Exam 20: Uncertainty, Risk, and Private Information

Use the following to answer questions: Scenario: Buying Shares Geordie is considering buying shares in two companies, Apple and Microsoft. If he invests $1,000 in Apple, there is a 40% probability that his investment will be worth only $800 and a 60% probability that it will be worth $1,200 at the end of a year. If he invests $500 in Apple, there is a 40% probability that his investment will be worth $400 and a 60% probability that it will be worth $600 at the end of a year. The corresponding numbers for investment in Microsoft are identical. -(Scenario: Buying Shares) Look at the scenario Buying Shares. The probability that Geordie will make a gain is _____ if he invests $1,000 in either Apple or Microsoft. The probability that he will make a gain is _____ if he invests $500 apiece in Apple and in Microsoft.

Which pair of events is NOT independent?

Use the following to answer questions: Scenario: Choosing Insurance The Ramirez family owns three cars and is considering buying insurance to cover the cost of repairs. They face two possible states: in state 1 their cars need no repairs and their income available for purchasing other goods and services is $50,000; in state 2 their cars need $10,000 worth of repairs and their income available for purchasing other goods and services is reduced to $40,000. The probability of repairs is 10%, while the probability of no repairs is 90%. -(Scenario: Choosing Insurance) Refer to the information in the scenario Choosing Insurance. For $1,000 the Ramirez family can buy insurance that will cover the full cost of repairs. If family members are risk-averse and want to maximize their expected utility:

An individual finds that as his income increases, his total utility also increases but at a decreasing rate. This can be attributed to:

An efficient allocation of risk occurs when those most willing to bear risk insure those who are least willing to bear risk.

Use the following to answer questions: -(Table: Natasha's Total Utility) Look at the table Natasha's Total Utility. Natasha earns $50,000 per year but faces losing $20,000 of it if she is late with her work. If there is a 25% probability that Natasha will be late with her work and her income will equal $30,000, what certain income leaves Natasha just as well off as her uncertain income?

Use the following to answer questions: -(Table: Income and Utility for Whitney) Look at the table Income and Utility for Whitney. Whitney's income next year is uncertain: there is a 40% probability she will make $40,000 and a 60% probability she will make $80,000. Whitney's expected utility is _____ utils.

Barcelona and Los Angeles are similar, except Barcelona has a good public transportation system and Los Angeles does not. Auto insurance will probably be more expensive in _____, since the _____ for insurance is _____.

Which pair of events is likely to be positively correlated?

Consider the marginal utility of income curves of Hank, Babe, Barry, and Willie. Hank's is constant; Babe's is slightly diminishing; Barry's is strongly diminishing; and Willie's is upward-sloping. All else equal, which of these individuals will be most risk-averse?

An individual can almost eliminate risk by taking a small share in many independent events or by taking advantage of the predictability associated with large numbers of independent events. This is known as:

Micah is considering turning pro before his senior year basketball season. If he turns pro, Micah expects a pro contract worth $2 million in present value. If he does not turn pro, there is a 50% chance an injury will prevent him from playing professionally and a 50% chance he will get a pro contract worth $4 million in present value. What is the expected present value of Micah's pro contract if he stays in college for his senior year?

Domingo has a total wealth of $500,000 composed of a house worth $100,000 and $400,000 in cash. He keeps the cash in a safe deposit box, so that it is completely safe. However, there is a 10% chance that his house will burn down by the end of the year and be worth nothing and a 90% chance that nothing will happen to it. Without insurance, the expected value of his end-of-year wealth is:

A fair insurance policy is one whose premium is _____ the expected value of the claims.

People faced with adverse selection use _____ to deal with it.

McDonald's and other fast-food chains rely mainly on franchisees to operate the restaurants to avoid the problem of:

Bikul has just started a great job and plans to buy a fancy car worth $100,000. Bikul is risk-averse in money matters, but he likes to drive fast, so the probability that he wrecks the car (a total loss of $100,000) is 0.10. The probability that he has no accidents is 0.90. If an insurance company offers Bikul a fair insurance policy, the premium will be:

Use the following to answer questions: -(Table: Utility for Terri and Mary) Look at the table Utility for Terri and Mary. Each has an income of $300. If each were offered insurance to offset the risk of falling income, _____ would pay a larger premium because she is the consumer with _____ risk aversion.

Use the following to answer questions: Figure: Risk Aversion -(Figure: Risk Aversion) Look at the figure Risk Aversion. Bob and Nancy have the same income and the same total utility. Nancy is _____ risk-averse than Bob because her marginal utility curve is _____ than Bob's.

Lucy decides to buy car insurance because: