Suppose that an individual is just willing to accept a gamble to win or lose $1000 if the probability of winning is 0.6. Suppose that the utility gained if the individual wins is 100 utils. How much utility does one lose if one loses the gamble
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Suppose that an individual is just willing to accept a gamble to win or lose $1000 if the probability of
winning is 0.6. Suppose that the utility gained if the individual wins is 100 utils. How much utility does one lose if one loses the gamble?
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- Donna just paid $800 for a new iPhone. Apple offers a two year extended warranty for $200 and Donna is considering purchasing it. She has utility given by U(X)=√X. Without the extended warranty, the iPhone becomes worthless if it breaks. What is the minimum probability, p, that the iPhone breaks in the next two years that will cause Donna to prefer to purchase the extended warranty? p=_____________ If the probability that her phone breaks is p=0.25, will Donna will prefer to buy or not buy the warranty?In a Godiva shop, 40% of the cookies are plain truffles, 20% are black truffles, 10% are cherry cookies, and 30% are a mix of all the others. Suppose you pick one at random from a prepacked bag that reflects this composition. a. What is the probability of picking a plain truffle? b. What is the probability of picking truffle of any kind? c. If you instead pick three cookies in a row, what is the probability that all three are black truffles?Arielle is a risk-averse traveler who is planning a trip to Canada. She is planning on carrying $400 in her backpack. Walking the streets of Canada, however, can be dangerous and there is some chance that she will have her backpack stolen. If she is only carrying cash and her backpack is stolen, she will have no money ($0). The probability that her backpack is stolen is 1/5. Finally assume that her preferences over money can be represented by the utility function U(x)=(x)^0.5 Suppose that she has the option to buy traveler’s checks. If her backpack is stolen and she is carrying traveler’s checks then she can have those checks replaced at no cost. National Express charges a fee of $p per $1 traveler’s check. In other words, the price of a $1 traveler’s check is $(1+p). If the purchase of traveler’s checks is a fair bet, then we know that the purchase of traveler checks will not change her expected income. Show that if the purchase is a fair bet, then the price (1+p) = $1.25.
- In the CRRA utility family u(x) = x^(1−γ). If this individual has autility where γ = 0.01, would he prefer the payment of $320 or the gamble?Now, imagine that Port Chester decides to crack down on motorists who park illegally by increasing the number of officers issuing parking tickets (thus, raising the probability of a ticket). If the cost of a ticket is $100, and the opportunity cost for the average driver of searching for parking is $12, which of the following probabilities would make the average person stop parking illegally? Assume that people will not park illegally if the expected value of doing so is negative. Check all that apply.Gary likes to gamble. Donna offers to bet him $31 on the outcome of a boat race. If Gary’s boat wins, Donna would give him $31. If Gary’s boat does not win, Gary would give her $31. Gary’s utility function is p1x^21+p2x^22, where p1 and p2 are the probabilities of events 1 and 2 and where x1 and x2 are his wealth if events 1 and 2 occur respectively. Gary’s total wealth is currently only $80 and he believes that the probability that he will win the race is 0.3. Which of the following is correct? (please submit the number corresponding to the correct answer). Taking the bet would reduce his expected utility. Taking the bet would leave his expected utility unchanged. Taking the bet would increase his expected utility. There is not enough information to determine whether taking the bet would increase or decrease his expected utility. The information given in the problem is self-contradictory.
- By using the expected utility theory approach with u(x)=x2, choose the optimal decision for three different possible outcomes with probabilities p(ω1)=1/2, p(ω2)=p(ω3)=1/4, rewards R(d1,ω1)=£49,R(d1,ω2)=R(d1,ω3)=£25, R(d2,ω1)=£36,R(d2,ω2)=£100,R(d2,ω3)=£0, R(d3,ω1)=£81,R(d3,ω2)=R(d3,ω3)=£0In the July 29, 2001, issue of The Journal News (Hamilton, Ohio), Lynn Elber of the Associated Press reported that “while 40 percent of American families own a television set with a V-chip installed to block designated programs with sex and violence, only 17 percent of those parents use the device.”(a)Use the report’s results to find an estimate of the probability that a randomly selected American family has used a V-chip to block programs containing sex and violence.find P(V and U)According to the report, more than 50 percent of parents have used the TV rating system (TV-14, etc.) to control their children’s TV viewing. How does this compare to the percentage using the V-chip?The promoter of a football game is concerned that it will rain. She has the option of spending $14,040 on insurance that will pay $39,000 if it rains. She estimates that the revenue from the game will be $65,040 if it does not rain and $30,040 if it does rain. What must the chance of rain be if buying the policy has the same expected return as not buying it? Write expressions showing the expected returns if the promoter does and does not purchase the insurance, using p to represent the probability of rain. Without insurance, E(return) = With insurance, E(return) = The chance of rain must be _%.
- how then can we find the total utility given q1=24, q2=30 and q3=15Are the following preferences consistent with von Neumann Morgenstern’s axioms to maximize expected utility? Explain. a. You would rather have a sure $200 to a gamble with p=0.7 chance of $200, p=0.1 chance of $50, p=0.2 chance of $300. b. You prefer the gamble of p=2/3 chance of $300 and p=1/3 chance of $50 than a sure $250 win.John is a farmer with $225 of wealth. He can either plant corn or beans. If he plants corn, John earns an income of $675 if the weather is GOOD and $0 if the weather is BAD. If he plants beans, John earns an income of $451 under both GOOD and BAD weather. The probability of GOOD weather is 0.7. The probability of BAD weather is 0.3. John’s utility function is U(c) = 5√c , where c is the value of consumption. Mae owns an insurance company in a nearby town and has decided to offer conventional crop insurance to corn farmers in the area. Assume that Mae has perfect information and can write and enforce an insurance contract that requires the farmer to plant corn. Here’s how the insurance contract works. At the beginning of the year, the corn farmer pays an insurance premium of $202.5. If the weather is GOOD, Mae makes no payment to the farmer. If the weather is BAD, Mae makes an indemnity payment of $675 to the farmer. a. If a farmer buys this insurance contract,what is Mae’s expected…
