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19.2. Ulity Manipulation II (a) A person is found to have the utity function: U(X) (400100x)/2,...
2. An individual has a vNM utility function over money of u(x) -Vx, where x is final wealth. Assu...
2. An individual has a vNM utility function over money of u(x) -Vx, where x is final wealth. Assume the individual currently has $16. He is offered a lottery with three possible outcomes; he could gain an extra S9, lose $7, or not lose or gain anything. There is a 15% probability that he will win the extra $9, what minimum probability, p, of losing S7 would ensure that the individual chooses to not play the lottery? (a) p >...
Suppose the utility function of a decision maker for the amount of money x is given...
Suppose the utility function of a decision maker for the amount of money x is given by U(x) = x2. (a) This decision maker is considering the following two lotteries: A: With probability 1, he gains 3000. B: With probability 0.4, he gains TL 1000, and with probability 0.6, he gains TL 4000. Which of the two lotteries will the decision maker prefer? What is the certainty equivalent (CE) for lottery B? Based on the CE for B, is the...
6. A decision maker has a vNM utility function over money of u(x) = x2. This...
6. A decision maker has a vNM utility function over money of u(x) = x2. This decision maker is (a) risk-averse. (b) risk-neutral. (c) risk-loving. (d) none of the above. 7. Consider two lotteries: • Lottery 1: The gamble (0.1, 0.6, 0.3) over the final wealth levels ($1, $2, $3). (The expected value of this lottery equals $2.2) • Lottery 2: Get $2.2 for sure. a) Any risk-averse individual will choose the first lottery. b) Any risk-averse individual will choose...
Carlos has a utlity function U wi, where W is his wealth in millons or dollars...
Carlos has a utlity function U wi, where W is his wealth in millons or dollars and U is the ueity he obtains from that weath. In the final stage of a game show, the host offers Carlos a choice between (A) 59 miltion 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 Carlos's utlity function at wealth levels of so, $1...
Suppose you are facing a lottery that has a payoff of 10b pounds with probability 0.01 and that of 0 with probability 0.99. You are an expected utility maximiser with a utility function, u(x) = −exp(−ax) where x is the payoff in money terms and a > 0 is a
Suppose you are facing a lottery that has a payoff of 10b pounds with probability 0.01 and that of 0 with probability 0.99. You are an expected utility maximiser with a utility function,u(x) = −exp(−ax) where x is the payoff in money terms and a > 0 is a parameter. What is the risk premium for this lottery - describe the risk premium as a function of ‘a’ and ‘b’.
5. A person has utility function u(x, y) = 100xy + x + 2y. Suppose that...
5. A person has utility function u(x, y) = 100xy + x + 2y. Suppose that the price per unit of x is $2, and that the price per unit of y is $4. The person receives $1 000 that all has to be spent on the two commodities x and y. Solve the utility maximization problem.
4. An individual has a VNM utility function over money of u(x)=x", where x is the...
4. An individual has a VNM utility function over money of u(x)=x", where x is the amount of money won in the lottery. She faces two scenarios: • Scenario 1: With a 50% probability she wins $36. With a 50% probability she wins $16. • Scenario 2: With a 50% probability she wins $0. With a 50% probability she wins $x. For what value of x will the risk premia be identical in these two scenarios? a. O b. 4...
Suppose a person has the utility function, U(I)=log(I), where I is income. He has income I2...
Suppose a person has the utility function, U(I)=log(I), where I is income. He has income I2 ($4,000) with the probability of p, but knows that some externally generated risk may reduce his income to I1 ($1,000) with probability of 1-p. Suppose p=0.8. 1) Is this person risk-averse? If so, why? 2) What is the expected income of this person? 3) What is the utility of expected income for this person? 4) What is the expected utility of this person? 5)...
1. a. Two investors, A and B, are evaluating the same investment opportunity, which has an expected value of £100. The u...
1. a. Two investors, A and B, are evaluating the same investment opportunity, which has an expected value of £100. The utility functions of A and B are ln(x) and x2, respectively. Which investor has a certainty equivalent higher than 100? Which investor requires the higher risk premium? b. (i) Describe suitable measures of risk for ‘loss-aversion’ and ‘risk aversion’. (ii) Concisely define the term ‘risk neutral’ with respect to a utility function u (w), where w is the realisation...
A person with the following utility function, u(x) = ln(x) faces a world where with probability...
A person with the following utility function, u(x) = ln(x) faces a world where with probability 0.1 will suffer of identity theft which will reduce their wealth from $250000 to $100000. This means that we can write: E{u(.)] = 0.91n(x) +0.1ln(y) where x would be the wealth under no identity theft and y the wealth under identity theft. This means that the marginal utilities are: MU 0.9, MUy = 0.1 Using this information answer the following questions 1) What is...
2. An individual has a vNM utility function over money of u(x) -Vx, where x is final wealth. Assume the individual currently has $16. He is offered a lottery with three possible outcomes; he could gain an extra S9, lose $7, or not lose or gain anything. There is a 15% probability that he will win the extra $9, what minimum probability, p, of losing S7 would ensure that the individual chooses to not play the lottery? (a) p >...
Carlos has a utlity function U wi, where W is his wealth in millons or dollars and U is the ueity he obtains from that weath. In the final stage of a game show, the host offers Carlos a choice between (A) 59 miltion 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 Carlos's utlity function at wealth levels of so, $1...
5. A person has utility function u(x, y) = 100xy + x + 2y. Suppose that the price per unit of x is $2, and that the price per unit of y is $4. The person receives $1 000 that all has to be spent on the two commodities x and y. Solve the utility maximization problem.
4. An individual has a VNM utility function over money of u(x)=x", where x is the amount of money won in the lottery. She faces two scenarios: • Scenario 1: With a 50% probability she wins $36. With a 50% probability she wins $16. • Scenario 2: With a 50% probability she wins $0. With a 50% probability she wins $x. For what value of x will the risk premia be identical in these two scenarios? a. O b. 4...
A person with the following utility function, u(x) = ln(x) faces a world where with probability 0.1 will suffer of identity theft which will reduce their wealth from $250000 to $100000. This means that we can write: E{u(.)] = 0.91n(x) +0.1ln(y) where x would be the wealth under no identity theft and y the wealth under identity theft. This means that the marginal utilities are: MU 0.9, MUy = 0.1 Using this information answer the following questions 1) What is...
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