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’.
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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
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...
Suppose an investor has exponential utility function U(x) = −exp(−ax) and an initial wealth level of W. The investor is faced with an opportunity to invest an amount w ≤ W and obtain a random payoff x. show that his evaluation of this incremental investment is independent of W.
A consumer who has $1000 is represented by the expected utility function u(x) = √x. A lottery ticket is sold at $80 whose prize is $10000 with probability 1/10 and zero with probability 9/10 Find the certainty equivalent of the lottery ticket. Find the risk premium of the lottery ticket. Should this consumer buy the ticket? Why?
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...
Consider the utility function u(x) = ax + b e^cx where a, b, c are positive scalars. (a) Compute the coefficient of absolute risk aversion. (b) Describe the risk attitude represented by u(x) and how it changes as x increases. (c) Write down the equations to determine the certainty equivalent and the risk premium of a gamble X for an individual with initial wealth w > 0. (d) What is the sign of the risk premium? How does the risk...
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)...
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...
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 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...
3. Suppose an individual has a utility function U=U(M, X)=10 MX^2, where U is her utility, M is her(daily) money income and x is her(daily) leisure hours. Each day, the individual needs 6 hours for sleeping and other essential personal matters 3. Suppose an individual has a utility function U = U(M,X) = 10 MX', where U is her utility, M is her (daily) money income and X is her (daily) leisure hours. Each day, the individual needs 6 hours...