A Risk Lover prefers the expected utility of wealth to the utility of the expected value of wealth. It is because a risk lover has a convex utility function It is because a risk lover has a concave utility function
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A Risk Lover prefers the expected utility of wealth to the utility of the expected value of wealth.
- It is because a risk lover has a convex utility function
- It is because a risk lover has a concave utility function
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- Microeconomics Wilfred’s expected utility function is px1^0.5+(1−p)x2^0.5, where p is the probability that he consumes x1 and 1 - p is the probability that he consumes x2. Wilfred is offered a choice between getting a sure payment of $Z or a lottery in which he receives $2500 with probability p = 0.4 and $3700 with probability 1 - p. Wilfred will choose the sure payment if Z > CE and the lottery if Z < CE, where the value of CE is equal to ___ (please round your final answer to two decimal places if necessary)A person will be risk seeking if his (or her) utility function shows increasing marginal utility of wealth. True FalseAdam has just purchased a new car and has to decide whether to buy insurance to cover his new car in the event of a loss. Assume that Adam knows the probability (p) of him having an accident and losing his new car. The car is valued at L and the amount of insurance to purchase for this value is X. Adam’s entire wealth after buying the car is W. Let r be unit price of insurance. Briefly explain the problem of the insurance company and show that for insurance to be actuarially fair, the premium must equal the probability of accident.
- Jamal has a utility function U = W1/2, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a game show, the host offers Jamal a choice between (A) $4 million for sure, or (B) a gamble that pays $1 million with probability 0.6 and $9 million with probability 0.4. a. b. c. d. Graph Jamal’s utility function. Is he risk averse? Explain. (2+2) Does A or B offer Jamal a higher expected prize? Explain your reasoning with appropriate calculations. (1) Does A or B offer Jamal a higher expected utility? Explain your reasoning with calculations. (2) Should Jamal pick A or B? Why?Khalid has a utility function U = W1/2, where W is his wealth in millions of dollarsand U is the utility he obtains from the wealth. In a game show, the host offershim a choice between (A) $4 million for sure, or (B) a gamble that pays $1million with probability 0.6 and $9 million with probability 0.4.i. Graph Khalid’s utility function with the help of above utility function. Ishe risk lover? Explain. ii. Does A or B choice offer Khalid a higher expected prize? Explain yourreasoning with appropriate calculations. iii. Does A or B offer Khalid a higher expected utility? Again, show yourcalculations. iv. Should Jamal pick A or B choice? Why?Antonio has a utility function U = W, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a game show, the host offers Antonio a choice between (A) $9 million for sure, or (B) a gamble that pays $1 million with probability 0.4 and $16 million with probability 0.6. Use the blue curve (circle points) to graph Antonio's utility function at wealth levels of $0, $1 million, $4 million, $9 million, and $16 million. ? Utility (Thousands) 5.0 4.5 4.0 3.5 3.0 25 2.0 1.5 1.0 0.5 0 + 0 2 4 6 8 10 12 14 Wealth (Millions of dollars) 16 18 True or False: Antonio is risk averse. 20 20 Utility Function Choice True O False offers Antonio a higher expected prize. (Hint: The expected value of a random variable is the weighted average of the possible outcomes, where the probabilities are the weights.) Choice offers Antonio a higher expected utility. Antonio should pick choice,
- 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%. a. If Steve's utility of income is U(I)=50I. What is Steve's expected utility from buying $1,000 worth of XYZ Corp. stock? b. If Steve's utility of income is U(I)=I0.5. What is Steve's expected utility from buying $1,000 worth of XYZ Corp. stock?Jamal has a utility function U= W1/2 where Wis his wealth in millions of 'dollars and Uis the utility he obtains from that wealth. In the final stage of a game show, the host offers Jamal a choice between (A) $4 million for sure, or (B) a gamble that pays $1million with a probability of 0.6 and $9 million with a probability of 0.4. a. Graph Jamal's utility function. Is he risk-averse? Explain. b. Does A or B offer, Jamal, a higher expected price? Explain your reasoning with appropriate calculations. (Hint: The expected value of a random variable is the weighted average of the possible outcomes, where the probabilities are the weights.) c. Does A or B offer Jamal a higher expected utility? Again, show your calculations. d. Should Jamal pick A or B? Why?Alex has a utility function U = W2, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a game show, the host offers Alex a choice between (A) $9 million for sure, or (B) a gamble that pays $1 million with probability 0.4 and $16 million with probability 0.6. Use the blue curve (circle points) to graph Alex's utility function at wealth levels of $0, $1 million, $4 million, $9 million, and $16 million. Utility (Thousands) 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0 0 2 4 6 8 10 12 14 Wealth (Millions of dollars) 16 18 20 V Utility Function (?)
- Economists define the 'certainty equivalent' of a risky stream of income as the amount of guaranteed money an individual would accept instead of taking a risk. The certainty equivalent varies between individuals based on their risk preference. Consider a risky bet that involves a 50-50 chance of losing $5,000 or winning $5,000 for an individual with starting income of $50,000. Calculate the certainty equivalent income that provides the same utility as this bet for individuals with these different utility functions: a. U(1) Vi b. U(1) = In(1) where In represents the natural logarithm function C. U(I) = -1/1 d. What can you conclude about the relative level of risk aversion for these three individuals? e What would be the certainty equivalent income for this bet for a risk neutral individual? f. What is the likelihood that a profit maximizing risk neutral insurance company would be willing and able to purchase these bets from the individuals in a, b and c? Explain.Draw a utility function over income u( I) that describes a man who is a risk lover when his income is low but risk averse when his income is high. Can you explain why such a utility function might reasonably describe a person’s preferences?After finishing high school, Klaus got a job selling towels to tourists in South Beach on the weekends. On a good weekend, he makes $450 and on bad ones, only $120. Assume good weekends and bad weekends are equally likely. If Klaus has a utility function u(x) = x0.5, what fixed salary with no risk would give him the same expected utility? a. $240.1 b. $246.5 c. $250.4 d. $258.7