Relax. Stop, take a deep breath, and think carefully before you answer any questions. Good luck!

Transcription

1 Midterm Exam #2; Page 1 of 5 Economics 441 Professor Scholz Midterm #2, Version #2 Brief Answers April 11, 2006 You have 75 minutes to complete the exam, which consists of 9 questions (and 75 points). Point totals (and the amount of time you should spend on each question) are given with the question. If you have a question during the exam, stay seated and please raise your hand. To show respect to your fellow students, please stay seated in your exam seat for the full 75 minutes. Please turn in the exam and answer sheet when you leave the room. Relax. Stop, take a deep breath, and think carefully before you answer any questions. Good luck! 1, (10 points): Consider a society of identical workers that each earn a wage W when they work. Each worker faces a 0.2 probability of sustaining an injury. If they sustain an injury, they have 1 no earnings (W=0). Workers have utility of the form: U = ln( C), where C=consumption=total 2 income in the period (they do no saving). Assume there is no moral hazard. Suppose that the government introduces a disability insurance program. Under this system, individuals pay some fraction of their wage when they are employed (i.e., their wage is taxed at a certain rate), and get a benefit when they are disabled. The system must break even at a point in time; that is, the benefits paid to disabled workers must be equal to the taxes collected from employed workers. What is the optimal disability insurance system? That is, what is the system that, subject to the constraint of breaking even, maximizes worker utility? Present both the tax rate and the benefit level for the system. Taxes equal.8*t*w, while benefits equal.2*b, and taxes must equal benefits. Therefore, b=4tw. The optimization problem looks like 1 1 du.8*.5 W.2*2W MaxU = max.8ln( W (1 t)) +.2ln( 4 tw ) = + t =.2 and b =.8W t t 2 2 dt.5 W (1 t) 2tW 2, (15 points): The superhero profession is a dangerous business. Every year, in fact, there is a probability p that a given superhero will be caught by a ruthless supervillain, who inflicts damage that requires $200 in medical costs to heal. Being a superhero doesn t pay well, but fortunately, superheros receive an annual income of $1,000 from their (covert) civilian job. They first spend money on any medical costs, and use the rest for consumption. Superheros have the utility function U = C. a) Suppose an insurance company charges an actuarially fair price for insurance. How much will insurance cost? Actuarially fair insurance will cost p*200.

2 Midterm Exam #2, Page 2 of 5 b) What is the maximum amount a superhero would be willing to pay for insurance, if p=0.4? With p=0.4, actuarially fair insurance will cost $80. The maximum amount they would pay can be found by calculating utility with no insurance, which equals U =.6* * 800 = The maximum the superhero is willing to pay is the amount X that solves 1000 X = , or X = c) Suppose there are also some clumsy goons living in the community who have the same utility function as superheros and the same income, but have a higher probability of getting injured (so pgoon > psuperhero ). Insurance companies cannot distinguish a clumsy goon from a superhero. How will the existence of clumsy goons affect the insurance market? This is a classic adverse selection problem. If the insurance company offers insurance to superheros, clumsy goons will buy the insurance and the insurance company will lose money (as long as the goon s probability of accidents are enough higher than the superhero probability). If insurance companies raise prices, superheros will no longer insure. Eventually (absent government intervention), the only group offered insurance will be clumsy goons. 3, 10 points): For each of the following, determine which group would have higher Social Security Wealth (SSW), all other things equal. Briefly explain your answers. a) male or female Females will have higher social security wealth because both pay the same taxes, but females live longer than males and so receive benefits for a longer time. b) born in 1925 or born in 1985 Someone born in 1925 would have the higher SSW because of the tax-rate growth effect and wage and growth population effects got smaller starting in the 1970s. c) single or married A married person has the higher SSW because spouses of workers are automatically entitled to 50% of the workers' benefits, and surviving widows receive 100% of the workers' benefits. So a married worker purchases not just his own benefits, but those for his wife as well. d) low-wage earners or high-wage earners A low-wage worker has higher SSW because of how Social Security redistributes income. e) single-earner couples or double-earner couples

3 Midterm Exam #2; Page 3 of 5 Single-earner couples have more SSW because even though only one person works, that couple gets 150% of the earner's benefit. The two-earner couple has to pay taxes on their full earnings even though they may not receive more benefits than the one-earner couple. 4, 5 points): Very briefly describe one issue about the Leave No Child Behind Act that was raised in the supplemental readings assigned in the course. One piece from the Economist provides an outline of the No Child Left Behind legislation. It describes some of the tensions that arise with its implementation, particularly between the supporters and critics of the legislation. The other article is from the New York Times. It describes one implementation difficulty, where a seemingly high performing school in the South Bronx is classified as under-performing, leading to corrective actions (that would be harmful to the school). An interesting (and disturbing) aspect of the story is that the school s Principal had a very harm time figuring out the reason the school received a failing grade. 5, 10 points): A city is currently trying to estimate the most amount of money it should offer to contractors as an incentive for finishing a disruptive road project early. The transportation lengthens transport times by 10 hours per week for 40,000 workers. Assume that the all workers are paid $10 per hour in a perfectly competitive labor market. What is the most that the city should pay to the contractors as an incentive for completing the project four weeks early? If each worker loses 10 hours per week at a rate of $10 per hour, each worker loses $100 per week. By completing the project 4 weeks early, each affected worker would be $400 better off. Since there are 40,000 affected workers, the total benefit from completing the project 4 weeks early is 40,000 * $400 = $16 million. 6, 5 points): In the Health Care portion of the course (Chapters 15 and 16) I asked you to read a New York Times article (from the Sunday Magazine, March 13, 2005, written by Roger Lowenstein). The piece described some of the ideas of a Harvard University economist, David Cutler. Cutler s ideas for improving the health care system focus on a) Providing universal, national health insurance, following the successful examples of England, Canada, and France. b) Providing a $6,000 health insurance voucher for poor families (the size of the credit would decrease with income) so all families would be able to purchase some sort of health insurance. c) Accurately measuring and publicizing information on the quality of care, so insurers and consumers can ensure that the money people pay for health care is buying good stuff and therefore, the system would spend less on what is wasteful. d) Establishing congestion charges for traffic in London, England. e) Developing greater competition in the health care sector by encouraging the expansion of HMOs (Health Maintenance Organizations) and PPOs (Prefered Provider Organizations). f) Answers a) and c) g) Answers b) and c) [5 points for g: I also gave 2 points for answers b or c]

4 Midterm Exam #2, Page 4 of 5 h) Answers c) and d) i) Answers c) and e) j) None of the above 7, 10 points): In the schools of Beat Town, students are educated to play music, which they then perform at home for their parents. When more money is spent on the schools, the students learn more songs, and their parents are more entertained. The family utility function for each Beat Town family is U = C S where S is Beat town s per-student expenditure on schooling and C is the amount of money the family has left over for other consumption after paying the school tax. All students attend the same school in Beat Town. a) Although all the families in Beat Town have the same utility function, they have different incomes. Suppose 50 families each earn $50,000; and 60 families each earn $80,000. If the town votes on the level of a lump-sum tax to finance schools, what level will win? Recall, since utility is invariant to monotonic transformations. So take the natural log of utility to find (note: you don t have to do this doing so just makes the algebra a little easier): U = (.5)ln( C) + (.5)ln( S), and C = Y S, so U =.5ln( T S) +.5ln( S), du 1 1 Y = + = 0. This implies S =. ds 2[ Y S] 2S 2 A simple majority vote will result in the $80,000 families winning the vote (since there are 60 of them and only 50 families with income of $50,000). From above, the $80,000 households prefer a lump-sum tax of $40,000. Consequently, all families will be assessed a lump sum tax of $40,000. b) Now suppose lump-sum taxes are found to be unconstitutional. Along with this court ruling, and the residents of Beat Town are ordered to substitute a flat percentage income tax levied at a rate of 50 percent. Explain how the welfare (utility) of Beat Town residents changes (if it changes). With a 50 percent tax, households with income of $80,000 will pay a tax of $40,000 and households with income of $50,000 will pay a tax of $25,000. So the total average tax payments are (50*(25,000)+60*(40,000))/110 = So the rich are worse off, since school spending is less than their optimal value (of 40,000), and private consumption remains unchanged. The poor are better off: consumption of 25,000 and school expenditures of 33, gives greater utility than consumption of 10,000 and school expenditures of 40,000. 8, (5 points): Assume that the marginal cost (supply) of influenza (flu) vaccinations is constant at $40, and there are no externalities associated with flu. Assume that everyone in society has health insurance that pays 80% of all medical services, including flu shots. Draw the market demand for flu shots and show graphically what the socially optimal number of flu shots is. Show how many flu shots will be provided in this market given the insurance. Show the deadweight loss caused by the health insurance.

5 Midterm Exam #2; Page 5 of 5 Without insurance, the market equilibrium quantity would be where private marginal benefit equals private marginal cost, resulting in Q 1 flu shots being made and purchased. With insurance, however, people will get flu shots as long as the marginal benefit from doing so exceeds the after-insurance cost. Given that insurance pays 80% of the cost of the flu shot, individuals with insurance pay only $8 for a flu shot, resulting in Q 2 flu shots being made and purchased. However, for every unit after Q 1 the social marginal benefit is less than the social cost of $40, implying that the production of those units creates a deadweight loss. Specifically, the deadweight loss is equal to the area of triangle ABC. The picture is given below: 9, (5 points): Which of the following describes the paradox of ordeal mechanisms? a) By their effectively targeting low-income individuals, those individuals are made worse off for having received welfare because of the corresponding reduction in selfworth. b) By their making the receipt of welfare benefits less attractive and less generous, it is possible that the worse off can actually be made better off. c) Welfare systems not only make the high-income individuals worse off, they reduce the well-being of low-income individuals in the long run. d) Welfare programs make the high-income individuals better off, even though they are the ones who are taxed to fund the welfare program. e) None of the above is correct.