(5.20) Jerome moonlights; he holds down two jobs. The higher-paying job pays w, but he can work at most eight hours. The other job pays w* but he can work as many hours as he wants. Show how Jerome determines how many hours to work.
(5.30) Cynthia buys gasoline and other goods. The government considers imposing a lump-sum tax, L dollars per person, or a tax on gasoline of τ dollars per gallon. If L and τ are such that either tax will raise the same amount of tax revenue from Cynthia, which tax does she prefer and why? Show your answer using a graph or calculus.
(16.4) A risk-averse individual has to choose between $100 with certainty and a risky option with two equally likely outcomes, $100−x and $100+x. Use a graph(or math) to show that this 1 person’s risk premium is smaller, the smaller x is (the less variable the gamble is).
(16.8) Illustrate how a risk-neutral plaintiff in a lawsuit decides whether to settle a claim or go to trial. The defendants offer $50,000 to settle now. If the plaintiff does not settle, the plaintiff believes that the probability of winning at trial is 60%. If the plaintiff wins, the amount awarded will be X. How large can X be before the plaintiff refuses to settle? How does the plaintiff ’s attitude toward risk affect this decision?
(16.14) What is the risk premium if, in Solved Problem 16.3, Jen’s utility function were ln(W)?
1) The graphic below shows the preferences of two persons over bets.
a) Who do you think puts a higher subjective probability on Tiger winning?
b) Can you draw the indi erence curves for the case that the decision-maker is certain that Tiger will win?
2) The graphic below shows the preferences of two people over bets. Who do you think is more risk averse? Can you find the approximate certainty equivalent for the bet (1,3)?
3) Consider the following bets on Donkey and Tiger: A=(1,3), B=(5,5), C=(10,0), D=(6,4) a) Calculate the variance and the expected value of the bets, if the probability that Tiger wins is θ=0.5.
Suppose a decision-maker has a utility function for money given by U(x) = √x. If she believes that Donkey and Tiger are equally likely to win, how will she rank the bets?
c) Calculate for each bet the certainty equivalent.
d)Suppose the utility function of the decision-maker is U(x) = 7x. How will she decide now? How will she decide if her utility is U(x) = 6x + 1? Can you explain your finding?
e)Suppose the utility function of the decision-maker is U(x) = x2 . How will she decide now? Can you explain your finding?
f) For the utility functions considered above, suppose the decision-maker has $10. Calculate the value of a gain of $1 and the value of a loss of $1. Illustrate the utility functions and the gains/losses in a graph.
4) For each of the following statements, state whether the statement is true, false, or uncertain and explain why.
5) Steve has the utility function U(w) = 3√w, where w is his wealth. Initially, Steve has w = $100. Would Steve pay $5 to take the following gamble: with probability 0.3 he wins $25;otherwise he wins nothing.
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Multiple Choice
M1)You pay$15 for an all-you-can-eat bu et. The food isn't so good, but de nitely edible. When you nish eating, what is the marginal value of the last bite of food you consumed?
A) zero
B) $15
C) positive
D) negative
M2) Mary purchased a stu ed animal toy for $5. After a few weeks, someone o ered her $100 for the toy. Mary refused. One can conclude that Mary's consumer surplus from the toy is
A) less than $5
B) at least $95
C) at least $100
D) $105
M3)Joe's demand for spring water can be represented as p = 10 Q, where p is measured in $/gallon and Q is measured in gallons. He recently discovered a spring where water can be obtained free of charge. His consumer surplus from this water is
A) $0
B) $50
C) $100
D) unknown based upon the information provided.
M4) The gure below shows the market demand curve for telecommunication while driving one's car (time spent on the car phone). The current price is $0.35 per minute. If the price were to increase by ten cents per minute, consumer surplus would
A) fall to $820
B) fall by $86
C) fall by $58
D) None of the above.
M5) People in a certain group have a 0.3% chance of dying this year. If a person in this group buys a life insurance policy for $3,300 that pays $1,000,000 to her family if she dies this year and $0 otherwise, what is the expected value of a policy to the insurance company?
A) $0
B) $300
C) $3,000
D) None of the above.
M6) If a payout is certain to occur, then the variance of that payout equals
A) zero.
B) one.
C) the expected value.
D) the expected value squared.
A) zero. The variance of a constant is always zero.
M7) All else held constant, as the variance of a payo increases, the
A) expected value of the payo increases.
B) risk of the payo increases.
C) expected value of the payo decreases.
D) risk of the payo decreases.
M8) The gure below 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 utility is
A) a.
B) b.
C) c.
D) d.
M9) The above gure shows Bob's utility function. Bob is
A) risk-averse.
B) risk-neutral.
C) risk-loving.
D) risk premium.
M11) A risk-preferring person is willing to pay
A) a risk premium.
B) a fee to make a fair bet.
C) to obtain decreasing marginal utility.
D) None of the above.
M12) If a person is risk-neutral, then she
A) is indi erent about playing a fair game.
B) will pay a premium to avoid a fair game.
C) has a horizontal utility function.
D) has zero marginal utility of wealth.
M13) Which of the following games involving the roll of a single die is a fair bet?
A) Bet $1 and receive $1 if 3 or 4 comes up.
B) Bet $1 and receive $1 if 3, 4, or 5 comes up.
C) Bet $1 and receive $4 if 6 comes up.
D) None of these bets is a fair bet.
M14) 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 it is likely that John
A) is risk-averse.
B) is risk-loving.
C) is risk-neutral.
D) has an increasing marginal utility of wealth.
M15) Bob invests $50 in an investment that has a 50% chance of being worth $100 and a 50% chance of being worth $0. From this information we can conclude that Bob is NOT
A) risk-loving.
B) risk-neutral.
C) risk-averse.
D) rational.