Question 1

Richard is a stock market day trader.His utility of wealth function is  Richard has seen a recent upward trend in the price of Yahoo stock.He feels that there is a 30% chance the stock will rise from $175 per share to $225.Otherwise,he believes the stock will settle to about $150 per share.Richard's current wealth is $1.75 million.Assume that if Richard purchases the stock,he will use his entire wealth.Given his risk preferences,will Richard buy Yahoo?

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Question 2

Virginia Tyson is a widow whose primary income is provided by earnings received from her husband's $200,000 estate.The table below shows the relationship between income and total utility for Virginia.
Income Total Utility
5,000 12
10,000 22
15,000 30
20,000 36
25,000 40
30,000 42
a.Construct the marginal utility table for Virginia.What is her attitude
toward risk? Explain your answer including a description of the marginal
utility for individuals whose risk preferences are different from Virginia's.
b.Virginia is currently earning 10% on her $200,000 in a riskless investment.
Alternatively,she could invest in a project that has a 0.4 probability of yielding
a $30,000 return on her investment and a 0.6 probability of paying $10,000.
Should she alter her strategy and move her $200,000 to the more risky project?

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Question 3

Calculate the expected value of the following game.If you win the game,your wealth will increase by 36 times your wager.If you lose,you lose your wager amount.The probability of winning is 1/38.Calculate the variance of the game.

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Question 4

C and S Metal Company produces stainless steel pots and pans.C and S can pursue either of two distribution plans for the coming year.The firm can either produce pots and pans for sale under a discount store label or manufacture a higher quality line for specialty stores and expensive mail order catalogs.High initial setup costs along with C and S's limited capacity make it impossible for the firm to produce both lines.Profits under each plan depend upon the state of the economy.One of three conditions will prevail:
growth (probability = 0.3)
normal (probability = 0.5)
recession (probability = 0.2)
The outcome under each plan for each state of the economy is given in the table below.Figures in the table are profits measured in dollars.The probabilities for each economic condition represent crude estimates.
Economic Condition Discount Line Specialty Line
Growth 250,000 400,000
Normal 220,000 230,000
Recession 140,000 20,000
a.Calculate the expected value for each alternative.
b.Which alternative is more risky? (Calculate the standard deviation of profits for each alternative.)
c.Taking into account the importance of risk,which alternative should an investor choose?

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Question 5

Tom Wilson is the operations manager for BiCorp,a real estate investment firm.Tom must decide if BiCorp is to invest in a strip mall in a northeast metropolitan area.If the shopping center is highly successful,after tax profits will be $100,000 per year.Moderate success would yield an annual profit of $50,000,while the project will lose $10,000 per year if it is unsuccessful.Past experience suggests that there is a 40% chance that the project will be highly successful,a 40% chance of moderate success,and a 20% probability that the project will be unsuccessful.
a.Calculate the expected value and standard deviation of profit.
b.The project requires an $800,000 investment.If BiCorp has an 8% opportunity cost on invested funds of similar riskiness,should the project be undertaken?

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Question 6

Farmer Brown grows wheat on his farm in Kansas,and the weather during the growing season makes this a risky venture.Over the many years that he has been in business,he has learned that rainfall patterns can be categorized as highly productive (HP)with a probability of .2,moderately productive (MP)with a probability of .6,and not productive at all (NP)with a probability of .2.With these various rainfall patterns,he has also learned that the inflation adjusted yields are $25,000 with NP weather,$10,000 with MP weather,and $50,000 with HP weather.Calculate the expected yield from growing wheat on Farmer Brown's farm.What can be learned about Brown's attitude toward risk from this problem? Explain.

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Question 7

Calculate the expected value of the following game.If you win the game,your wealth will increase by 100,000,000 times your wager.If you lose,you lose your wager amount.
The probability of winning is  .

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Question 8

Connie's utility depends upon her income.Her utility function is U = I^1/2.She has received a prize that depends on the roll of a pair of dice.If she rolls a 3,4,6 or 8,she will receive $400.Otherwise she will receive $100. a.What is the expected payoff from this prize? [Hint: The probability of rolling a 3 is 1/18,the probability of rolling a 4 is 3/36,the probability of rolling a 6 is 5/36,and the probability of rolling an 8 is 5/36] b.What is the expected utility from this prize? c.Connie is offered an alternate prize of $169 (no dice roll is required).Will she accept the alternate prize or roll the dice? d.What is the minimum payment that Connie will accept to forego the roll of the dice?

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Question 9

Jonathan and Roberto enjoy playing poker.Jonathan's utility as a function of winning a poker hand is  Roberto's utility as a function of winning a poker hand is  Unfortunately for Jonathan,he has a habit of whistling only when he gets a full-house or better.Roberto,however,has not noticed this habit.Roberto currently has three-of-a-kind (which will lose to a full-house or better).Roberto believes that the probability Jonathan can beat his three-of-a-kind is 1/10.Roberto could choose to fold or play the hand.Calculate Roberto's expected utility according to his beliefs.Jonathan is currently whistling.How much could Roberto increase his utility by recognizing Jonathan's whistling habit?

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Question 10

Irene's utility of income function is U(I)= 20I + 300.Irene is offered the following game of chance.The odds of winning are ¹/₁₀₀ and the pay-off is 75 times the wager.If she loses,she loses her wager amount.Calculate Irene's expected utility of the game.

Accepted Answer

The answer of Irene's utility of income function is U(I)=...

Question 11

Sandra lives in the Pacific Northwest and enjoys walking to and from work during sunny days.Her utility is sharply diminished if she must walk while it is raining.Sandra's utility function is U = 1,000 I₁ + 250 I₂ + 1 I₃ where I₁ = 1 if she walks and there is no rain and I₁ = 0 otherwise,I₂ = 1 if she drives to work and I₂ = 0 otherwise,and I₃ = 1 if she walks and it rains and I₃ = 0 otherwise.Sandra believes that the probability of rain today is ³/₁₀.Given her beliefs,what is her expected utility from walking to work? What is her expected utility from driving to work according to her beliefs? If Sandra maximizes her expected utility according to her beliefs,will she drive or walk to work? Sandra missed the weather report this morning that stated the true probability of rain today is ⁴/₅.Given the weather report is accurate,what is Sandra's true expected utility from walking and driving to work? How much could Sandra increase her expected utility if she read and believed the weather report?

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Question 12

Steve has received a stock tip from Monica.Monica has told him that XYZ Corp.will increase in value by 100%.Steve believes that Monica has a 25% chance of being correct.If Monica is incorrect,Steve expects the value of XYZ Corp.will fall by 50%.What is Steve's expected utility from buying $1,000 worth of XYZ Corp.stock? Steve's utility of income is
U(I)= 50I.Should Steve purchase the stock?

Accepted Answer

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Question 13

George Steinbrenner,the owner of the New York Yankees,has a utility function of wins in a season given by U(w)= w².Mr.Steinbrenner has been offered a trade.He believes if he completes the trade,his probability of winning 125 games is 15%.There is also an 85% chance the team won't gel and the Yankees will win only 90 games.Without the trade,Mr.Steinbrenner believes the Yankees will win 94 games.Given Mr.Steinbrenner's risk attitude,will he complete the trade?

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Question 14

The relationship between income and total utility for three investors (A,B,and
C)is shown in the tables below.
A B C
Income TU Income TU Income TU
5,000 14 5,000 4 5,000 6
10,000 24 10,000 8 10,000 14
15,000 32 15,000 12 15,000 24
20,000 38 20,000 16 20,000 36
25,000 43 25,000 20 25,000 52
30,000 47 30,000 24 30,000 72
35,000 49 35,000 28 35,000 100
Each investor has been confronted with the following three investment opportunities.The first opportunity is an investment which pays $15,000 risk free.Opportunity two offers a 0.4 probability of a $25,000 payment and a 0.6 probability of paying $10,000.The final investment will either pay $35,000 with a probability of 0.25 or $5,000 with a probability of 0.75.Determine the alternative each of the above investors would choose.Provide an intuitive explanation for the differences in their choices.

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Question 15

Sam's utility of wealth function is U(w)= 15  .Sam owns and operates a farm.He is concerned that a flood may wipe out his crops.If there is no flood,Sam's wealth is $360,000.The probability of a flood is 1/15.If a flood does occur,Sam's wealth will fall to $160,000.Calculate the risk premium Sam is willing to pay for flood insurance.

Accepted Answer

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Question 16

Mary is a fervent Iowa State University Cyclone Basketball fan.She derives utility as a function of the ISU team winning the Big XII championship and from income according to the function and w is her level of wealth.Mary believes the probability of a Cyclone championship is ¹/₄.Mary has been offered the following "insurance policy." The insurance policy costs $16.If the Cyclones win the championship,she pays only the policy cost of $16.If the Cyclones lose,she will receive $21.50 (so that after taking into account the policy cost of $16,her net return is $5.50).Will Mary's expected utility increase if she purchases the policy?

Accepted Answer

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Question 17

Describe Larry,Judy and Carol's risk preferences.Their utility as a function of income is given as follows Larry: U_L(I)= 10 . Judy: U_J(I)= 3I². Carol: U_C(I)= 20I.

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Question 18

John Smith is considering the purchase of a used car that has a bank book value of $16,000.He believes that there is a 20% chance that the car's transmission is damaged.If the transmission is damaged,the car would be worth only $12,000 to Smith.What is the expected value of the car to Smith?

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Question 19

United Plastics Company produces large plastic cups in a variety of colors.United can produce plain plastic cups that are sold in department stores in inexpensive ten cup bundles.Alternatively,United can sell Novelty Cups which are imprinted with slogans and designs.The printed cups cost more to produce,but they sell for a higher price.The appropriate strategy for United depends upon the state of the economy.Plain cups do better during a recession,while Novelty Cups earn higher profits during normal economic conditions.During a recession,United will earn a $100,000 profit selling plain cups and $40,000 with the Novelty line.Under normal economic conditions,United will earn $120,000 with the plain cups and a $200,000 profit with Novelty Cups.United currently does not use economic forecasts and simply assigns equal probabilities to a recession and normal conditions.
a.Using the probabilities assumed by United,what is the expected value of each alternative? Which alternative should the firm pursue? (Your recommendation should include separate recommendations for alternative attitudes toward risk.)
b.Calculate and interpret the value to the firm of complete information.

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Question 20

Marsha owns a boat that is harbored on the east coast of the United States.Currently,there is a hurricane that is approaching her harbor.If the hurricane strikes her harbor,her wealth will be diminished by the value of her boat,as it will be destroyed.The value of her boat is $250,000.It would cost Marsha $15,000 to move the boat to a harbor out of the path of the hurricane.Marsha's utility of wealth function is  .
Marsha's current wealth is $3 million including the value of the boat.Past evidence has influenced Marsha to believe that the hurricane will likely miss her harbor,and so she plans not to move her boat.Suppose the probability the hurricane will strike Marsha's harbor is 0.7.Calculate Marsha's expected utility given that she will not move her boat.Calculate Marsha's expected utility if she moves her boat.Which of the two options gives Marsha the highest expected utility?

Accepted Answer

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Quiz 5: Uncertainty and Consumer Behavior

Calculate the expected value of the following game.If you win the game,your wealth will increase by 36 times your wager.If you lose,you lose your wager amount.The probability of winning is 1/38.Calculate the variance of the game.

Calculate the expected value of the following game.If you win the game,your wealth will increase by 100,000,000 times your wager.If you lose,you lose your wager amount. The probability of winning is .

Irene's utility of income function is U(I)= 20I + 300.Irene is offered the following game of chance.The odds of winning are 1/100 and the pay-off is 75 times the wager.If she loses,she loses her wager amount.Calculate Irene's expected utility of the game.

Describe Larry,Judy and Carol's risk preferences.Their utility as a function of income is given as follows Larry: UL(I)= 10 . Judy: UJ(I)= 3I2. Carol: UC(I)= 20I.

John Smith is considering the purchase of a used car that has a bank book value of $16,000.He believes that there is a 20% chance that the car's transmission is damaged.If the transmission is damaged,the car would be worth only $12,000 to Smith.What is the expected value of the car to Smith?

Irene's utility of income function is U(I)= 20I + 300.Irene is offered the following game of chance.The odds of winning are ¹/₁₀₀ and the pay-off is 75 times the wager.If she loses,she loses her wager amount.Calculate Irene's expected utility of the game.

Describe Larry,Judy and Carol's risk preferences.Their utility as a function of income is given as follows Larry: U_L(I)= 10 . Judy: U_J(I)= 3I². Carol: U_C(I)= 20I.