Chapter 7 – Income Redistribution: Conceptual Issues1. Utilitarianism suggests that social welfare is a function of individuals’ utilities. Whetherthe rich are vulgar is irrelevant, so this part of the statement is inconsistent with utilitarianism. O n the other hand, Stein’s assertion that inequality per se is unimportant is inconsistent with utilitarianism.2. a. To maximize W, set marginal utilities equal; the constraint is I s + I c = 100.So,400 - 2I s = 400 - 6I c.substituting I c = 100 - I s gives us 2I s = 6 (100 - I s ).Therefore, I s = 75, I c = 25.b.If only Charity matters, then give money to Charity until MU c = 0 (unless all themoney in the economy is exhausted first).So,400-6 I c = 0; hence, I c = 66.67.Giving any more money to Charity causes her marginal utility to become negative,which is not optimal. Note that we don’t care if the remaining money ($33.33) isgiven to Simon or not.If only Simon matters, then, proceeding as above, MU s. 0 if I s = 100; hence, givingall the money to Simon is optimal. (In fact, we would like to give him up to $200.)c.MU s = MU c for all levels of income. Hence, society is indifferent among alldistributions of income.3. The main conceptual problem with the poverty gap is that it doesn’t account fo r theincome effect on labor force participation rates. The poverty gap is calculated assuming there are no behavioral responses; e.g., that labor income would remain unchanged even after the income was transferred to the poor population, but economic theory predicts that this will not be so. In fact, if the poor household were given enough income to bring it out of poverty, we would believe that the household would work less as a result of receiving this transfer. This complicates the analysis, of course, because once the household works less, then it will generate less labor income, thus lowering its overall income. This means that the poverty gap actually understates the amount of money necessary to alleviate poverty in the United States. In addition, the poverty gap is based on the official poverty line, which is thought to be an ad-hoc measure of the true “needs”of a family.4. A day care center is an example of an in-kind compensation. The figure below is similarto Figure 8.2 in the text. The original budget line is G1 H1 If the employee received $5,000 cash, the budget line moves to G2 H2 . An employee who uses the day care center may not be $5,000 better off. The employee consumes at point A, but would be better off at point B, which represents consumption after a cash transfer of $5,000.5. a. This would increase the incomes of the providers of computer equipment and theindividuals who maintain the equipment. In the long run, this might also increasethe incomes of the students who use the equipment. Moreover, giving a laptop toall seventh graders (rather than poor seventh graders) may simply “crowd-out”computer transfers from parents to children. One could imagine that nowadaysmany children do have a computer at home, paid for by the parents. Thisgovernment transfer may simply result in less parental transfer to the child.b.Providing free after-school programs for children in impoverished families largelyacts as an in-kind transfer for poor, working households. The program is of littlevalue for unemployed households, as the alternative would be childcare at home.For those who are employed, and paying for childcare, this program provides analternative and effectively changes the after-tax, after-working-cost wage. Thisalso may affect work behavior on the extensive margin. The likely “losers” fromsuch a program are childcare providers, who see a reduction in demand for theirservices. In principle, this reduction in demand could lower the hourly childcarecost for all workers with children, though this effect is likely to be modest becausemost impoverished families do not have a very large labor force attachment and,thus, their effect on the childcare market as a whole is likely to be small.6. a. False. Society is indifferent between a util to each individual, not a dollar to eachindividual. Imagine that U L=I and U J=2I. Then each dollar given to Jonathanraises welfare more than the same dollar given to Lynne.b. True. The social welfare function assumes a cardinal interpretation of utility sothat comparisons across people are valid.c. False. Departures from complete equality raise social welfare to the extent thatthey raise the welfare of the person with the minimum level of utility. Forexample, with the utility functions U L=I and U J=2I, the social welfare functionW=min[U L,U J] would allocate twice as much income to Lynne than Jonathan.7. Initially the price of food was $2 and the price of other goods was $1. The black marketfor food stamps changes the price of food sold to $1. In Figure 7.2 of the textbook, as one moves to the “northwest” from point F, the segment will now have a slope (in absolute value) of 1 rather than 2. The black market may make the individual better off if the best point on her budget constraint AFD was initially at the corner solution of point F, and the black market certainly does not make her worse off. It is important to note that the black market does not always make the recipient better off. If the (absolute value) of the marginal rate of substitution (MRS) were between 1 and 2, the indifference curve would not “cut” into the new part of the budget constraint with the black market.If the MRS were less than (or equal to) 1 in absolute value, the person would be made better off and would reduce food consumption by selling the food stamps on the black market.Food StampGuarantee Food8. Pareto efficient redistribution is a reallocation of income that increases (or does notdecrease) the utility of all consumers. With these two consumers, Marsha’s utility increases as Sherry’s utility increases. Thus, it may be possible to reallocate income from Marsha to Sherry and raise both of their utility. With Sherry’s initial utility function of U S=100Y S1/2, her utility with $100 of income is U S=100($100)1/2, or U S=1,000. With Marsha’s initial utility function of U M=100Y M1/2+0.8U S, her utility with $100 of income is U M=100($100)1/2+0.8(1,000), or U M=1,800. If the social welfare function is additive, then initial welfare is W=U S+U M=1,000+1,800=2,800. If $36 is reallocated from Marsha to Sherry, then Sherry’s income is now $136 and Marsha’s is now $64. With Sherry’s utility function, her utility with $136 of income is U S=100($136)1/2, or U S=1,166.190.With Marsha’s utility function, her utility with $64 of income is U M=100($64)1/2+0.8(1,166.190), or U M=800+932.952=1,732.952. In this case, Sherry’s utility increases from 1,000 to 1,166.190, while Marsha’s utility falls from 1,800 to 1,732.952. Social welfare increases with this redistribution, going from 2,800 to 2,899.142. Thus, this redistribution increases social welfare, but is not Pareto efficient redistribution.Chapter 8 – Expenditure Programs for the Poor1. a. Note that the figure below shows the correct shape of the budget constraint, butthe numbers themselves are outdated. With a wage rate of $10 per hour,Elizabeth earns $100. Because the deduction in California is $225, none of herearnings are counted against the $645 welfare benefit. Thus, her total income is$745 (=$100+$645).b.The actual welfare benefits collected by a person equals B=G-t(Earnings-D),where B=actual benefits, G=welfare grant, t=tax rate on earned income, andD=standard deduction. Thus, (Earnings-D) is the net earnings that are taxed awayin the form of reduced benefits. When benefits equal zero (B=0), the expressionbecomes 0=G-t(Earnings-D), which collapses to: Earnings=G/t+D. This is knownas the “breakeven formula.” In the California context here, the expressionbecomes Earnings=$645/0.5 + 225, or Earnings=$1,515. With a wage rate of $10per hour, this corresponds to 151.5 hours of work per month.c.The diagram shows the correct shape of the budget constraint, but the “577” figureshould be r eplaced with “645” and the “9” hours should be replaced with “22.5”.d.The diagram above shows one possibility – in this case, Elizabeth is both workingand on welfare – but she collects a reduced welfare benefit in this case.2. One could gather data on the earnings of those in the program, as well as earnings datafrom nonparticipants. Regress the earnings variable on demographic variables and other factors that determine earnings (such as education and experience), and a variable that indicates whether the individual participated in the training program. Factors that affect local employment conditions, such as unemployment levels, may help explain earnings, but they may also explain participation in the program. The econometric strategy should be chosen carefully to account for this.3. If the quantity of leisure consumed by X appears as an argument in the utility function ofY, then X’s consumption of leisure creates an externality. If the externality is negative(i.e., Y likes X to work), then a wage subsidy of X might induce him to work the efficientnumber of hours. Alternatively, a workfare program might achieve the same goal by simply forcing X to work. However, to the extent that the feasible quantity of labor supply is determined less through market incentives now, workfare would be less efficient.4. He participates in the public housing program as long as P1P2ca cef.5. As illustrated below, the budget constraint with food stamps has a “notch” in it, similar tothe analysis of Medicaid in Figure 8.9 of the textbook. At the notch, the marginal tax rate is greater than 100%. One key difference from the figure in the textbook is that the marginal tax rate on earned income for Medicaid is 0% until the “Medicaid notch,” while the marginal tax rate on earned income for food stamps is 24% until the “food stamp notch.” The reason the food stamp notch exists at all is that there is a “gross income test,” where a recipient is ineligible if income is higher than the limit. The characterization in the Rosen textbook on page 189 that “at some point near the poverty line, food stamps worth about $1,250 are suddenly lost” implicitly assumes that childcare costs are quite high. This is likely to be true for many households. In the year 2004, this monthly (annual) gross income limit was $1,994 per month ($23,928 per year) for a family of four, while the monthly guarantee was $471 ($5,652 per year). Assuming the family had earnings at the limit of $1,994 of earnings during the month, and after applying a 20% earnings deduction and a $134 monthly standard deduction, the household would receive a monthly (annual) benefit of $32 ($384). We arrive at this number using the equation B=G-t(E-.2E-D)=471-.3(.8*1994-134)=$471-$438.36=$32.64, which is then rounded down to $32. In this case, B=actual benefits received, G=food stamp guarantee, t=tax rate, E=earnings, and D=standard deduction. Increasing annualearnings by $1 from $23,928 to $23,929 would reduce food stamp benefits from $384 to $0; hence the “food stamp notch.” This notch would be even higher if the household qualified for a childcare deduction, child support deduction, or shelter deduction. The childcare deduction ranges between $175 and $200 per child per month. Assuming this family of four consisted of a mother and three children, each with $175 of monthly childcare costs, then B=G-t(E-.2E-D-C)=471-.3(.8*1994-134-525)=$471-$280.86=$190.14, which is then rounded down to $190. The modification here is that C=childcare costs. This amount corresponds to an annual food stamp benefit of $2,280. Figure 8.5 below draws the budget constraint using annual levels for the food stamp program, using 2004 rules and assumes no childcare expenses.6. For an individual who is not working while on welfare, in this case the highestindifference curve touches the budget constraint on the right vertical axis. Note that the marginal rate of substitution (MRS) does not necessarily equal the after-tax wage rate at the time endowment – rather, it is possible that the person would want to consume more leisure than the time endowment but is obviously constrained from doing so.Leisure$23,928Leisure7.In all cases, the demand curve for housing slopes downward. a. If the price of low income housing gets bid up but there is no increase in the stock of housing, then the supply curve is perfectly inelastic, e.g., vertical.Q 0Q HOUSINGFIGURE 8.7a – Demand curve shiftsb.If there is no increase in the price of housing, but there is an increase in the stockof housing, then the supply curve is perfectly elastic, e.g., horizontal.Q 0Q HOUSINGFIGURE 8.7b – Demand curve shifts Q 1c.If there is an increase in both the price and quantity of housing, then the supplycurve slopes upward.According to Sinai and Waldfogel, there is partial crowding out, consistent with case cabove. Although the underlying housing stock itself is probably quite inelastic in the short-run, the number of rental homes can be more elastic as (potential) landlords convert vacation homes or vacant homes into rental units.8. a.When Eleanor’s hours (earnings) go from 0 to 1,000 ($0 to $8,000), she qualifiesfor an additional earned income tax credit (EITC) worth $3,200 (=0.4*8,000).Thus, her income goes up from $0 to $11,200. Note to instructors – thedistinction between earnings and income may cause confusion in the students’answers. b.When Eleanor’s hours (earnings) go from 1,000 to 1,500 ($8,000 to $12,000), shequalifies for the maximum EITC (according to Figure 8.8 in the textbook). Shereceives the full EITC when her earnings exceed $10,510, at which time the creditequals $4,204 (=0.4*$10,510). The earnings between $10,510 and $12,000 face neither a subsidy nor phase-out from the EITC. Thus, her income goes up from $11,200 to $16,204.c. When Eleanor’s hours (earnings) go from 1,500 to 2,000 ($12,000 to $16,000),she moves into the range where the EITC is phased out. According to Figure 8.8 Q 0Q HOUSINGFIGURE 8.7c – Demand curve shifts outward,Q 1in the textbook, she receives the maximum subsidy of $4,204 until her earningsexceed $14,730. For the marginal earnings between $14,730 and $16,000, theEITC is reduced at a 21.06% tax rate. Thus, her EITC falls by $267.46 from$4,204 to $3,936.54 (=4,204-0.2106*(16,000-14,730)). Her income rises from$16,204 to $19,936.54.Chapter 9 – Social Insurance I: Social Security and Unemployment Insurance1. With adverse selection, insurance contracts with more comprehensive coverage arechosen by people with higher unobserved accident probabilities. To make up for the fact that a benefit is more likely to be paid to such individuals, the insurer charges a higher premium per unit of insurance coverage.2. There are many possible implications of a voluntary Social Security system. Onepossibility is that people would save less for retirement, betting that society would not put up with having great numbers of elderly poor. Part of the effect of the Friedman program, then, would depend on the government's credibility when it promises not to bail out people who do not save enough to survive during retirement.3. Use the basic formula for balance in a pay-as-you-go social security system:t =(N b/N w)*(B/w).Call 1990 year 1 and 2050 year 2. Thent1 = .267*(B/w)1t2 = .458*(B/w)2It follows that to keep (B/w)1=(B/w)2 we require t2/t1=.458/.267=1.71. That is, tax rates would have to increase by 71 percent. Similarly, to keep the initial tax rate constant, we would require (B/w)2/(B/w)1=.267/.458=0.58. Benefits would have to fall almost by half.4. If Social Security benefits are partially taxed for those who have other income over acertain level, then there is an implicit means test in receiving full, untaxed benefits.However, there is no explicit means test for eligibility for the program. Everyone receives benefits, though some recipients must pay some tax on them. Thus, the two statements are somewhat inconsistent with each other.5. Austen’s quote seems like it could relate adverse selection, but perhaps more likely, tomoral hazard. The q uote “If you observe, people always live forever when there is any annuity to be paid them” in a sense sounds like they act differently (e.g., better diet, more exercise, etc.) when an annuity is to be paid –the idea of moral hazard. In contrast, adverse selection suggests that people who expect to live a long time to be the ones who purchase annuities. A recent paper by Finkelstein and Poterba (NBER working paper, December 2000) found that “mortality patterns are consistent with models of asymmetric inf ormation” and that annuity “insurance markets may be characterized by adverse selection.”6. Equation (9.1) relates taxes paid into the Social Security system to the dependency ratioand the replacement ratio, that is, t=(N b/ N w)*(B/w). If the goal of public policy is to maintain a constant level of benefits, B, rather than a constant replacement ratio, (B/w), then taxes may not need to be raised. If there is wage growth (through productivity), then it is possible to maintain B at a constant level, even if the dependency ratio is growing.By rearranging the equation, we can see that B=t*w*(N b/ N w)-1. That is, increases in wage rates (the second term) offset increases in the dependency ratio (the third term).Thus, constant benefits do not necessarily imply higher tax rates.7. The statement about how the different rates of return in the stock market and governmentbond market affect the solvency of the trust fund is false. If the trust fund buys stocks, someone else has to buy the government bonds that it was holding. So, there is no new saving and no new capacity to take care of future retirees.8. Diamond and Gruber’s calculations suggest that the additional year of work (and delayedretirement) lowers the present discounted value of expected Social Security wealth by $4,833. If the adjustment were actuarially fair, Social Security wealth would neither rise nor fall. Since wealth falls, the adjustment is actuarially unfair.9. For those who argue that the scheme for financing Social Security is unfair becausepeople with low earnings are taxed at a higher rate than those with high earnings, the key issue is that the cumulative payroll tax of 12.4 percent is capped for each person, after which the payroll tax is zero (this ignores the 2.9 percent uncapped Medicare tax, however). The earnings ceiling in 2004 is $87,900. Hence, Social Security payroll taxes as a share of earnings fall after the ceiling is passed – thus, the Social Security payroll tax may be thought of as regressive. The opponents to this view note that the above analysis only focuses on taxes paid, not benefits received. As shown in Table 9.3, Social Security redistributes from high earners to low earners, and the formula for the primary insurance amount offers extremely high replacement rates to very low earners, and much lower replacement rates to high earners. Thus, the net tax payment(taxes minus benefits) is likely to be progressive, not regressive. One critical assumption in this kind of analysis is how one computes lifetime benefits –e.g., do we assume that low earners and high earners live the same number of years?10. Let G stand for the individual’s gross earnings. The question assumes that the personfaces a marginal tax rate of 15% and a payroll tax of 7.45%. Thus, the person’s after-tax earnings (denoted by N) are N=(1-t earn-t payroll)G, or N=(1-0.15-0.0745)G, or N=0.7755G.It is assumed that the gross unemployment benefits, U, are equal to 50 percent of before-tax earnings, or U=0.5G. Net unemployment benefits, B, take out income taxes, so B=(1-t earn)U=(1-t earn)0.5G=(1-0.15)0.5G=0.425G. The percentage of the individual’s after-tax income that is replaced by UI is therefore equal to B/N, or 0.425G/0.7755G, which is approximately 54.8%.Unemployment benefits are about 55% of the individual’s previous after-tax income. The effects of unemployment insurance on unemployment area matter of considerable debate. While the high replacement rates from UI may increasethe duration of unemployment, the longer search time may reduce recurrence of unemployment by allowing time for a worker to find a better job match. Empiricalstudies seem to show that the hazard rate into employment spikes up around the time that benefits run out – perhaps suggesting that job matches are not really improving.Chapter 10 – Social Insurance II: Health Care1. The quotation contains several serious errors. First, concern with health care costs doesnot mean that health care is not a “good.” Economists do not care about the cost of health care per se. Rather, the issue is whether there are distortions in the market that lead to more than an efficient amount being consumed. Second, it makes a lot of difference how money is spent. One can create employment by hiring people to dig ditches and then fill them up, but this produces nothing useful in the way of goods and services. Thus, employment in the health care sector is not desirable in itself. It is desirable to the extent that it is associated with the production of an efficient quantity of health care services.2. a. Those who have a relatively high probability of needing the insurance are the oneswho are most likely to buy it. This raises the premium, which in turn, leads toselection by people who have an even higher probability of using it. The cyclecontinues until the price is so high that virtually no one purchases the policy.b.Employer-provided health insurance is deductible to the employer and not taxed tothe employee.c.Because of the tax subsidy, individuals may purchase more than the efficientamount of health insurance. That is, they “over-insure.” An interesting exampleof how the tax system leads to overinsurance is given in a recent Wall StreetJournal (January 19, 2004) article by Martin Feldstein. He gives an example oftwo different California Blue Cross health plans – identical in all respects exceptfor the deductible and annual premiums. The low-deductible plan (the “generous”plan) has a deductible of $500 per family member, up to a maximum of two andan annual premium of $8,460. Thus, the maximum out-of-pocket expense is$1,000. The high-deductible plan (the “less generous” plan) has a deductible of$2,500 per family member, up to a maximum of two, and an annual premium of$3,936. Thus, the maximum out-of-pocket expense is $5,000. Note that thepremium savings of $4,524 actually exceeds the maximum incremental deductiblepayment of $4,000 (which would only occur if the family had very high healthexpenses). In principle, the high deductible plan is unambiguously better. But thetraditional tax rules could lead an employer to choose the low deductible policy.If the employee faced a marginal tax rate of 45% (the sum of federal, state, andpayroll tax rates), then if the $4,524 premium saving was turned into taxablesalary, the individual’s net income would only rise by $2,488. Thus, families withhigh expected medical expenses do better with the “generous” plan, even though itis more costly in terms of premiums.3. a. D d=4.22–(0.044)(50)=2 visits per year.Total expenditure =(2)(50)=$100b.Now the individual pays only $5 per visit.D d = 4.22 – (0.044)(5) = 4 visits, with out-of-pocket costs of $20.Insurance company pays ($45)(4) = $180Total expenditure = $200, double its previous level.4. Examining Figure 10.1, we can see why health care costs increased for the state ofTennessee. As insurance coverage increases, this lowers the cost of medical expenses for those who were previously did not have insurance, which increases the overall amount of medical services they consume. Before receiving insurance, these people demand M o units of medical services, and the amount they pay is represented by the area OP o aM o.But after receiving insurance coverage, they demand M1amounts of medical services, paying only OjhM1, while their insurance pays jP o bh. The increase in insurance payments is sizable for two reasons – first, by providing coverage, it pays for the majority of the already sizable medical expenses incurred by this group, and second, the introduction of insurance makes the group consume even more medical services. In short, if the people who designed the Tennessee program had realized that the demand curve for medical services is downward sloping, they would not have been surprised at the consequences of their program.To explain why HMOs have been unable to contain long-run health care costs, it is necessary to consider the effect of technology on health care costs in the long-term. The inherent problem is that the market for medical care places a large premium on using the latest and most-developed medicines and machinery for treating patients. These technologies tend to be expensive. Hence, while introducing HMOs can lead to a once and for all decrease in the rate of change in health care costs, there is nothing that an HMO can do to lower the cost of continually providing the latest in medical treatments. 5. The goal of making the Medicare prescription drug benefit a one-time, permanentdecision is to reduce the adverse selection problem (no te: the current “Medigap”program operates in this manner to some extent – a senior citizen has choice over all 10 of the Medigap plans for only a short period of time after they turn 65, after which they may be denied based on their health). Imagine a cohort of people turning age 65 and becoming eligible for the Medicare drug benefit. If the decision to enter (or exit) could be made every year, then healthy senior citizens would have a strong incentive to wait until they became unhealthy and needed drugs, and then enter the prescription drug program (presumably resulting in economic losses for the program). Similarly, when people who were collecting the prescription drug benefit became healthy, they would have a strong incentive to “opt-out” of the prog ram. By making the decision opt-in at the beginning or not at all, the healthy younger seniors are likely initially cross-subsidizing the older seniors. Note that this “opt-in at the beginning” works because bad health and older age are positively correlated with each other. If, for example, younger seniors used more drugs (and perhaps older seniors used more inpatient care, etc.), then older seniors could simply stop paying annual premiums and give up their option of being in the program. If this scenario held empirically, this would exacerbate the adverse selection problem and the opt-in scenario would not completely solve the adverse selection problem.6. The budget constraint initially has units of Medigap on the x-axis, and other goods on they-axis. Given initial prices of $1 per unit for each good, and $30,000 of income, the budget constraint has a slope of -1, and the intercepts on both axes are at 30,000 units. It is assumed that the initial utility maximizing bundle consumes 5,000 units of Medigap, hence the indifference curve is tangent at (5000,25000). All of this is illustrated in the figure below.Medigapefficiency units30,000 5,000After the “minimum Medigap” mandate, the consumer can either choose 0 units of Medigap or 8,000 or more units of Medigap. Thus, part of the budget constraint is eliminated (though the overall shape remains the same as before). After the mandate, the point (0,30000) is available, as well as all of the points to the southeast of the point (8000,22000). Clearly, the person’s utility must fall since the preferred choice, (5000,25000) is no longer available. If the person attains a higher level of utility as (0,30000) compared with (8000,22000), the person chooses to not purchase Medigap. In this case, the marginal rate of substitution is no longer equal to the price ratio. This is illustrated below.Medigapefficiency units30,000 5,000 8,000。
