재정학2차과제_&euml

재정학2차과제_ë

Info iconThis preview shows pages 1–18. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 14
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 16
Background image of page 17

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 18
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2010231511; 13W] KIM-lit 2%} Fill] as chap.9 4. Major League Baseball used to use what is known as a 5-3—1 system to vote for the Most Valuable Player {MVP} in each league. Each yoter gets to vote fer three different players they consider worthy of the award. Their first-place candidate gets 5 points, their second-place candidate gets 3 points, and their third-place candidate gets 1 point. Points are then added up across all voters, and the player with the most total points wins the award. Suppose there are three yoters—Neyer, Law, and Phillips—and fiye potential candidates for the award—Alex, David, Raffy, Manny, and Mario. The table below shows how each yoter ranks the candidates. Raffy is embroiled in a sub— stance abuse scandal. The “guilty” or “innocent” yerdict will come out the day before voting, and a guilty verdict will ban him from being voted on as an MVP. mum Rani- Third Best salty Refiiy' Fourth Best .‘v-lanny .‘v-Iat'to amen a. Who will win the MVP if Raffy is found innocent? IfRaffy is found innocettt. David gets Hi points [5 frotn Meyer and S frotn Law]. Ales gets 9' points [3 from each voter]. Raffy gets ?' poittts. and lvlanny gets 1 point. David wins the MVP. b. Who will win the MVP if Raffy is found guilty? IfRaffy is fouttd guilty. David still gets ll} points. But Ales now gets 1 1 points: 5 fmnt Phillips and 3 each fiatntbleyer and Law. So .fitles wins the MVP. c. What problem with consistent aggregation does this illustrate? This illustrates a violation of the independence of irrelevant alternatives. Raffy wasn‘t going to win the competition either way. but the winner changes depending on whether he is in the cotttpetition or not. T. A problem with the median yoter outcome is that it does not take into account inten- sity of preferences. Suppose that the government decided to give multiple votes to people with strong preferences, pro or con. Does this solve the problem? 1I.I"~t|'hy or why not? This does not necessarily solve the problettt of preference intensities. For example. cott- sider a vote involving a sitnple "yes" or "no" decision [as opposed to one with multiple op- tions]. If individuals are multiple votes on this issue. they will not divide the votes between "yes" and "no" in proportion to their preferences. Instead. they will sitttply cast all of their votes in favor the position they prefer. regardless of their preference intensity. There will be no change in the outcotne of the vote. Giving individuals tnultiple votes tnay help to solve the problettt of preference intensitie.t when individuals can decide to split those votes across various different initiatives. .-'-‘l. person with stmng opinions about education but only tnild preferences about building bike paths could cast all of her votes for her favorite school councilor. for example. and none of her votes for whether to build a bike path. This sort of tnechanistn has its own problems. how- ever: it provides strong incentives for strategic voting. for example. 11. Alfie, Bill, and Coco each value police protection differently. Alfie’s demand for the public good is Cl = 55— 5F, Bill’s demand is Cl = El)— 4P, and Coco’s demand is Cl = 10:)— 10P. If the marginal cost of providing police protection is $13.5,what is the so- cially optimal level of police provision? Under Lindahl pricing,what share ofthe tax burden would each of the three people pay? To answerthese questions. first rewrite each demand so that P is expressed as a function of Q.- Alfie: PA — ll— {1.29; Bill: PB— Eli — {1259 Coco: PC— ll} — fl. [9. Adding each person ‘s willingness to pay yields PA I FBI PC — 41— {1559. The left- hand side gives the marginal social benefit of providing the ch unit of the good. Setting this marginal benefit equal to the marginal cost gives the socially optimum level of provision: 41— {1559— 13.5.or Q— fill 1|.‘ifhen Q— 50. Alfie‘s marginal benefit is H — {lilfifll — 1. Similarly. Bill‘s marginal benefit is El} — {125(501— IS. and Coco‘s is H) — B. [(5-0] — 5. Ilence. Alfie‘s share ofthe tax burden under Lindahl pricing is [£115 a 14%. and Bill and Coco‘s shares are approximatel y Sfifi‘lfi and 31%. respectively. 12. Carrboro has three equal-sized groups of people: {1} type A. people consistently prefer more police protection to less; {2} type B people prefer high levels of police protec- tion to low levels and they prefer low levels to medium levels; {3} type C people prefer medium levels to low levels, which they in turn prefer by a modest amount to high levels. a. Which types of people have singlepeaked preferences? Which have multipeaked preferences? Types Aand C have single-peaked preferences. with peaks at "high" and "medium" respectively. Type B has multiple-peaked preferences. with peaks at "high" and "low" and a dip at "medium." b. Will majority voting generate consistent outcomes in this case? Why or why not? Majority voting does not usually generate consistent outcomes when some voters have preferences that fail to be single peaked. But they do happen to generate consistent out- comes in this case. If "high" and "low" are the two options on the ballot. "high" will win. since types A and B will vote for it. Similarly "high" wins when "high" and "medium" are the two options on the ballot. 1|.‘v‘hen "low" and "medium" are on the ballot. "medium" wins. since types A and C will vote for it. Finally. when all three are on the ballot. types A. and B will both vote for "high." which will therefore win. Notice that there are no cycles. so the voting outcomes are. in fact. consistent. The decisions coincide with those that would be made by a society that prefers "high" to “medium” and “medium” to "low." chap.12 12. There are two types of drivers on the road today. Speed Racers have a 5% chance of causing an accident per year, while Low Riders have a 1% chance of causing an acci— dent per year. There are the same number of Speed Racers as there are Low Riders. The cost of an accident is $12,000. a. Suppose an insurance company knows with certainty each driver’s type. What pre— mium would the insurance company charge each type of driver? The insurance company expects to pay out $11000 in claims to 5% of the Speed Rac- ers it covers. so it must collect at least 0.05[$12.000] — $000 from each one. Similarly. it must collect at least 0.01 [$ [2.000] — S [20 from each Low Rider. 0. Now suppose that there is asymmetric information so that the insurance company does not know with certainty the driver’s type. Would insurance be sold if i. drivers self—reported their types to the insurance company? Every individual would claim to be a Low Rider. bth if the insurance company sold insurance to everyone for $120. it would lose money because of the presence of Speed Racers in the population. The insurance company would quickly increase premiums. bth if it increased them by too much the Low Riders would leave the market. It cannot be deter- mined here exactly how much more than $120 the Low Riders would tolerate. as their risk aversion is not specified. As more Low Riders chose not to purchase insurance. the pool of covered drivers would include a higher and higher proportion of Speed Racers. requir- ing the insurance company to increase premiums again to coverthe claims. ii. no information at all is known about individual driver’s types? The insurance company could offer a premium that averages the expected claims. In a population of half Low Riders and half Speed Racers. the pooling premium would be [$600 ' $120131 — $3 I50. The Low Riders would have to be extremely risk averse to be willing to pay $3 60 to cover an expected loss of $120. If they [the Lo w Riders] opted out of the market. the insurance company would be back to the adverse selection problem dis- cussed above: an insured pool containing a high proportion of Speed Racers. 13. Your utility function is U: ln|[2C',l where Cis the amount of consumption you have in any given period. Your income is $40,000 per year and there is a 2% chance that you will be involved in a catastrophic accident that will cost you $30,000 next year. a. What is your expected utility? Expected utility is the sum of the expected utility in each state. Assuming consump- tion of your entire income. when income is $40,000. utility is Inffiflflflflj e [1.30; when income is $0.000. utility is ln|f20.000] a 0.0-0. Therefore. expected utility is 93(11301 ‘ 02(00012 [1.262. b. Calculate an actuarially fair insurance premium. What would your expected utility he were you to purchase the actuarially fair insurance premium? The insurance company would expect to pay 330.000 each year to 2% of its cus- tomers. so over the population it would pay 002(530000] — $600 per person. So $600 would be an actuarially fair premium. A person who purchased actuarially fair insurance would have utility in both states of lniEHflflflfl — 60011211375. c. What is the most that you would be willing to pay for insurance, given your utility function? To answerthis question. first go back to the original utility to determine how much money would yield the same utility as the expected utility of taking the risk. The wealth that would yield utility of l [.262 solves lnEEl’I’] — .Dfilntfiflflflfll ‘ .02lni20.000]. so W — explfflfilnififlflflfl] * .02lnt20.000]].-"2 2 $3 FLU-06.20. You are indifferent between the risky situation and certain wealth of 533306.20 because they yield the same utility. Therefore. you should be willing to pay 340.000 — 33306.20 — $1003.30 for insurance. 14. Billy Joe has utility of U = Inlcl, while Bobby Sue has utility of U = Nl'EWhich person is more risk averse? Which person would pay the higher insurance premium to smooth consumption? It is not obvious from looking at the two utility functions which is more risk averse. A numerical example is helpful. Consider starting from a wealth of [00 and having a 50% chance of losing 0-0. Billie .loe‘s expected utility is 13: lnflflfl] ‘ I": Infill] a 3.45. The amount of [riskless] wealth Billie .Toe would need to have to be just as well off solves InEWHJ] — 1»? Inlflflfll ‘ 13: lnElfl]. or Wm e $3l.62. Bobby Sue‘s expected utility is Hilflfllj ‘ 1*?[101-5 e 6.53. The amount of [riskless] wealth Bobby Sue would need to have to be just as well off solves (WES? — 6.53. or Was a 43.3 1. This means that Billie Joe is more risk averse than Bobby Sue. To see this. note that the 50% risk of losing 0-0 is "like" losing 6333(100 — 31.62] for Billie Joe and like losing only 56.60 for Bobby Sue: the same risk hurts Billie .Toe more. Equivalently. Billie .Toe would be willing to pay up to a 63.33 to fully insure himself. while Bobby Sue would be willing to pay only up to 56.60. 15. Chimnesia has two equally sized groups of people: smokers and nonsmokers. Both types of people have utility U = ln|[C}, where C is the amount of consumption that peo— ple have in any period. So long as they are healthy, individuals will consume their en— tire income of$15,000. lfthey need medical attention {and have no insurance}, they will have to spend $1 0,000 to get healthy again, leaving them with only $5,000 to con— sume. Smokers have a 12% chance of requiring major medical attention, while non— smokers have a 2% chance. Insurance companies in Chimnesia can sell two types of policy. The “low de ductible" {L—J policy covers all medical costs above $3,000, while the “high de- ductible" {H-j policy only covers medical costs above 00,000. a. What is the actuarially fair premium for each type of policy and for each group? The actuarially fair premium for selling an L-pol icy to smokers is given by {1. [Eff lflflflfl — $3.{}{}{}]— .1 BEHIND] — $3M}. since this is the expected amount the insur- ance company has to pay for medical care. Similarly. the actuarially fair premium for sell- ing an L-policy to nonsmokers is .flEf $10M] — $l4fl. The actuarially fair premiums for selling an Il-policy to smokers and nonsmokers are $fl.12[$lfl.flflfl — seem] — $24fl and .flEfflflflfl] — $4fl. respectively. b. If insurance companies can tell who is a smoker and who is a nonsmoker and charges the actuarially fair premiums for each policy and group, show that both groups will purchase the L—policy. fine can compute the expected utility of each group with each policy to answer this. bth there is an easier way. Since both policies are actuarially fairly priced for each group. both groups will prefer the policy that is closer to full insurance—the L-policy. Suppose th at smoking status represents asymmetric information: each individual knows whether or not they are a smoker, but the insurance company doesn‘t. c. Explain why it is impossible, at any prices, for both groups to purchase L—policies in this setting. Which groups, if any, do you expect to buy L-policies, and at what price? With asymmetric information. companies can‘t offer one price to smokers and another to nonsmokers: if. for example. the price offered to nonsmokers is lower. smokers will simply pretend to be nonsmokers. Ilence. if both groups purchase L-policies. they must both pay the same premium. and the premium must be at least [$R4fl : $ Hill-"2 — $490 or the finn will lose money when it sells to both groups. E We use a to compute the average cost of claims.] But at this high premium. nonsmokers won‘t find it worthwhile to buy in- surance. To wit. their utility fi"om no insurance is .Dfilnfliflflfli : .flElttHfi.flflfl — [H.Wie 9.594 and their utility from an L-policy with premium $490 is: .Dfilnflfififlfl —4E|'fl] : .flElnHfiflflflI— 49-0 — lflflflfll ‘ Willi] e 9.5m. The only group that would want L-policies at this [or higher] prices is smokers. And if only smokers are buying insurance. it must have a premium of at least $340 for finns to l'lflt lflfi'fl lllflllfly. d. Show that it is possible for both groups to purchase insurance, with one group buying L—policies and one group buying H—policies. Imagine offering a menu of two insurance policies: an $R4fl L-policy and a W Il- policy. We know fi"om c that nonsmokers prefer no policy to the high-priced L policy. Since a W Il-policy is actuarially fair for them. we know they prefer this policy to no policy [they value insurance]. Ilence. when offered this menu. nonsmokers will choose the cheap Il-policy. Firms will break even selling these policies to them. (in the other hand. smokers get expected utility .Efilm’ liflflfl — R40] : .l Elnl.r l iflflfl — Hill} — lflflflfl ' 1000] 2 9.53171 from the L-policy and expected utility .33 lnIfliflflfl — 4D] I .12 Iniliflflfl — 4fl— lflflm I Eflflfl] — 9.521 from the Il-policy. Ilence. when offered this menu of options. smokers will choose the hi gh-priced L-policy. Firms will break even selling these policies to them. too. chap.13 12. Lalaland is an extremely stable country with 200,000 residents, half of whom are young workers and half of whom are retirees. At the end of each “year,” the 100,000 retirees die, the 100,000 young workers retire, and 100,000 new young workers are born. Workers earn atotal of $5,000 for the year. Lalaland operates a “pay as you go" social security system, where each current worker is taxed $2,500 and the revenue collected is used to pay a $2,500 pension to each retiree. The neighboring country, Gogovia, is larger and more dynamic. Gogovia has an active stock market that Lala- landians can invest in and earn a 10% rate of return. It also has an active banking sector, which will gladly lend the Lalalandian government money, charging them 10% interest per year. Lalaland is considering moving to a system of personal accounts, where each Lalalander would take her $2,500 and invest it in Gogovian markets {and earn a much higher rate of returnl]. The government would borrow $250 million {$2,500 x 100,000] from Gogovian bankers to pay for current retirees. It would then tax retirees each year by just enough to pay the interest on this debt. Would this new system be better or worse for Lalaland? The new system would be neither better nor worse for Lalanland. In fact. it is an entirely equivalent system. The interest due on the debt would be [0% x [$25 0m] — $25 m. so taxes would have to be flint-"100.000 — $250 per retiree. This is exactly enough to offset the higher returns Lalalanders would earn in the stock market. (1}. Suppose that you had information about the amount of private savings during the .r" 1?. years before and after the introduction of the Social Security program. How might you carry out a difference—in—difference analysis of the introduction of the Social Security program on private savings? How to apply differences-in-di fferences to examine private savings would depend on the nature of the data. If one had data on only nggmgnie private savings. one could evaluate the effects of introducing Social Security by comparing changes in the US. savings rate [the dif- ference between sav'ings before and savings after Social Security was introduced] to changes in. say. the Canadian savings rate. In particular. one would compute the difference in the US. and Canadian savings rates before and after the Social Security system was introduced and the date the difference between these two differences. The validity of this estimate would rely on there being no major contemporaneous changes that affected one country bth not the other. Better data would be on imfe'viifuni levels of private savings. Then one could use the fact that some individuals E for example. certain government employees] were and still are outside the Social Security system. fine could thus compute the difierence in savings rates before and after the introduction of Social Security for individuals [ say. of a given age and income level] affected by Social Security. CIne could then compute a similar difference for similar individu- als not affected by Social security. The difference between these differences would provide an estimate of the change in private savings that was due to the introduction of Social Security. Consider an economy that is composed of identical individuals who live for two peri- ods. These individuals have preferences over consumption in periods 1 and 2 given by U = Infci] + Infflz]. They receive an income of100 in period 1 and an income of 50 in period 2. They can save as mu ch of their income as they like in bank accounts, earning an interest rate of 1 0% per period. They do not care about their children, so they spend all their money before the end of period 2. Each individual’s lifetime budget constraint is given by It":1 + C2!“ + r} = Y1 + Y2!“ + r]. Individuals choose consumption in each period by maximizing lifetime utility sub- ject to this lifetime budget constraint. a. What is the individual’s optimal consumption in each period? How much saving does he or she do in the first period? Individuals solv'e max U— ln{C'|] I ln{C2] subject to C" I (TE-"fill — lflfl I Sit-"Nil. Rearrange the budget constraint C2 — l if) I if} — l. [CI and plug into the maximand: max U— ln{C'|] I Inflfifl — MCI]. Then take the derivative and set it equal to zero: l.-"C'| — l.l.-"{lfi{i — MCI]. or 2.2CI — lfifl. So C" a Tl'f. and savings [DD — C" a 213. The optimal consumption in the second period is then if} I l.l{l{}[}— CI] — Rf}. b. How the government decides to set up a social security system. This system will take $10 from each individual in the first period, put it in the bank, and transfer it to him or her with interest in the second period. Write out the new lifetime budget constraint. How does the system affect the amount of private savings? How does the system affect national savings {total savings in society}? What is the name for this type of social security system? Individuals now solv'e max [f—lnfC‘ll I In“:le subjectto C" I (2'2.-"{l.l]— lflfl— if} I {SDI lflfl.l]].-"{l.l]. Rearranging the budget constraint giv'es C2 — lfifl — [.1le again—so the consumption levels are the same as in a. Since after-tax income is H) lower in period 1. however. this means that private savings falls by Hi per individual. Total savings is unchanged. how- ever. since the increased savings through the government exactly offsets the decreased pri- vate savings. This is an example of a funded social security system: the money needed for second period benefits is saved in the first period. c. Suppose instead that the government uses the 31D contribution from each individ— ual to start paying out benefits to current retirees {who did not pay in to a social security when they were working}. It still promises to pay current workers their 31D {plus interest} back when they retire using contributions from future workers. Simi- larly, it will pay back future workers interest on their contributions using the contri- butions of the next generation of workers. An influential politician says: “This is a free lunch: we help out current retirees, and current and future workers will still make the same contributions and receive the same benefits, so it doesn’t harm them, either." Do you buy this argument? If not, what is wrong with it? The Senator makes it seem as if we can pay benefits to current retirees without ever paying for it. bth there ‘s {usually} no such thing as a free lunch. which makes us think someone is harmed by this policy. The key observation is that this policy lowers the na- tional savings rate as compared with b. 1|.‘v‘ith lower national savings. the economy will grow less quickly. and future generations will. in fact. be worse off. 15. For each ofthe reforms listed, briefly discuss the pros and cons ofthe reform, paying attention in particular to efficiency implications {through potential behavioral re— spon ses to the change} and equity implications {who wins and who loses}. [N ote that all reforms are intended to save the system money, so you do not need to list this as a benefit.] a. In crease the number of years used to calculate benefits from 35 to 40. Increasing the number of years used to calculate benefits could lower benefit s. be- cause more low- or zero-earning years would be included in a retiree‘s average wage. To avoid this reduction in benefits. workers might choose to delay retirement so that they had 40 high-earning years included in the calculation. Wflfkflffi' who spent many years in col- lege and graduate schnnl might be mnst vulnerable. as they wnnld have had fewer full- time wnrking years by the time they reach retirement age. Similarly. wnrkers whn had snme intermptinns in their emplnyment—tn raise a family nr tn retrain fnr a new career. fnr example—alsn have tn delay retirement tn avnid inclusinn nf zern-wage nr lnw-wage yea rs. . Reduce benefits for beneficiaries with high asset levels {wealth}. Means-testing by cnnsidering asset levels wnnld increase the redistributive nature nf Sncial Security but wnnld induce snme perverse behavinr. Penple might be able tn in- crease their benefits by hiding assets by setting up trusts nr nther entities. fnr example. They might alsn change the timing nf selling snme nf their assets tn retain Sncial Security benefits. which distnrts resnnrce mnbility. an efficiency cnncem. 1|.‘v‘hile this plan may ap- pear tn benefit the less wealthy at the expense nf the wealthy elderly. it seems vulnerable tn lnnphnles and evasive behavinr. . Add new state and local government workers to the pool of covered workers {i.e., they pay payroll taxes now and receive benefits when they are old}. Brnadening the tax base tn include these wnrkers wnnld yield a net increase tn the system. Current Sncial Security participants wnnld. nvertheir lifetimes. pay in mnre than they wnnld withdraw. Therefnre. increasing the number nf wnrkers cnvered wnnld prnvide a net increase tn the cash flnw in the system. The new wnrkers wnnld stand tn lnse fi"nm this system relative tn a plan in which they had their nwn retirement accnnnts [because with Sncial Security they wnnld pay in mnre than they receive]. bth the Sncial Security system wnnld benefit. This new rule might induce snme tn exit these jnbs. bth since mnst wnrkers are cnvered by the system. they wnnld have little chnice as tn where else tn wan tn avnid this tax. . Gradually increase the normal retirement age {NRA} from 65 to TD {under current laws, the NRA will gradually rise to E? by 2022; the proposal is to speed up this process so that the NRA will be TD by 2022}. Gradually increasing the nnrmal retirement age will save the fund mnney by reducing the nnmbernf years during which retirees can cnllect. Penple whn need tn retire earlier fnr health nr physical limitatinn reasnns will be adversely affected. If they are able tn. they may attempt tn find less physically demanding wan nr they may increase private savings in nrder tn be able tn affnrd tn retire earlier. chap.19 2. The demand for rutabagas is C] = 2,000 —100P and the supply of rutabagas is C] = —100 + 200P. Who bears the statutory incidence of a $2 per unit tax on the sale of rutaba- gas? Who bears the economic incidence ofthis tax? If the tax is on the sale of rutabagas. the buyer bears the statutory incidence. since the "sticker price“ of rutabagas does not include the tax. Economic incidence is determined by relative elasticities. In this case. the quantity supplied is more responsive to a change in price. so the less elastic consumers will bear most of the economic incidence. To calculate the relative burdens. solve the equilibrium condition with and without the tax. Without the tax: 2.000 — 100P — — 100 I 200.”. Price — $71.00. With the tax. the price the supplier receives is reduced by $2.00. The equilibrium condition is 2.000 — 100P — 2001? — 2] — 100 2.000 — 100P — 200? — 500 2.500 — 300.”. Price — $51.33. The consumers‘ tax burden — [posttax price — pretax price] I tax payments by con- sumers. here $51.33 — $71.00 I 0 a $1.33. The producers‘ tax burden — [pretax price — posttax price] I tax payments by producers. here $71.00 — $51.33 I $2.00 a $01 In this case the consumer bears a larger share of the tax burden than the producer. 4. The demand for football tickets is C] = 300 — 10F and the supply of football tickets is C] = 20F. Calculate the gross price paid by consumers after a per—ticket tax of $4. Calcu— late the after-tax price received by ticket sellers. For this answer. it does not matter whether the tax is added to the price paid by the con- sumers or subtracted from the price the sellers keep. Adding it to the consumers‘ price yields demand of 360 — 101? I 4]. which is set equal to supply to yield the equilibrium after-tax price: 360 — 10F — 40 — 20F. Simplified. 320 — 30?. so base price — $10.6]r and price I tax — $14.15]r paid by con- sumers. Producers keep only $14.15]r — $4 — $10.07*. Without the tax. 360 — 10F — 20F ; 360 — 30F; the price paid by consumers and kept by sellers is $12. 13. Massive Products, Inc., is a monopolist whose cost of production is given by 10C] + Gziso its marginal cost curve—equivalently, its inverse supply curve—is given by 10 + 2G]. Demand for Massive Products’ massive products is C] = 200 — 2P. a. What price will the monopolist charge, and what profits will the monopolist earn? What will consumer surplus be? First we calculate the profit-maximizing quantity by setting marginal cost equal to marginal revenue. Marginal cost is 10 I 29. Marginal revenue can be found by solving for the inverse demand curve. P — 100 — HQ and noting that the marginal revenue curve has the same P-axis intercept and is twice as steeply sloped. Ilence. marginal revenue is 100 — Q. Setting MR — MC and solving for Q. 10I 2Q—100—Q,orEQ—00.orQ—30. Therefore. the profit-maximizing quantity is 30. and the profit-maximizing price can be found from the inverse demand curve: P — 100 — ‘xf 130] — $515. Profits are computed as the difference between total revenue and total cost. or $515 [30] — 10130] — 302 — 2.550 — 1.200 — 1.350. Consumer surplus can be computed as the area of the triangle with width (3— 30 and height 100 — R5 — 15 [the difi"erence between the P-intercept of demand and the price paid]. Computing. consumer surplus — 13.1 130 ]1 15] — 225. b. How will the monopolist’s price and profits change if atax of $15 per unit is im— posed on the buyers of the product?1 Imposing a $15 tax on buyers will change their demand curve to Q — zoo — 2IP‘ l5 1. or Q — lTfl — 2?. where P is the pretax [“sticker"] price. The new inverse demand is P — R5 — 13: Q. and the new marginal revenue is P — R5 — Q. Setting equal to marginal cost and solving gives ma 29—35 —Q,or3Q—T5.orQ—25. The profit-maximizing price is thus P— 35 — I": Q— $T2.5fl_ Profits are given by $22.51?) [25 I — lflf25] — 252 — [.312 — 325 — 937.5. c. What is the deadweight burden of the tax? To compute the deadweight burden of the tax. we look at the change in total surplus [including tax revenue as surplus]. The after-tax consumer surplus can be computed from the new demand curve: I»? [25 ]I [2.510] — l5fi_25. where 25 is the quantity purchased and [2.50 — R5 — 22.5 is the difference between the P-intercept of demand and the price paid. The tax revenue is 25Lr l 5] — 3T5. Ilence. the deadweight burden of the tax is I,r l .3 5i} 1 225] — [932.5 I l5fi_25 I 325 I — [5T5 — Hot-3.25 — lflfi_25_ 15. The city of Malaise is considering a 10% tax on the revenues of all hotelsimotels in- side the city limits. Although not completely different from hotels and motels in the nearby suburbs, the ones in Malaise have a distinct advantage in their proximity to the interesting sights and convention centers. 5o individuals will pay some premium to stay in Malaise rather than to stay nearby. Furthermore, all land is used equally well by hotelsimotels and other forms of business; any Malaise land not talten by a hotelimotel is readily absorbed by other forms of business. Mayor Maladroit calls you in to advise him on the incidence of such a tax. He is particularly concerned with who will bear this tax in the short run {one month} and the long run {five years}. a. What is the incidence of the tax in the short run? Answer intuitively, and use a dia- gram if possible. In the short run. the city hotels and motels will share the burden of the tax with their guests. From the description of the town. it appears that demand for lodging near the city center is relatively inelastic. so the businesses will be able to increase their rates without losing many customers. Ilowever. the supply of hotel and motel space is likely to be fairly inelastic too. particularly in the short run: it takes some time to convert hotels and motels to other uses. and vice versa. Graphically. both demand and supply will be steep: Ron m rates {FIFlW‘} Goneumer page film P l-lo1elJMotel Ioeepa Rooms pornlght In the short run. this tax yields very little quantity change but a significant price change. b. What is the long-run incidence? Once again, use a diagram if possible. In the long run. the number of hotel and motel rooms can be adjusted: thus. supply is more elastic. In the long run the tax incidence will fall primarily on the inelastically de- manding guests. The price kept by the firms is close to the original price. Room rates {PFIW} CDI'IEIJI'HEI' paya Gunmen P Hoteiila'lmei keeper c. How would your analysis in b change if hotelslmotels in the suburbs were perfect substitutes for those in Malaise? What would happen to tax revenues? The availability of an untaxed substitute in the suburbs would make demand more price elastic. This elasticity would have two effects on the market. First. the firms would not be able to shift the lion‘s share of the tax burden to the consumers. because if they did. visitors to the area would simply stay in the suburbs. Second. the number of rooms rented would fall. so the revenue raised by this tax would decline relative to a. chap.20 1. The marltet demand for super—sticky glue is G = 24D — BF and the marltet supply is G = —ED + 4F. a. Calculate the deadweight loss of a tax of $4 per unit levied on producers of super— sticlty glue. Dead weight loss is calculated as the area of a triangle. the height of which is the dol- lar amount of the tax and the base of which is the change in quantity purchased resulting from the tax. First. determine the change in quantity associated with this tax. 1|.‘viithout the tax. equi- librium is 24H — fiP — —fi{} I 4?. or 3TH} — lflP. Equilibrium price is El]. so equilibrium quantity is —fifl I [4 X 3’0] — [El] — Frfl— so. A tax levied on producers changes the supply function to Q — —fir| I 4E.” — 4] because the price the producers can keep from any sale is reduced by $4. Recalculating equilib- rium. 24C! — fiP— —fifl I 4P — lb. or 3 [Fr — lflP. Equilibrium price is $3 Lot}. so equilib- rium quantity is 240 — 6(31 .fifl] — 5&4. The change in quantity is fit} — 5&4 — as. so the area of the deadweight triangle is a [9.fiil’4] — [9.2. b. How does deadweig ht loss change if the tax is levied on consumers of super— sticlty glue? Intuitiver you would expect the deadweight loss to be exactly the same. The legal li- ability for the tax does not change the economic incidence of the tax. In this case. the height of the triangle is still the $4 tax. 1|Mhen the tax increases the price a consumer must pay. the new demand function is Q— 240 — fit? I 4]. The new equilibrium condition is 240 — 6P — 24 — —so I 4?, or 2T6 — lflP. Price is flint}. and quantity is —fifl[4 x 216-0] — 5&4. exactly the quantity that re- sulted when the tax was imposed on the produce r. 1'. You are a consultant to the government of Buttony. The government has decided to cut taxes on either apples, bananas, or cantaloupe, and it wants your input on which fruit would be the best choice for a tax cut. It provides you with the following informa- tion. What is your recommendation, and why? Marginal lax .‘fl arginal revenue deadweight loss (thousands of [thousands of Sales dollars per $1 dollars per $1 ("rood L'nit Price [thousands] L'nil lax additional tax} additional tax} Apples SJ Jflfl HUD 2f] 5 Bananas 52 Hit] H125 3f] 2-D Cmtaloupc 54 5f] SH] 5 H] 2-H Taxe s should be set so that the marginal dead weight burden per marginal dollar of re venue generated is equal across goods. This is not true in Buttony. The marginal deadweightburden per marginal dollar of revenue is much higher for cantaloupe [2W 1 {1 — 2 is Ell-"Ell 'JI SEEM than for the other goods. Cutting taxes on cantaloupe would be the most efficient: for a given rev- enue reduction, cutting cantaloupe tax es would reduce the deadweight loss the most. 10. The marltet demand for stuffed rabbits is Cl = 2,600 — 20F, and the government in- tends to place a $4 per bunny tax en stuffed rabbit purchases. Calculate the clearl- weightless of this tax when: a. Supply of stuffed rabbits is Cl = 400. The quantity befe re the tax is 400; the quantity after the tax is 400. 1|.‘fhen snppl y is al- ways 400 rabbits. the deadweight less ef the bunny tax is 13: [4 X 0]. er 0. There is ne change in supply. se there is ne deadweight less. b. Supply of stuffed rabbits is Cl =12P. In this case. supply is net cetnpletely inelastic. se befere-tax ancl after-tax quantities must be calculated. Befere tax: 2.600 — 20P— 12?; P— $01.25; 9— [2 X 01.25 — 015. After tax: 2.600 — 20P— l2fP—4]: 2.600 — 20P— l2P — 40 2.640 — 32?; P— 02.15; 9— 2.600 — [20 X 02.?5]— 045. The quantity change is 025 — 045 — 30. se the area ef the cleaclweight less triangle is 1»? [30 X 4] — 60. c. Explain why the deadweight less calculatiens differ between a and b. Deadweight less is caused by changes in the equilibrium quantity. In a. because sup- ply was perfectly inelastic. there was ne change in quantity. 1|I-‘r'hen quantity clees net change. the tax has caused ne clistertien. Thus. there is ne deadweight less. enly a transfer ef tneney fretn the seller te the get-'erntnent 15. The demand for snorkels in Eerhama is given by as = fibb— 3P5 and the supply of snorkels in Berhama is given by as = Ebb + 4P5. The demand for kayaks is given by Gk = Ebb — BF]: and the supply of kayaks is given by Gk = Eb + 1.5Pk. Both goods are currently untaxed, but the government of Eerhama needs to raise $5,0bb {to finance a new lighthouse} by taxing snorkels and kayaks. What tax should it levy on each ofthe two goods? If it puts a tax of r3 on snorkels. the equilibrium price will solve fiflfl — EFF — Eflfl ‘ 4TB? — 1'3]. or [2P3 — 301'} 3 41'], or PR — 25 I 3.33. The quantity of snorkels sold will be QR — Sflfl — REES I try-"3] — 31313 — Sty-"3. 1|.‘v'ith no tax. 3th} snorkels are sold. Hence. the deadweight burden of taxation is DWIR — 1.321} :19? — 1.321} [Eff-"3]. The tax revenue from the snorkel tax is: TR? _ r.st- _ Eflfl rs _ RFE'IG' The marginal DWI is thus Eff}. and the marginal revenue is 31313 — [diff-"3. A similar exercise for kayaks yields D iflk — [3'2 q, fig — [.3213 [r5 ff’fii and TR}? — rd, Qk— 4 lflrk— erg-'3. The marginal DWI. is thus fit} I 5. and the marginal revenue is 4 ll} — [Err-"5. The optimal taxes must equate the ratio of the marginal D WI to the marginal revenue: Br]. 3 6ri :3 300 916:]. ..-'3 ' 41:3— 12ri fit" [3;]. 3] 3 1 a — [3r]. 3] {1 3ri :3] = {my 3] (a:i 3] fit" [3331333er = 333:] Hence, tf-“tk— Infill-"325m — [Bi-"4W for an efficient tax. Setting taxes 1", and r3 — E [Si-"illflirkand yields total revenues 4-. or: 413:,r 43:; 33+ 300l135.-"410th _ $13334 may] Setting this equal to the $5,000 in revenue they need to raise [and solving numerically] yields r,t =10.13 and r5. = 3.33. chap.21 0. Suppose that the government introduces an Earned Income Tax Credit such that for the first $0,000 in earnings, the government pays 50¢ per dollar on wages earned. For the next $3,000 ofearnings, the credit is held constant at $4,000, and after that point the credit is reduced at a rate of 20¢ per dollar earned. When the credit reaches zero, there is no additional EITC. a. Draw the budget constraint that reflects this earned in come tax credit for a worker who can work up to 4,000 hours per year at an hourly wage of $10 per hour. The 50;: cent subsidy applies to the first $0.000 of earnings. or the first 000 hours of work. This corresponds to 3.200 hours of leisure and a consumption of $l2.000. The nest $3.000 of earnings—300 hours of labor—is untaxed. Ilence. at 2.000 hours of leisure. the worker gets a consumption of $ [5.000. The $4.000 EITC benefit is phased out gradually. disappearing after $20.000 in additional earnings. Ilence. at 000 hours ofleisure. the worker gets to consume $31.000. Cons umption $40,000 31 ,0 00 1 5,000 1 2,000 000 2,000 3,200 4,000 Leisure {hours} b. Illustrate on your graph the portions of the budget constraint where the labor sup— ply effects ofthe policy are positive, negative, or ambiguous, relative to the “no policy" status duo. Consumption $40,000 31,000 - --------- D ism“ rages work Discourages work 15.naa ; - -- X 1 2‘ D ............... ............................................ .. . I Amhl guous l-Im'ourngcs n or'k .1. 000 2.0003200 4,000 Leisure {hours} @ Suppose that you estimate the following female labor supply relation ship: Labor supplyj— —32fl I fifitafter-tax wagelj. ‘ 32fltcollege graduate 11.—[2W marri edif. where labor supply is measured in annual hours worked and wages are expressed in hourly wages. a. Interpret the coefficient on after-tax wages. What does this coefficient imply about the effect of increasing wages from $6 to $10 per hour on labor supply? The coefficient on after-tax wages is positive. indicating that a higher after-tax wage increases labor supply. The magnitude of the effect is 35: for each dollar increase in after- tax wage. all else equal. a female will work 35 more hours per year. For a $4 increase [from $5 to f [H]. that translates to 4 X 35 — 340 hours. b. What can we learn from this estimate about the income and substitution effects of wages on labor supply? This estimate does not explicitly include a measure of nonlabor income. The approach described in the text subtracts the nonwage income effect from the wage effect to isolate the substitution effect of wages on labor supply. That cannot be done here. The most we can confidently state is that the total of income and substitution effects is positive. so any negative effect on labor supply arising from the income effect is more than offset by the substitution effect. The substitution effect. which induces more work as leisure becomes more expensive. must be greater than the income effect. which induces less work as in- come increases. c. How might this coefficient estimate be biased? Explain. This estimate holds marital status and having a college degree constant. Given those controls. the coefficient of interest is ‘ 35. indicating that women who earn a higher wage work more hours. A number of other explanatory variables would have to be included to avoid bias. There is no control for family size or presence of children. and it may be the case that mothers are more likely to work part-time and to accept a lower hourly wage in exchange for work hour flexibility. It is also possible that the women who are earning the highest wages and working the longest hours are somehow different from other women. notjust in presence of children bth in chosen careers. in attitudes aboth working. or in ambition. Thus. there are a number of competing explanations for the observed correlation between wages and hours that this cross-sectional estimate cannot distinguish. 11. Why does the Earned In come Tax Credit exacerbate the marriage penalty for low-in— come workers? Euggest an alternative method of calculating the EITC that reduces this penalty. The EITC exacerbates the marriage penalty by combining both spouses‘ incomes to de- termine eligibility for the credit. Two fairly low incomes can combine to equal a total family income high enough to place the family in the phase-out portion of the EITC. In that situa- tion. adding a second income to the first puts the second income in the range of a very high marginal tax rate. This effect could result in a labor supply reduction for secondary earners in these families. To counter this effect. the EITC.‘ could be amended so that the ave rage of the two spouses‘ salaries detennined the family income. it could provide for a much longer plateau before pha se-out for two-eamer families. or it could be applied to :‘ndiw'tfmrl in- comes. regardless of marital status. ratherthan to family income. 13. You graduate from college and take a job at a consulting firm with a wage of $25 per hour. Your job is extremely flexible: you can choose to work any number of hours from 0 to 2,000 per year. a. Suppose there is an income tax of the following form: Income up to $10,000: no tax Income from 010,000—030,000: 20% tax rate Income from $30,000 up: 30% tax rate Draw a graph in hours workedlconsumption space, showing your opportunity set with and without the tax system. With the tax system in place, are there any points that you are particularly unlikely to ch oose? Why or why not? With an hourly wage of $25. the points of interest in the labor-"leisure budget con- straint will be $10000 and 400 hours of labor [ [.600 hours of leisure] and $30000 and [.200 hours of labor [000 hours ofleisure]. At leisure ofmore than [.600 hours. the slope of the budget constraint is the wage of 25; between [.000 and 000 hours of leisure. the slope is 00% of the wage. or 20; at less than 000 hours of leisure. the slope is T0% of the wage. or [15. The y-intercept will be $10000 + .0[$20.000] + .T[$20.000] — $40000. Consu mptlon 550.000 540.000 526.0(1) $10.0fl) 0 300 1.600 2.000 Lolsuro{l1:|urs]l There are no points that you are particularly unlikely to choose because the re are no sharp discontinuities or perfectly flat portions of the budget constraint. A marginal tax rate of l [or even greater!] would completely discourage work. bth there are no such tax rates in this system. 0. Say you choose to work 1,500 hours per year. What is your marginal tax rate? What is your average tax rate? Do these rates differ? Why or why not? 1|.‘vhrking [.500 hours per year would yield an income of [.500 a $25 — $3 2.500 and would put you in the highest tax bracket. with a marginal tax rate of 30%. To calculate the average tax rate. divide total taxes paid by income: the first $l0.000 of income is untaxed; the next $20000 of income is taxed at the rate of 20%. or $4.000; the remaining $2.500 is taxed at the rate of 30%. or $2.250. Total taxes are $0,250. The average tax rate is 0250-31500 2 [0.00%. The marginal tax rate is higher than the average tax rate because the progressive stmcture of' this tax system taxes the last dollar earned at the highest rate; the average tax rate includes the lower marginal rates paid on the first $30000 of income. c. Suppose th at the two tax rates are increased to 25% end 50%. What is the likely ef— fect on the labor supply of men? Wh at is the likely effect on the labor su pplyr of married women? Explain how the responses might differ between these groups, both in terms of underlying economic effects and in terms of the empirical evi— dence on labor supply responses. The 25% rate is a slight increase o1.-'er the current Efl‘tfi rate; the fifl‘fi: rate is H} per- centage points higher than the original tax rate for the higher bracket. The labor supply of men is generally thought to be inelastic: the empirical estimate of elasticity is approxi- mately —0. 1. This inelasticity suggests that the labor supply of men would be minimally affected by this change. The labor supply of married women. though. has been estimated to be much more elastic: a higher tax rate would tend to reduce their work hours by more. These predictions based on empirical evidence are supported by economic theory. Sec- ondary earners (historically. married women] face high marginal tax rates e1.-'en if they earn low wages. since the primary earner‘s income pushes the family into a higher tax bracket. This provides a strong di sincenti1.-'e to work. particularly if the secondary worker has home production alternatives such as child care. ...
View Full Document

This note was uploaded on 12/10/2010 for the course ECONOMICS 432 taught by Professor Jannett during the Spring '10 term at Brown.

Page1 / 18

재정학2차과제_ë

This preview shows document pages 1 - 18. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online