04 Jun Question Homework Assignment 4 Name: 1. Suppose that your utility function is given by , whe
Question
Homework Assignment 4
Name:
1. Suppose that your utility function is given by , wherestands for the natural logarithm of x, and I is the amount of income you make in a given year. Suppose that you typically make $30,000 per year, but there is a 5 percent chance that, in the next year, you will get sick and lose $20,000 in income due to medical costs.
a. What is your expected utility if you do not have insurance to protect against this adverse event?
b. Suppose you can buy insurance that will cover your losses if you get sick. What would be the actuarially fair premium? What is your expected utility if you buy the insurance policy?
c. What is the most that you would be willing to pay for this policy?
2. Suppose that your city government is interested in reducing littering. Currently, there is a $100 fine for littering and there is a 10 percent probability of being caught if you litter. The city deciding between two different policies: (1) It can increase the number of police that monitor littering, which would make the probability of being caught if you litter 20 percent rather than 10 percent; or (2) it can keep the monitoring the same yet raise the fine for littering from $100 to $200. (Notice that both policies have the same expected cost of littering.) If litterers are risk averse, which policy would lead to a larger reduction in littering? What if litters are risk loving (that is, they have a concave utility function, and so prefer an uncertain outcome to the certain outcome with the same expected cost)?
3. Consider two households, the Smiths and the Joneses. The Smiths are a two-earner household: both Dick and Jane Smith work and earn the same amount each year. The Joneses are a one-earner household: Sally Jones works while Harry Jones is a homemaker and stay-at-home dad. Use the way spousal benefits are treated in the Social Security system to address the following:
a. How do the relative rates of return on Social Security payroll taxes compare for the two families?
b. After the kids go off to college, Harry considers taking a small part-time job. How might the Social Security system of taxes and benefits affect his decision?
c. Suppose that both families have retired and have started to receive Social Security benefits. By what fraction will these benefits fall for each of these families if one member of the household dies? What implications does this have for relative consumption smoothing in these two households?
4. Suppose the average Social Security benefits in the nation are $14,000 per year. The number of Social Security pension recipients is currently 50 million. There are 150 million workers in the workforce this year and the average taxable wage per worker is $30,000 per year.
a. Calculate the dependency ratio (the ratio of the number of retirees to the labor force).
b. Calculate the average replacement rate (the ratio of Social Security pension benefits to average wage prior to retirement).
5. Suppose that you had information about the amount of private savings during the years before and after the introduction of the Social Security program. How might you carry out a difference-in-difference analysis of the effect of the Social Security program on private savings?
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