Question 1

Prufrock is risk averse.He is offered a gamble in which with probability 1/4 he will lose $1,000 and with probability 3/4, he will win $500.

Accepted Answer

A) Since he is risk averse, he will certainly not take the gamble. 
B) Since the expected value of the gamble is positive, he will certainly take the gamble. 
C) If Prufrock's initial wealth is greater than $1,500, he will certainly take the gamble. 
D) If Prufrock's initial wealth is smaller than $1,500, he will certainly not take the gamble. 
E) Not enough information is given to determine for sure whether he will take the gamble. 
A) Since he is risk averse, he will certainly not take the gamble. 
B) Since the expected value of the gamble is positive, he will certainly take the gamble. 
C) If Prufrock's initial wealth is greater than $1,500, he will certainly take the gamble. 
D) If Prufrock's initial wealth is smaller than $1,500, he will certainly not take the gamble. 
E) Not enough information is given to determine for sure whether he will take the gamble.

Question 2

Buck Columbus is thinking of starting a pinball palace near a large Midwestern university.Buck is an expected utility maximizer with a von Neuman-Morgenstern utility function, U(W)= 1 - (6,000/W), where W is his wealth.Buck's total wealth is $24,000.With probability .2 the palace will be a failure and he'll lose $18,000, so that his wealth will be just $6,000.With probability .8 it will succeed and his wealth will grow to $x.What is the smallest value of x that would be sufficient to make Buck want to invest in the pinball palace rather than have a wealth of $24,000 with certainty?

Accepted Answer

A) $28,500 
B) $150,000 
C) $96,000 
D) $72,000 
E) $30,000 
A) $28,500 
B) $150,000 
C) $96,000 
D) $72,000 
E) $30,000

Question 3

Portia has waited a long time for her ship to come in, and she has concluded that it will arrive today with probability 1/4.If it does come, she will receive $16.If it doesn't come in today, it never will and she will have zero wealth.She has a von Neumann-Morgenstern utility function equal to the square root of her total income.What is the minimum price at which she would sell the rights to her ship?

Accepted Answer

A) $1 
B) $2 
C) $2.50 
D) $4 
E) None of the above. 
A) $1 
B) $2 
C) $2.50 
D) $4 
E) None of the above.

Question 4

Quincy's expected utility function is pc1/21 + (1 - p)c1/22, where p is the probability that he consumes c1 and 1 - p is the probability that he consumes c2.Wilbur is offered a choice between getting a sure payment of $Z or a lottery in which he receives $3,600 with probability .60 and $12,100 with probability .40.Wilbur will choose the sure payment if

Accepted Answer

A) Z > 6,400 and the lottery if Z 12,100 and the lottery if Z 9,250 and the lottery if Z 5,000 and the lottery if Z 7,000 and the lottery if Z < 7,000. A) Z > 6,400 and the lottery if Z 12,100 and the lottery if Z 9,250 and the lottery if Z 5,000 and the lottery if Z 7,000 and the lottery if Z < 7,000.

Question 5

Yoram's expected utility function is pc1/21 + (1 - p)c1/22, where p is the probability that he consumes c1 and 1 - p is the probability that he consumes c2.Wilbur is offered a choice between getting a sure payment of $Z or a lottery in which he receives $2,500 with probability .30 and $3,600 with probability .70.Wilbur will choose the sure payment if

Accepted Answer

A) Z > 3,249 and the lottery if Z 2,874.50 and the lottery if Z 3,600 and the lottery if Z 3,424.50 and the lottery if Z 3,270 and the lottery if Z < 3,270. A) Z > 3,249 and the lottery if Z 2,874.50 and the lottery if Z 3,600 and the lottery if Z 3,424.50 and the lottery if Z 3,270 and the lottery if Z < 3,270.

Question 6

Tom Cruiser's car is worth $100,000.But Tom is careless and leaves the top down and the keys in the ignition.Consequently his car will be stolen with probability .5.If it is stolen, he will never get it back.Tom has $100,000 in other wealth and his von Neumann-Morgenstern utility function for wealth is u(w)= ln(w).Suppose that Tom can buy $K worth of insurance at a price of $.6K.How much insurance will Tom buy?

Accepted Answer

A) $0 
B) $100,000 
C) More than $0 but less than $50,000 
D) More than $50,000 but less than $100,000 
E) Exactly $50,000 
A) $0 
B) $100,000 
C) More than $0 but less than $50,000 
D) More than $50,000 but less than $100,000 
E) Exactly $50,000

Question 7

Mabel and Emil were contemplating marriage.They got to talking.Mabel said that she always acted according to the expected utility hypothesis, where she tried to maximize the expected value of the log of her income.Emil said that he too was an expected utility maximizer, but he tried to maximize the expected value of the square of his income.Mabel said, "I fear we must part.Our attitudes toward risk are too different." Emil said, "Never fear, my dear, the square of income is a monotonic increasing function of the log of income, so we really have the same preferences." Who is right about whether their preferences toward risk are different?

Accepted Answer

A) Mabel is right. 
B) Emil is right. 
C) Emil is right about small risks but wrong about large risks. 
D) Mabel is right about small risks but wrong about large risks. 
E) They are both wrong. 
A) Mabel is right. 
B) Emil is right. 
C) Emil is right about small risks but wrong about large risks. 
D) Mabel is right about small risks but wrong about large risks. 
E) They are both wrong.

Question 8

If Paul is risk loving and his basketball team has a probability of .5 of winning, then Paul would rather bet $10 on his team than $100.(When Paul bets X, he wins X if his team wins and loses X if his team loses.)

Accepted Answer

A) True 
 B)False

Question 9

Timmy Qualm's uncle gave him a lottery ticket.With probability 1/2 the ticket will be worth $100 and with probability 1/2 it will be worthless.Let x be Timmy's wealth if the lottery ticket is a winner, and y his wealth if it is a loser.Timmy's preferences over alternative contingent commodity bundles are represented by the utility function U(x, y)= min{2x - y, 2y - x}.He has no risks other than the ticket.

Accepted Answer

A) Timmy would sell his lottery ticket for $25 but not for less. 
B) Timmy hates risk so much that he'd be willing to throw away the lottery ticket rather than worry about whether he won. 
C) Timmy satisfies the expected utility hypothesis. 
D) Timmy is misnamed.He is a risk lover. 
E) None of the above. 
A) Timmy would sell his lottery ticket for $25 but not for less. 
B) Timmy hates risk so much that he'd be willing to throw away the lottery ticket rather than worry about whether he won. 
C) Timmy satisfies the expected utility hypothesis. 
D) Timmy is misnamed.He is a risk lover. 
E) None of the above.

Question 10

Willy's only source of wealth is his chocolate factory.He has the utility function pc1/2f + (1 - p)c1/2nf, where p is the probability of a flood, 1 - p is the probability of no flood, and cf and cnf are his wealth contingent on a flood and on no flood, respectively.The probability of a flood is p = 1/4.The value of Willy's factory is $300,000 if there is no flood and $0 if there is a flood.Willy can buy insurance where if he buys $x worth of insurance, he must pay the insurance company $5x/18 whether there is a flood or not but he gets back $x from the company if there is a flood.Willy should buy

Accepted Answer

A) enough insurance so that if there is a flood, after he collects his insurance, his wealth will be 1/25 of what it would be if there were no flood. 
B) enough insurance so that if there is a flood, after he collects his insurance, his wealth will be the same whether there was a flood or not. 
C) no insurance since the cost per dollar of insurance exceeds the probability of a flood. 
D) enough insurance so that if there is a flood, after he collects his insurance, his wealth will be 1/6 of what it would be if there were no flood. 
E) enough insurance so that if there is a flood, after he collects his insurance his wealth will be 1/11 of what it would be if there were no flood. 
A) enough insurance so that if there is a flood, after he collects his insurance, his wealth will be 1/25 of what it would be if there were no flood. 
B) enough insurance so that if there is a flood, after he collects his insurance, his wealth will be the same whether there was a flood or not. 
C) no insurance since the cost per dollar of insurance exceeds the probability of a flood. 
D) enough insurance so that if there is a flood, after he collects his insurance, his wealth will be 1/6 of what it would be if there were no flood. 
E) enough insurance so that if there is a flood, after he collects his insurance his wealth will be 1/11 of what it would be if there were no flood.

Question 11

Sally Kink is an expected utility maximizer with utility function pu(c1)+ (1 - p)u(c2), where for any x < $3,000, u(x)= 2x, and for x greater than or equal to $3,000, u(x)= 3,0001 + x.

Accepted Answer

A) Sally will be risk averse if her income is less than $3,000 but risk loving if her income is more than $3,000. 
B) Sally will be risk neutral if her income is less than $3,000 and risk averse if her income is more than $3,000. 
C) For bets that involve no chance of her wealth exceeding $3,000, Sally will take any bet that has a positive expected net payoff. 
D) Sally will never take a bet if there is a chance that it leaves her with wealth less than $6,000. 
E) None of the above are true. 
A) Sally will be risk averse if her income is less than $3,000 but risk loving if her income is more than $3,000. 
B) Sally will be risk neutral if her income is less than $3,000 and risk averse if her income is more than $3,000. 
C) For bets that involve no chance of her wealth exceeding $3,000, Sally will take any bet that has a positive expected net payoff. 
D) Sally will never take a bet if there is a chance that it leaves her with wealth less than $6,000. 
E) None of the above are true.

Question 12

Oskar's preferences over gambles in which the probability of events 1 and 2 are both 1/2 can be represented by the von Neuman-Morgenstern utility function .5y.51 + .5y.52, where y1 is his consumption if event 1 happens and y2 is his consumption if event 2 happens.A gamble that allows him a consumption of $9 if event 1 happens and $25 if event 2 happens is exactly as good for Oskar as being sure to have an income of

Accepted Answer

A) $12.5. 
B) $9. 
C) $16. 
D) $17. 
E) None of the above. 
A) $12.5. 
B) $9. 
C) $16. 
D) $17. 
E) None of the above.

Question 13

Oliver takes his wealth of $1,000 to a casino.He can bet as much as he likes on the toss of a coin but the "house" takes a cut.If Oliver bets $x on heads, then if heads comes up, he gets $.8x and, if tails comes up, he pays $x.Similarly if he bets $x on tails and if tails comes up, he wins $.8x and, if heads comes up, he pays $x.Draw a graph with dollars contingent on heads and dollars contingent on tails on the two axes.Show Oliver's budget constraint.Oliver is an expected utility maximizer with the utility function U(h, t)= 1/2h2 +1/2t2, where h is his wealth if heads comes up and t is his wealth if tails comes up.Draw the highest indifference curve that Oliver can reach with his budget.What bets if any does he make?

Accepted Answer

His budget curve kinks at (1000, 1000);

Question 14

After graduating, Sallie Handshake's best job offer will either be with a Big-8 accounting firm for $160,000 a year or as a State Farm agent in Grand Rapids, Michigan, for $40,000 a year.She can increase the probability of the former outcome by studying more, but such studying has its costs.If S represents her amount of studying (where S = 0 is no study and S = 1 is all-out effort), her probability of getting the job with a Big-8 firm just equals S.Her utility depends on how hard she studies and her subsequent annual income Y.She tries to maximize the expected value of the von Neuman-Morgenstern utility function U(S, Y)= Y1/2 - 400S2.If she chooses S to maximize her expected utility, how much will she study?

Accepted Answer

A) S = 0.1. 
B) S = 0.25. 
C) S = 0.5. 
D) S = 0.75. 
E) S = 0.9. 
A) S = 0.1. 
B) S = 0.25. 
C) S = 0.5. 
D) S = 0.75. 
E) S = 0.9.

Question 15

There are two events, 1 and 2.The probability of event 1 is p and the probability of event 2 is 1 - p.Sally Kink is an expected utility maximizer with a utility function is pu(c1)+ (1 - p)u(c2), where for any number x, u(x)= 2x if x < 1,000 and u(x)= 1,000 + x if x is greater than or equal to 1,000.

Accepted Answer

A) Sally is a risk lover. 
B) Sally will be a risk averter if she is poor but will be a risk lover if she is rich. 
C) Sally will be a risk lover if she is poor but a risk averter if she is rich. 
D) If there is no chance of her wealth exceeding $1,000, then she will take any bet that has positive expected net winnings. 
E) None of the above. 
A) Sally is a risk lover. 
B) Sally will be a risk averter if she is poor but will be a risk lover if she is rich. 
C) Sally will be a risk lover if she is poor but a risk averter if she is rich. 
D) If there is no chance of her wealth exceeding $1,000, then she will take any bet that has positive expected net winnings. 
E) None of the above.

Question 16

Wilma is not risk averse.She is offered a chance to pay $10 for a lottery ticket that will give her a prize of $100 with probability .06, a prize of $50 with probability .1, and no prize with probability .85.If she understands the odds and makes no mistakes in calculation, she will buy the lottery ticket.

Accepted Answer

A) True 
 B)False

Question 17

Linus Piecewise is an expected utility maximizer.There are two events, H and T, which each have probability 1/2.Linus's preferences over lotteries in which his wealth is h if event H happens and t if event T happens are representable by the utility function U(h, t)= u(h)/2 + u(t)/2.The function u takes the following form.For any x, u(x)= x if x < 100 and u(x)= 100 +x/2 if x is greater than or equal to 100.Draw a graph showing the indifference curves for Linus that pass through
a.the point (50, 0)
b.the point (50, 100)
c.the point (100, 100)
d.the point (150, 100)

Accepted Answer

Curve a is a line with slope -1.Curve b

Question 18

Ronald has $18,000.But he is forced to bet it on the flip of a fair coin.If he wins he has $36,000.If he loses he has nothing.Ronald's expected utility function is .5x.5 + .5y.5, where x is his wealth if heads comes up and y is his wealth if tails comes up.Since he must make this bet, he is exactly as well off as if he had a perfectly safe income of

Accepted Answer

A) $16,000. 
B) $15,000. 
C) $12,000. 
D) $11,000. 
E) $9,000. 
A) $16,000. 
B) $15,000. 
C) $12,000. 
D) $11,000. 
E) $9,000.

Question 19

An expected utility maximizer's preferences between two bundles contingent on event 1 happening must be independent of what he will get if event 2 happens.

Accepted Answer

A) True 
 B)False

Exam 11: Uncertainty-Part A

Prufrock is risk averse.He is offered a gamble in which with probability 1/4 he will lose $1,000 and with probability 3/4, he will win $500.

If Paul is risk loving and his basketball team has a probability of .5 of winning, then Paul would rather bet $10 on his team than $100.(When Paul bets X, he wins X if his team wins and loses X if his team loses.)

Sally Kink is an expected utility maximizer with utility function pu(c1)+ (1 - p)u(c2), where for any x < $3,000, u(x)= 2x, and for x greater than or equal to $3,000, u(x)= 3,0001 + x.

An expected utility maximizer's preferences between two bundles contingent on event 1 happening must be independent of what he will get if event 2 happens.

Budget Constraint-Part A

Budget Constraint-Part B

Preferences-Part A

Preferences-Part B

Utility-Part A

Utility-Part B

Choice-Part A

Choice-Part B

Demand-Part A

Demand-Part B

Revealed Preference-Part A

Revealed Preference-Part B

Slutsky Equation-Part A

Slutsky Equation-Part B

Buying and Selling-Part A

Buying and Selling-Part B

Intertemporal Choice-Part A

Intertemporal Choice-Part B

Asset Markets-Part A

Asset Markets-Part B

Uncertainty-Part B

Risky Assets-Part A

Risky Assets-Part B

Consumers Surplus-Part A

Consumers Surplus-Part B

Market Demand-Part A

Market Demand-Part B

Equilibrium-Part A

Equilibrium-Part B

Auctions-Part A

Auctions-Part B

Technology-Part A

Technology-Part B

Profit Maximization-Part A

Profit Maximization-Part B

Cost Minimization-Part A

Cost Minimization-Part B

Cost Curves-Part A

Cost Curves-Part B

Firm Supply-Part A

Firm Supply-Part B

Industry Supply-Part A

Industry Supply-Part B

Monopoly-Part A

Monopoly-Part B

Monopoly Behavior-Part A

Monopoly Behavior-Part B

Factor Markets-Part A

Factor Markets-Part B

Oligopoly-Part A

Oligopoly-Part B

Game Theory-Part A

Game Theory-Part B

Game Applications-Part A

Game Applications-Part B

Behavioral Economics

Exchange-Part A

Exchange-Part B

Production-Part A

Production-Part B

Welfare-Part A

Welfare-Part B

Externalities-Part A

Externalities-Part B

Information Technology-Part A

Information Technology-Part B

Public Goods-Part A

Public Goods-Part B

Asymmetric Information-Part A

Asymmetric Information-Part B

Filters

Sally Kink is an expected utility maximizer with utility function pu(c₁)+ (1 - p)u(c₂), where for any x < $3,000, u(x)= 2x, and for x greater than or equal to $3,000, u(x)= 3,0001 + x.