -exercise”: you observe the new-car-purchasing behavior of families with children graduating in 2006. Why is this a useful exercise? Suppose that you had found large increases in new-car purchases amongst students grad- uating high school starting in 2007. While it is suggestive, this does not necessarily implythat the increases in new-car purchases are a result of the new program. There may be otherreasons for increased new-car purchases that happened to occur at the same time—for exam-ple, a price war amongst car manufacturers. The “falsification exercise” can help to rule outmany of these other explanations. For example, if the falsification exercise “works,” you willnot observe any change in the new-car purchases by families of 2006 graduates. This helpsto rule out things like “price wars” that would affect families of 2006 graduates as well asfamilies of 2007 graduates. It therefore makes you more confident that the increase in new-car purchases was a result of the policy, not of something else. Conversely, if the falsifica-tion exercise “fails” and you observe a similar increase in new-car purchases by families of2007 graduates, you would have to re-think your results. The falsification exercise wouldsuggest to you that something other than the policy was driving changes in car purchases.Either way, the falsification exercise helps you to better understand your results. 14. Your state introduced a tax cut in the year 1999. You are interested in seeing whether this tax cut has led to increases in personal consumption within the state. You observe the following information: a. Your friend argues that the best estimate of the effect of the tax cut is an increase in consumption of 30 units, but you think that the true effect is smaller, becauseconsumption was trending upward prior to the tax cut. What do you think is a bet-ter estimate? Prior to the tax cut, there was a steady increase in consumption of 10 units every two years. If that trend had continued, and there had not been a tax cut, you might have pre-dicted that consumption in 2000 would be 330. The actual consumption was 350, so an ar-gument could be made that the additional increase of 20 units can be attributed to the taxcut, over and above the general trend. b. Suppose that you find information on a neighboring state that did not change its tax policy during this time period. You observe the following information in thatstate: Given this information, what is your best estimate of the effect of the tax cut on consumption? What assumptions are required for that to be the right estimate ofthe effect of the tax cut? Explain. This new information suggests that growth in consumption would have been even greater than the past trend indicates even if there had been no tax cut. We can make use adifference in difference estimate, using the neighboring state as a control.CHAPTER 3 / Empirical Tools of Public Finance - 5 - Year Consumption in neighboring state 1994 260 1996 270 1998 280 2000 300Year Consumption in your state 1994 300 1996 310 1998 320 2000 3501998-2000 difference in consumption in your state: 30 1998-2000 difference in consumption in neighboring state: 20Difference in difference estimate: 30-20=10 We therefore estimate that the tax cut increased consumption by 10 units. For this estimate to be correct, it must be the case that the trends in the two states would have been the same except for the tax cut in your state. This is suggested by thecommon trends prior to the tax cut, but the common trend before doesn’t guarantee thatthe common trend would have continued. Other consumption-affecting policy changes im-posed at the same time as the tax cut, in either state, could make the estimates incorrect,for example. Or there may have been a sudden employment boom in the neighboring statethat did not affect your state (a large company decided to build a new plant there, for ex-ample). The difference in difference estimate relies on no such sudden changes occurringin state-specific consumption trends. Activities and Projects Understanding and interpreting empirical data takes practice, as does identifying alternative ex-planations for apparent relationships among variables. Following are some ways of developingthese skills: 1.Ask students to name several pairs of phenomena that are correlated, and then ask them to decide whether they are causally related and if so the direction of that causality. This taskcan be jump-started with some examples: • Wages and gender, race, or ethnicity • Crime rates and race or ethnicity, which could segue into a discussion of profiling• Geographic location and socioeconomic variables (for example, the prevalence of high- poverty states in the South) 2.Ask students to brainstorm possible explanations for puzzling correlations (possibly from pairs named in the previous exercise) and then to determine what evidence or data couldbe used to eliminate or bolster some of those explanations. 3.A number of articles in the labor economics literature use control variables in fairly trans- parent ways to explain the gender gap in wages. Examples from this literature could beused to illustrate empirical techniques. See, for example, “Trends in the Well-Being ofAmerican Women: 1970–1995” by Francine Blau, Journal of Economic Literature (March 1998).CHAPTER 3 / Empirical Tools of Public Finance - 6 -1Solutions and Activities for CHAPTER 4 TOOLS OF BUDGET ANALYSIS Questions and Problems 1. We say that a variable is cyclical if it increases with economic booms and declines with economic recessions. We say that a variable is countercyclical if the opposite is true. Which elements of the U.S. federal budget are cyclical and which are counter-cyclical? (To get a sense of the main elements of the budget, visitwww.whitehouse.gov/omb/budget/fy2007/pdf/hist.pdf, Tables 2 [for revenues] and 3[for expenditures].) For fun, you could also check out Nathan Newman and AndersSchneiderman’s National Budget Simulator at www.budgetsim.org/nbs/shortbud-get06.html, where you can experiment with what might happen to the federal budgetunder various taxation and spending scenarios. Many categories of federal revenue are cyclical. For example, both the personal income tax and the corporate income tax tend to move with the economy: during a downturn, indi-viduals and corporations have lower tax burdens, and during boom times their tax burdensincrease. Revenue from excise and other taxes on consumption (such as import taxes and gifttaxes) also increase during particularly prosperous (high consumption) times and decreaseduring downturns in the economy. In contrast, there are a number of expenditure categories that tend to be countercyclical. Examples include human services, which includes some income-support payments. Thesepayments tend to rise during a recession, as more people become unemployed. Payments tobail out struggling companies or to honor insurance commitments (Federal Depository Insur-ance for banks, for example) also tend to increase during bad economic times. 2. How have the major federal laws to promote balanced budgets lost their effectiveness over time? The Gramm-Rudman-Hollings act was a major federal law designed to promote bal- anced budgets. It set annual targets for federal deficit spending and included a provision forautomatic spending cuts if the targets were not met. In practice, the law was rendered inef-fective because, for example, deficit targets were simply reset when it became clear that thetargets were not going to be met. The Budget Enforcement Act tried to promote balanced budgets by setting caps on the amount of discretionary spending that could take place in future years. Recently, the capshave been avoided by making use of the provision in the law that allows for unlimited“emergency” spending beyond the cap. Such “emergency” spending has been used for fi-nancing spending for nonemergency purposes. 3. Suggest one way in which generational imbalances might be understated and one way in which they might be overstated. Calculated generational imbalances suggest that our current deficit will be balanced on the backs of future generations, to their detriment. These imbalances might be understated, inwhich case they will be even worse than anticipated for the next generation, if assumptions about continued growth are too optimistic; if the actual interest rate is less than the assumedrate of 3.6%; or if future policies entail higher expenditures than anticipated. The imbalances might be overstated if assumptions about continued growth are too pes- simistic; if the actual interest rate is greater than the assumed rate; if the quality of life of fu-ture generations (possibly including their economic productivity) is enhanced byexpenditures made today; or if demographic shifts or policy changes result in lower expendi-tures than anticipated. 4. What is the intuition behind the notion of Ricardian equivalence? How might you look for evidence to test the suggestion that people account for future generations’ taxburdens by saving more today? According to the theory of Ricardian equivalence, whenever there is a deficit, the current generation realizes that it is paying less in taxes than is being spent by the government. Theyrealize that this will result in a heavier tax burden on future generations than there would beif they were paying enough taxes to balance the current budget. To reduce this intergenera-tional inequity, the current generation saves more than they would if their taxes were higher.This will mean that children will inherit the means to pay higher taxes later. If this theorywere accurate, individuals would respond to lower taxes (for the same levels of governmentexpenditures) by raising their savings rate. To investigate whether the theory is accurate,then, one could look at how private savings rates have changed when new tax cuts (or tax in-creases) were passed. 5. From 1962 to 1965, federal spending on non-defense-related education and training rose from $9.6 billion to $19.5 billion, while from 2002 to 2005, it rose from $196.0 bil-lion to $232.1 billion. Given that the Consumer Price Index (in January) was 30.0 in1962, 31.2 in 1965, 177.1 in 2002, and 190.7 in 2005, which period saw the larger in-crease in education and training spending? Despite the large nominal numbers in the early part of this millennium, the real increase during the 1960s was greater, as illustrated in the following table: 6. Why does the Congressional Budget Office construct a cyclically adjusted budget deficit for the purposes of monitoring federal income and outlays? A number of factors can cause short-run fluctuations in tax collections and expenditures; for example, an economic downturn can temporarily reduce tax collections while increasingexpenditures on income-support programs. These fluctuations have only short-term effectson the budget, however, and given the nature of business cycles, they will be offset by eco-nomic growth cycles when tax revenues are temporarily high and social expenditures low.Removing these ups and downs from the deficit calculation provides a better long-term pic-ture of revenues and expenditures. 7. The federal government is considering selling tracts of federally owned land to private developers and using the revenues to provide aid to victims of an earthquake in a foreign country. How would this policy affect the levels of federal revenues, CHAPTER 4 / Tools of Budget Analysis - 2 - e 1962 1965 Difference 2002 2004 Difference Nominal $9.6b $19.5b $9.9b $196.0b $232.1b $36.1b CPI 30.0 31.2 177.1 190.7 Real (divide by CPI/100) $62.5b $32b $30.5b $110.7b $121.7b $11.0bexpenditures, and deficits under a cash accounting system? What would be different under a capital accounting system? Under a cash accounting system, there would be no effect on the current level of the deficit. Revenue would increase by the amount of the sale, but the revenue increase wouldbe exactly offset by the increased expenditures on foreign aid. A capital accounting systemwould recognize that the government has sold off a valuable asset. It would therefore regardthe policy as increasing the overall deficit. The capital account deficit would be unchanged:the additional revenue from the sale would be offset by the decrease in the value of assetsheld by the government. The cash account would move towards deficit as a result of the in-creased consumption expenditures. 8. A government is considering paving a highway with a newly developed “wear-proof” material. Paving the highway would cost $2 billion today, but it would save $300 mil-lion in maintenance costs for each of the next 10 years. Use the concept of presentvalue to determine whether the project is worth undertaking if the government canborrow at an interest rate of 5%. Is it worth it if the interest rate is 0%? 10%? A politi-cian says to you, “I don’t care what the interest rate is. The project is clearly a goodinvestment: it more than pays for itself in only 7 years, and all the rest is money in thebank.” What’s wrong with this argument, and why does the interest rate matter? As the following table shows, the project is worth undertaking at 0% and 5% interest, but it is not worth undertaking at 10%. The politician’s argument is incorrect because it failsto take into account the interest the government must pay on the money borrowed to financethe project. 9. Table 4-1 in the textbook shows the remarkable difference across generations in their likely net tax payments to the federal government. What is responsible for these largeintergenerational differences? The generational accounting used to generate Table 4-1 assumes that our current deficit will be paid for by future generations. Specifically, this accounting sets current plus futuretax payments equal to the current debt plus future government consumption. Future tax pay-ments will need to be sufficient to pay off the current deficit as well as to pay for the com-mitments the government has made to the current generation, including the commitment tomake Social Security and Medicare payments when that generation retires. The baby boomgeneration will require high government expenditures when they retire. Those commitmentsplus current deficit spending (which benefits the current generation) mean that future taxpayments will have to be high to keep this account in balance. Thus the tax burden of futuregenerations will be greater than the benefits they are predicted to receive.CHAPTER 4 / Tools of Budget Analysis - 3 - r= 0% r= 5% r= 10% Initial Costs –$2b –$2b –$2b Savings, year 1 .3b 0.2857 b 0.2727 b Savings, year 2 .3b 0.2721 b 0.2479 b Savings, year 3 .3b 0.2592 b 0.2254 b Savings, year 4 .3b 0.2468 b 0.2049 b Savings, year 5 .3b 0.2351 b 0.1863 b Savings, year 6 .3b 0.2239 b 0.1693 b Savings, year 7 .3b 0.2132 b 0.1539 b Savings, year 8 .3b 0.2031 b 0.1400 b Savings, year 9 .3b 0.1934 b 0.1272 b Savings, year 10 .3b 0.1842 b 0.1157 b Net benefits $1b $316.5m –$156.6m