Exam 16: Uncertainty

16.2 Attitudes Toward Risk -The above figure shows Bob's utility function.He currently has $100 of wealth,but there is a 50% chance that it could all be stolen.Bob will buy theft insurance to cover the full $100

16.2 Attitudes Toward Risk -The above figure shows Bob's utility function.He currently has $100 of wealth,but there is a 50% chance that it could all be stolen.If Bob could keep $50 with certainty,his utility would be

For the following, please answer "True" or "False" and explain why. -A risk-averse investor will decide whether or not to invest by determining if the expected value of the investment is positive.

Derive the Arrow-Pratt measure of risk aversion for the following utility functions.Which represents the greatest level of risk aversion according to the measure? a.U(X)= b.U(X)= -e⁻ˣ c.U(X)= 1 - 1/X

Concerning an investment project,which of the following is TRUE?

For the following, please answer "True" or "False" and explain why. -Expected value represents the average of all outcomes if one were to undertake the risky event many times over and over again.

On any given day we know a salesman can earn $0 with a 40% probability,$100 with a 20% probability or $300 with 40% probability.His expected earnings equal

In a small town,it snowed 10 times on Christmas Eve during 25 years.What is the frequency of snowing on Christmas Eve in that small town?

A deductible is an amount of a claim not covered by insurance.A deductible is a fixed portion of the accident cost that the insured person must pay in order to make a claim to their insurer (this is similar to a co-pay in which you must pay a portion of the medical costs in the case you get sick).For example,if I break my arm,I have to pay a $50 deductible to the insurance company in order to get them to cover the rest of my medical costs from the accident. Rosa has a 10% chance of getting sick in the next year.If she gets sick,her medical bills will amount to $500.She has a wealth of $1,000.Suppose she has the utility function U(X)= X⁰.⁵ where x is her net wealth at the end of the year. Suppose Rosa can purchase insurance.The insurance company provides two plans for Rosa to select from,both providing $500 of coverage in the case that Rosa gets hurt.Plan A has zero deductibles (good!)but charges a high premium (bad!).Specifically,Plan A charges $55 for $500 of coverage.Plan B has a deductible of $K,where K<500,but charges a premium of just $(55 - .11K). a.Suppose K = $100.Will Rosa purchase insurance and if so,which plan? Show this mathematically. b.If Rosa can choose the deductible,K,what amount of deductible will she choose? c.Suppose Rosa knows her chance of getting sick is really just 5%.How will this affect the deductible she chooses? You only need to provide intuition (in words)for this part,not explicit computation.

Sarah buys little stuffed animals for $5 each.They come in different varieties.If the producer stops making (retires)a certain variety,a stuffed animal of that variety will be worth $100; otherwise it is worth $0.There is 50% chance that any variety will be retired.When Sarah buys her next stuffed animal,the expected profit is

For a risk-neutral person,the expected utility associated with various levels of wealth

A person is betting a coin will come up heads or tails.The coin always lands on one of these two outcomes.This person can bet to

Without usury laws,banks will

For the following, please answer "True" or "False" and explain why. -For a given expected value,the smaller the standard deviation of the expected value,the larger the risk.

Explain why the variance of an investment is a useful measure of the risk associated with it.

John derives more utility from having $1,000 than from having $100.From this,we can conclude that John

Suppose an individual has $100 to invest.Two assets are available.One asset will yield a return of 10%,while the other risky asset will yield 0% with probability .5 and 21% with probability .5.Suppose the investor's utility function is given by U(x)= ln(x)where x is the wealth after investing (assume she is investing for just one period).How much will she invest in the risky asset?

Stephan has the utility function U(w)= 3 ,where w is his wealth.Initially,Stephan has w = $100.Would Stephan pay $5 to take the following gamble: With probability 0.03 he wins $25; otherwise,he wins nothing.

John's utility from an additional dollar increases more when he has $1,000 than when he has $10,000.From this,we can conclude that John

A risk-preferring person is willing to pay