Suppose a risk averse person is given the choice between the following lotteries: L1 = {(-200,...
Suppose a risk averse person is given the choice between the following lotteries: L1 = {(-200, 0.5), (200,0.5)}; L2 = {(-100, 0.5), (100, 0.5)}; L3 = {(-100, 0.8), (400, 0.2)}, where the first parameter is the payoff and the second the probability. Which lottery will he/she prefer?
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Suppose a risk averse person is given the choice between the
following lotteries: L1 = {(-200,...
Question 2: Lottery basics Consider the following four lotteries. $200,000 0.5 $100,000 L2 L1 -$1,000 0.6...
Question 2: Lottery basics Consider the following four lotteries. $200,000 0.5 $100,000 L2 L1 -$1,000 0.6 s65,000 0.5 L3 $30.000 0.4 $30,000 Anıswer the following questions (a) Based on your preferences and the utility you perceive, rank the four lotteries. (b) Based on your answer in part (b), calculate 1/2, 14, and ra (c) Using ro, T1/4, 1/2, Ts/a, and Fı, draw a curve that fits your utility. From observation, are you risk-seeking, risk-neutral, or risk-averse? What is your risk...
5. Expected Utility Suppose there are lotteries: Lotter 1: 50% chance of getting 100 million and...
5. Expected Utility Suppose there are lotteries: Lotter 1: 50% chance of getting 100 million and 50% chance of getting 500 million Lotter 2: 50% chance of getting 200 million and 50% chance of getting 400 million two If I prefer Lottery 1 to Lottery 2, I am risk averse or risk neutral or risk seeking?
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...
Anne has been given a choice between two lotteries. In lottery A a fair coin is...
Anne has been given a choice between two lotteries. In lottery A
a fair coin is flipped. If it comes up heads, Anne wins $50, if it
comes up tails, she wins $150. In lottery B a fair coin is also
flipped. If it comes up heads, Anne wins nothing, if it comes up
tails, she wins $200.
Problem 4 - Choice under uncertainty (20 points) Anne faces an uncertain World with two possible states, good and bad. In the...
i) Suppose that Mary’s utility function is where W is wealth. Is she risk averse? Suppose...
i) Suppose that Mary’s utility function is where W is wealth. Is she risk averse? Suppose that Mary has initial wealth of $125,000. How much of a risk premium would she require to participate in a gamble that has a 50% probability of raising her wealth to $160,000 and a 50% probability of lowering her wealth to $90,000? ii) Suppose that Irma’s utility function with respect to wealth is U(W) = 100 + 80W − W2. Find her Arrow-Pratt risk...
4. Suppose Kate has a utility of income function given in the following table Utilit 0...
4. Suppose Kate has a utility of income function given in the following table Utilit 0 Income 0 100 200 300 400 500 600 700 800 900 1000 12 35 48 58 72 76 78 (a) Kate has a choice between $200 with certainty and receiving $100 with probability 0.5 and receiving $300 with probability 0.5. Which will Kate choose? (b) Kate has a choice between $800 with certainty and receiving $600 with probability 0.5 and receiving $1000 with probability...
. Julia and John prefer more money to less and have transitive prefernces. Each of them...
. Julia and John prefer more money to less and have transitive prefernces. Each of them faces the following decision problem. S260 $80 M T SX 30% 50% 20% S320 $80 $0 $320 S0 (a) Suppose that Julia is risk neutral. If she chooses A and then U, what can we deduce about the possible values of X and p? (b) Continue to assume that Julia is risk neutral. Suppose that X-250, p 0.9. Julia is given a choice between...
4. Risk aversion Suppose an investor, Erik, is offered the investment opportunities described in the table...
4. Risk aversion Suppose an investor, Erik, is offered the investment opportunities described in the table below. Each investment costs $1,000 today and provides a payoff, also described below, one year from now. Option Payoff One Year from Now 100% chance of receiving $1,100 50% chance of receiving $1,000 50% chance of receiving $1,200 50% chance of receiving $200 50% chance of receiving $2,000 If Erik is a risk neutral investor, which investment will he prefer? Erik will be indifferent...
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...
Question 2: Lottery basics Consider the following four lotteries. $200,000 0.5 $100,000 L2 L1 -$1,000 0.6 s65,000 0.5 L3 $30.000 0.4 $30,000 Anıswer the following questions (a) Based on your preferences and the utility you perceive, rank the four lotteries. (b) Based on your answer in part (b), calculate 1/2, 14, and ra (c) Using ro, T1/4, 1/2, Ts/a, and Fı, draw a curve that fits your utility. From observation, are you risk-seeking, risk-neutral, or risk-averse? What is your risk...
5. Expected Utility Suppose there are lotteries: Lotter 1: 50% chance of getting 100 million and 50% chance of getting 500 million Lotter 2: 50% chance of getting 200 million and 50% chance of getting 400 million two If I prefer Lottery 1 to Lottery 2, I am risk averse or risk neutral or risk seeking?
Anne has been given a choice between two lotteries. In lottery A
a fair coin is flipped. If it comes up heads, Anne wins $50, if it
comes up tails, she wins $150. In lottery B a fair coin is also
flipped. If it comes up heads, Anne wins nothing, if it comes up
tails, she wins $200.
Problem 4 - Choice under uncertainty (20 points) Anne faces an uncertain World with two possible states, good and bad. In the...
4. Suppose Kate has a utility of income function given in the following table Utilit 0 Income 0 100 200 300 400 500 600 700 800 900 1000 12 35 48 58 72 76 78 (a) Kate has a choice between $200 with certainty and receiving $100 with probability 0.5 and receiving $300 with probability 0.5. Which will Kate choose? (b) Kate has a choice between $800 with certainty and receiving $600 with probability 0.5 and receiving $1000 with probability...
. Julia and John prefer more money to less and have transitive prefernces. Each of them faces the following decision problem. S260 $80 M T SX 30% 50% 20% S320 $80 $0 $320 S0 (a) Suppose that Julia is risk neutral. If she chooses A and then U, what can we deduce about the possible values of X and p? (b) Continue to assume that Julia is risk neutral. Suppose that X-250, p 0.9. Julia is given a choice between...
4. Risk aversion Suppose an investor, Erik, is offered the investment opportunities described in the table below. Each investment costs $1,000 today and provides a payoff, also described below, one year from now. Option Payoff One Year from Now 100% chance of receiving $1,100 50% chance of receiving $1,000 50% chance of receiving $1,200 50% chance of receiving $200 50% chance of receiving $2,000 If Erik is a risk neutral investor, which investment will he prefer? Erik will be indifferent...
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