Given a lottery P, let E (P) be the expected value of the lottery P. For...
Given a lottery P, let E (P) be the expected value of the lottery P. For example, if P = ($10, 0.5; $0, 0.5), then E (P) = 0.5 × 10 + 0.5 × 0 = 5
(1) Ann has vNM utility u1 (x) = x, Bob has utility u2 (x) = √ x and Carl has utility u3 (x) = x^3 . Who is risk neutral, risk averse and risk loving?
(2) Consider the lottery P again. Find the dollar amount x such that each person is indifferent between the lottery P and $x (x is the certainty equivalent of P)
Homework Answers
Ann is risk neutral bcoz utility function is linear in wealth
Bob is risk averse bcoz utility function is concave
Carl is risk lover as utility function is convex
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Given a lottery P, let E (P) be the expected value of the
lottery P. For...
(1) Ann has vNM utility u1 (x) = x, Bob has utility u2 (x) = √...
(1) Ann has vNM utility u1 (x) = x, Bob has utility u2 (x) = √ x and Carl has utility u3 (x) = x 3 . Who is risk neutral, risk averse and risk loving? (2) Consider the lottery P again. Find the dollar amount x such that each person is indifferent between the lottery P and $x (x is the certainty equivalent of P) (3) Calculate the Arrow-Pratt coefficients for everyone. How do they compare? Does this agree...
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...
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...
Lottery - Let $1,000 be your current wealth. There are 100 people and each buys a...
Lottery - Let $1,000 be your current wealth. There are 100 people and each buys a lottery ticket at $5. The administrative cost of the lottery ticket per person is $5. If you win the lottery, you will get $500. There is only one person who can win the lottery. a. Define the gamble b. Calculate the expected value of the gamble c. Is this gamble favorable, fair, or unfavorable? d. Now, suppose your utility function is U = W5/2....
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...
a. If your are offered a gift card valued $50 or the chance at a raffle...
a. If your are offered a gift card valued $50 or the chance at a raffle for a giftcard valued $100, with a 50% chance at getting the giftcard or a 50% chance of getting nothing, which would you choose? Given this answer explain whether you are risk averse, risk loving, or risk neutral and why. 30 50 75 100 7) The above figure shows Bob's utility function. He currently has $100 of wealth, but there is a 50% chance...
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)...
. 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...
John has a utility function given by the expression U(x) = E(r) -½A(s²). Where E(r) is...
John has a utility function given by the expression U(x) = E(r) -½A(s²). Where E(r) is the expected return on an asset and s is the standard deviation of returns on that asset.John has the opportunity to purchase the XJKsecurity that returns 25.9% with 23% probability and returns 8.6% the remainder of the time. The security has a price of $33 and A=11 a) What is the risk-neutral valuation of the XJK security? Recall the risk-neutral value is simply 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...
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...
Lottery - Let $1,000 be your current wealth. There are 100 people and each buys a lottery ticket at $5. The administrative cost of the lottery ticket per person is $5. If you win the lottery, you will get $500. There is only one person who can win the lottery. a. Define the gamble b. Calculate the expected value of the gamble c. Is this gamble favorable, fair, or unfavorable? d. Now, suppose your utility function is U = W5/2....
a. If your are offered a gift card valued $50 or the chance at a raffle for a giftcard valued $100, with a 50% chance at getting the giftcard or a 50% chance of getting nothing, which would you choose? Given this answer explain whether you are risk averse, risk loving, or risk neutral and why. 30 50 75 100 7) The above figure shows Bob's utility function. He currently has $100 of wealth, but there is a 50% chance...
. 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...
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...
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