Q1. Suppose the state of New Jersey is considering a public works project that would improve the quality of its ocean beaches. Proponents argue that the project would increase tax revenues from tourism by $4 million per year for the next 10 years (after that the beaches will return to their current condition). Assume the project will require an immediate payment of $35 million and the project offers no other benefits.
a) Suppose the interest rate is 5 percent. Should the government undertake this project? Briefly explain your answer.
b) Suppose instead that the government can finance the project by paying $20 million now and $15 million in 5 years. Would you recommend the government undertake the project now? Briefly explain your answer.
c) Problems like this can be evaluated using different discount rates, such as the pre-tax return on investment, the after-tax return on investment, or the social discount rate. Discuss some of the criteria that should be considered when choosing the correct rate to use. Which rate should be used for evaluating this particular project?
Q2. Suppose there are two risk groups for a certain type of medical problem. The people in the high risk group have a 5% chance of needing $50,000 in health care and the people in the low risk group have a 2% chance of needing $5,000 in health care. Individuals know which risk group they fall into but insurance companies don't. Each person has initial wealth of $60,000 and the utility function u(w) = w½ where w is wealth.
a) What is the most a person in each group would pay for insurance?
b) Let θ be the probability that a person falls into the high risk group. Find the highest value of θ for which both groups can be insured. (Assume the insurance company can't lose money and must charge everyone the same price and everyone must be covered.)
Q3. There are two types of people in the economy. All individuals have utility functions over consumption, c, and leisure, l, given by
u(c, l ) = cl
All individuals have 24 units of time to divide between work and leisure. The price of the consumption good is $2/unit. There are 1000 type 1 people who each earn $15 per unit of time worked and 500 type 2 people who each earn $6 per unit of time worked. Suppose the government announces it will tax all labor income at 25% and transfer $40 to all type 2 people.
a) How much will each type of person work?
b) Will the government run a surplus or a deficit with this program? Of how much?
c) Let G represent the amount of money the government transfers to each type 2 person. What is the amount of G for which type 2 people will be indifferent between working and not working?
Q4. An individual has preferences over consumption, c, and leisure, l, in periods one (t=1) and two (t=2) of life given by u(ct, lt) = ln(ct) + ln(lt). (So total utility is U = u(c1, l1) + βu(c2, l2).) Each individual has two units of time in each period, which they can divide between leisure and labor; a person earns $10 for each unit of time worked. Individuals in this economy can save or borrow any amount at an interest rate of 10%. Assume that the price of the consumption good is $1 per unit in both periods and that β = 0.9.
a) Determine how much this person will work and consume in each period and how much they will save or borrow.
Now the government develops a Social Security system in which all old people are given a transfer of $5. To finance the Social Security system the government taxes the income of young people only at a rate of 25%.
b) Now how much will the individual work and consume in each period and save or borrow?
c) Are your answers to part (b) consistent with your expectations of the effects of a social security system? Clearly explain your answers.
d) How many young people are needed to finance the social security transfer received by each old person?
Get detailed answers for the above four questions.