Question 1) Dave is an expected utility maximizer and his von Neumann-Morgenstern utility function is given by u(w) = 199 (w). He has an initial wealth of $27,000. √99+7 (a) Determine the risk attitude of this economic agent. b) If John is facing a risk of losing $19,000 with probability 0.1, write down his prospective final wealth and the associated probabilities in the form of a lottery. (c) Facing the risk of losing $19,000 with probability 0.1, what would be the maximum that Dave is willing to pay for 19,000 units of a contingent claim that pays $1 if and only if the loss occurs.

Question 1) Dave is an expected utility maximizer and his von Neumann-Morgenstern utility function is given by u(w) = 199 (w). He has an initial wealth of $27,000. √99+7 (a) Determine the risk attitude of this economic agent. b) If John is facing a risk of losing $19,000 with probability 0.1, write down his prospective final wealth and the associated probabilities in the form of a lottery. (c) Facing the risk of losing $19,000 with probability 0.1, what would be the maximum that Dave is willing to pay for 19,000 units of a contingent claim that pays $1 if and only if the loss occurs.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Janet's broad attitude to risk (risk averse, risk neutral, or risk loving) is independent of her wealth. She has initial wealth w and is offered the opportunity to buy a lottery ticket. If she buys it, her final wealth will be either w + 4 or w – 2, each equally likely. She is indifferent between buying the ticket and not buying it. Janet offers her friend Sam (who has identical preferences and initial wealth) the following proposition: They buy the ticket together, and share the cost and proceeds equally. Sam has another idea: They buy two tickets (that have independent outcomes) and share the costs and proceeds equally. Suppose that Janet's and Sam's utility of income is given by u(x) = In x and the initla wealth of each one of them is equal to w = 4. Which of the following statements is true? O a. Both agents prefer Sam's solutions to Janet's solution. b. Both agents prefer Janet's solutions to Sam's solution. The agents are indifferent between Janet's solutions to Sam's solution.…
Lucy and Henry each have $1652. Each knows that with 0.1 probability, they will lose 85% of their wealth. They both have the option of buying a units of insurance, with each unit costing $0.1. Each unit of insurance pays out $1 in the event the loss occurs. The cost of the insurance policy is paid regardless of whether the loss is incurred. Lucy's utility is given by u²(x) = x, Henry's utility is given by u¹(x) = √√x. Answer the following: (If rounding is needed, only round at the end and write your answer to three decimal places.) a) Without insurance, what is the expected value of the loss? b) c) d). e) ( For Henry, facing the "lottery " above without any insurance is as bad as losing how many dollars for sure? Find Lucy's utility maximising choice of a. If more than 1 exist, enter the largest a. Now suppose insurance costs $0.2. Find Lucy's utility maximising choice of a. If more than 1 exist, enter the largest a. What is Henry's utility maximising choice of a with the new price of…
The value of a successful project is $420,000; the probabilities of success are 1/2 with good supervision and 1/4 without. The manager is risk neutral, not risk averse as in the text, so his expected utility equals his expected income minus his disutility of effort. He can get other jobs paying $90,000, and his disutility for exerting the extra effort for good supervision on your project is $100,000. (a) Show that inducing high effort would require the firm to offer a compensation scheme with a negative base salary; that is, if the project fails, the manager pays the firm an amount stipulated in the scheme. (b) How might a negative base salary be implemented in reality? (c) Show that if a negative base salary is not feasible, then the firm does better to settle for the low-pay, low-effort situation.
You have a net worth of $901395 and a utility function given by u(w) = w0.5. If your house %3! catches fire, a 3% likelihood of occurring, you expect it to be total loss and it was recently assessed at $792999. What is the risk premium ($) you'd be willing to pay for full coverage against this fire risk? Hints: Compute the certainty equivalent (CEQ) as you did in Comm 220 and recall that the risk premia is the amount you'd be willing to pay over the expected loss Answer:
Suppose you have an exponential utility function given by U(x) =1- exp(-x/R) where, for you, R = 1000. Further, suppose you have an investment with a 50/50 chance of returning either 0 or 2000 dollars. Note U(0) = 0 and U(2000) = 0.865, so the utility of the lottery is 0.432. What is the certain equivalent of that investment?
A widely used utility function in the economics literature is the constant rate of risk aversion utility function. It is given by: utc) = c*(1-n) (1-n) Assume that an agent lives tor three periods (t-0,1,2) and discounts future utity at rate B (per period), The agent is born with asset level ag and his/her labour market income is yo and y, for periods O and 1 respectively, the agent retire in the last period (no labour income). The interest rate in this economy is Please answer the following questions based on the information displayed here. Choose the best option avallable. Select one: O a. The budget constrain in period te2 is given by: C2 + ay = az(1+r) O b. The budget constrain in period te2 is given by: c2= az{1+1) O G. The budget constrain in period t=2 is glven by: ute, )+ ag = a;(1+1) +ya d. The budget constrain in period t=2 is given by: C2= az(1+r) +y3 e. The budget constrain in period te2 is given by: c, + ag = az(1+) +ya
Suppose Alex’s utility function is u ($x) = √x. Assume her initial wealth is 0. Is it possible that Alex’s expected utility from the prospect equals $5, why? What is the possible range of Alex’s expected utility?
Use the utility function u = E (r,) – 0.5 A o, where A is the risk aversion parameter and A = 3.5. Use the average annual return on the S&P 500 as E(r,). Use the average annual interest rate on the US Government 10-year treasury bond over the past decade as r Solve for the investor's optimal allocation between the risky and the risk-free asset.
Prospect Y = ($6, 0.25 ; $15, 0.75) If Will's utility of wealth function is given by u(x)=x0.25, what is the value of CE(Y) for Will? (In other words, what is Will's certainty equivalent for prospect Y?) (The certainty equivalent represents the maximum amount a person would be willing to pay to acquire a risky prospect, and equivalently, the lowest price for which they would be willing to sell a risky prospect if they already owned it) (Note: The answer may not be a whole number; please round to the nearest hundredth) (Note: The numbers may change between questions, so read carefully)
Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index . There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. a) Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain. b) What would be the highest price (premium) that she would be willing to pay for an insurance policy that fully insures her against the flooding damage?