Exam 16: Uncertainty

Which of the following games involving the roll of a single die is a fair bet?

For each of the following statements,state whether the statement is true,false,or uncertain and explain why. i.A risk neutral person is indifferent to a gamble and the expected value of the gamble. ii.A risk-averse person will never accept a gamble. iii.A risk-loving person will accept any gamble.

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?

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

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 25% chance that any variety will be retired.For the purchase of an individual animal,what is the value to Sarah of knowing ahead of time whether or not that variety will be retired?

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)= X^0.5 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.

-The above figure shows Bob's utility function.He currently has $50 and is considering investing all of it in an investment that has a 50% chance of being worth $100 and a 50% chance of being worth $0.Bob will

On any given day,a salesman can earn $0 with a 30% probability,$100 with a 20% probability,or $300 with a 50% probability.His expected earnings equal

-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's expected wealth is

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 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

If two events are perfectly positively correlated,then

Searching the Internet for information to help select a product that is more reliable is most likely to be done by a

Sarah has the utility function U(x)= 1 - 1/x,where x is the present value of her lifetime income.Sarah is trying to select a career.If she goes into teaching,she will make x=5 with certainty.If she pursues acting,she will make x=400 if successful or x=2 if unsuccessful (and therefore ends up waiting tables).The chance of succeeding in acting is 1% if she pursues acting. a.Determine which career Sarah will choose.Is she choosing the career with the higher expected value? Explain. b.An acting career expert charges 0.01 to determine if a person will succeed at acting.By going to an expert,Sarah can choose the best career according to her skills.Assuming that the expert is able to correctly determine if Sarah will be a successful actor,will she pay for this service?

Which of the following helps to reduce risk?

A risk-neutral person will invest in a project by examining if

If a person is risk averse,then she has negative marginal utility of wealth.

Insurance companies do not cover losses that would

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.What is the value to Sarah of knowing ahead of time whether a variety will be retired?

Usury laws result in banks making less credit available to lower-income households because