ZuoTi.Pro
Question

My von Neumann Morgenstern utility function is U (W) = 32 + (9/5)w1/2 for wealth w. I face a gamble that pays 1 with probabil
business   economics   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

u(x) = 32 + (9/5)√w
Now w = 1, p =.5
w = 4, p = .5
So EU = .5[32 + 1.8√1] + .5*[32+ 1.8√4]
= .5*33.8 + .5*35.6
= 16.9 + 17.8
= 34.7


So for CE, √CE = EU

CE = EU2
so CE = 34.72
CE = 1204.09

Expected Consumption EC = .5*1 + .5*4 = 2.5

Risk Premium RP = Expected Consumption - CE

= 2.5 - 1204.09

= -1201.59

0 1
Add a comment
Know the answer?
Add Answer to:
My von Neumann Morgenstern utility function is U (W) = 32 + (9/5)w1/2 for wealth w....
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • Billy Pigskin is a football player with a von Neumann-Morgenstern utility function U(c) = c 1/2....

    Billy Pigskin is a football player with a von Neumann-Morgenstern utility function U(c) = c 1/2. If Billy is not injured this season, he will receive an income of $16 million. If he is injured, his income will be only $10,000. The probability that he will be injured is 0.1 and the probability that he will not be injured is 0.9. What is the certainty equivalent of the gamble that Billy is facing? (See the hint to problem 3.)

  • 2) (20 points) Lynn has a utility function U(W) = W1/2, where W is the amount...

    2) (20 points) Lynn has a utility function U(W) = W1/2, where W is the amount of wealth that she has. Lynn has two assets. She has $40,000 in a bank account, and she has a house worth $600,000, so her total wealth is initially $640,000. There is a 2% chance that her house is destroyed by a fire. a) (4 points) Considering the probability that there is a fire, what is Lynn’s Expected Wealth, E(W)? E(W) = ____________________________ b)...

  • W 2 Assume you have the following von Neumann-Morgenstern utility function: U(w) = 200 – (12...

    W 2 Assume you have the following von Neumann-Morgenstern utility function: U(w) = 200 – (12 – 1000) where w denotes wealth measured in pounds. Your friend believes that it will rain in Reading tomorrow while you think that there is a 75% probability that it will not rain. You are going to take a bet. Your friend will pay you x pounds if it does not rain and you pay your friend x pounds if it rains. Your current...

  • b. My utility is U(w) with initial wealth W. There is a 50% chance I gain...

    b. My utility is U(w) with initial wealth W. There is a 50% chance I gain $x (so my wealth becomes W +x), and a 50% chance I lose $x so my wealth falls to W-x. Let c be my certainty equivalent for this gamble. Explain how the sign of the derivative dc/dx depends on my attitude towards risk.

  • 4. Kate has von Neumann-Morgenstern utility function U(x1,x2) = m 2 . She currently has $2025....

    4. Kate has von Neumann-Morgenstern utility function U(x1,x2) = m 2 . She currently has $2025. a. Would she be willing to undertake a gamble that involves a gain $2875 with probability ) and a loss of $1125 with probability Ž ? Show your work and explain your answer. b. Would she be willing to undertake a gamble that involves a gain $2599 with probability { and a loss of $800 with probability — ? Show your work and explain...

  • 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...

  • Consider the utility function u(x) = ax + b e^cx where a, b, c are positive...

    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...

  • (Mathematical Question) Suppose you have a utility function   where W  is the level of wealth you end...

    (Mathematical Question) Suppose you have a utility function   where W  is the level of wealth you end up with. You are currently in possession of 81  dollars. There is a  1/3 chance that a miserable event will happen and cost you all 81  dollars. Assume your preference over uncertainty is characterized by the expected utility. a. (5pts) Define the gamble b. (5pts) What is the expected value of this gamble? c. (10pts) Find the certainty equivalent of the gamble. Then find the insurance premium...

  • 8) Kurt is an expected utility maximizer with a Bernoulli utility u(w) = w1/2 facing the...

    8) Kurt is an expected utility maximizer with a Bernoulli utility u(w) = w1/2 facing the choice between two gambles. Gamble 1 would give him $100 with probability 0.7, $50 with probability 0.1 and $150 otherwise. Gamble 2 would give $200 with probability 0.6, $100 with probability 0.2 and $0 otherwise. Which of the following is true. a. Kurt is indifferent between the two gambles. b. the two gambles yield the same expected wealth. Kurt prefers Gamble 1 over Gamble...

  • 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)...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
Active Questions
ADVERTISEMENT