$10000, faces a1. Calculate the expected utility of a person who has wealth Wpotential loss of C $5000 with probability π and has a utility index u(x) overmoney:=(i) π = 0.01 and u(x) = x²;(ii) π = 0.01 and u(x) = √√√√x;(iii) π = = 0.1 and u(x) = −2-x/10000.(iv) π = : 0.1 and u(x) = ln(x) with the natural base(v) π = = 0.1 and u(x) = log₁0 (x) with the base 10=

Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

$10000, faces a 1. Calculate the expected utility of a person who has wealth W potential loss of C $5000 with probability and has a utility index u(x) over money: = (i) π = 0.01 and u(x) = x²; (ii) π = 0.01 and u(x): = √x; (iii) π = 0.1 and u(x) = -2-x/10000. (iv) π = 0.1 and u(x) = ln(x) with the natural base (v) π = 0.1 and u(x) = log₁0 (x) with the base 10 =

$10000, faces a 1. Calculate the expected utility of a person who has wealth W potential loss of C $5000 with probability and has a utility index u(x) over money: = (i) π = 0.01 and u(x) = x²; (ii) π = 0.01 and u(x): = √x; (iii) π = 0.1 and u(x) = -2-x/10000. (iv) π = 0.1 and u(x) = ln(x) with the natural base (v) π = 0.1 and u(x) = log₁0 (x) with the base 10 =

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

1. George maximizes expected utility and he has a von-Neumann-Morgenstern utility function u (c) = √e. He has an initial wealth of $1,000. He finds an investment opportunity. The project has a startup cost of $1000, and a 9% chance of success. If the project succeeds, the payoff is $100,000; if it fails, its payoff is $0. (a) Would George invest in this project? (b) Suppose George has an initial wealth of $100, 000 instead of $1,000. Would he invest in this project? (c) Comparing your answers in parts (a) and (b), how does George's risk appetite change? Why?
The size and direction of the income effect depend on all of the following EXCEPT: O whether the good is normal or inferior. the change in the quantity of X when purchasing power is transformed. the amount of the good (X) the consumer buys the change in the consumption of X as the price of X changes, holding utility constant.
4) Consider investors with preferences represented by the utility function U = E(r) – Ao². (a) Draw the indifference curve representing a utility level of 10% for an in- vestor with a risk aversion parameter A = 3 in expected return-standard deviation space. (b) In the same graph, draw the indifference curve representing a utility level of 15% for an investor with a risk aversion parameter A = 3. (c) In the same graph, draw the indifference curve representing a utility level of 10% for an investor with a risk aversion parameter A = 5.
Question 15 W(1-x) Selwyn has a utility function of the formu (W) = - -, where x=0.3. Calculate Selwyn's coefficient of relative 1-x risk aversion when his wealth is equal to £12. Round your answer to 1 decimal place. Add your answer
None
Micro Question 1 Please help to solve this. Thank you
2
4) Luke is planning an around-the-world trip on which he plans to spend $10,000. The utility from the trip is a function of how much she spends on it (Y ), given by U(Y) = InY a). If there is a 25 percent probability that Luke will lose $1000 of his cash on the trip, what is the trip's expected utility. b). Suppose that Luke can buy insurance to fully against losing the $1,000 with a actuarially fair insurance. What is his expected utility if he purchase this insurance. Will he purchase the insurance? c). Now suppose utility function is U(Y) = Y/1000 What is his expected utility if he purchase the insurance in b). Will he purchase the insurance?
19. An individual has initial wealth Wo = 3 and has the opportunity to invest some quantity of money x in an extremely risky corporate bond. With probability p= 1/4, the bond will be worth 10x at maturity. With probability 1 – p, it will be worth zero. The individual's utility function over final wealth is u(W) = W0.5. What is the level of investment x that maximizes expected utility? (а) 0 (b) 1 (c) 4/3 (d) V3 (e) 2
Find the Pratt - Arrow risk - aversion function for a utility function U(W) = log(0.5-W + 500), where W is the amount of wealth in €. Suppose that an investor's wealth is subject to outcomes -800 €, 500 €, 500 € and 1, 000 € which affect the initial amount of 2,500 € with probabilities of their occurrence 40%, 15%, 15% and 30%, respectively. a) Using the Taylor approximation to certainty equivalent, calculate an approximate expected utility value. b) Calculate the certain equivalent of the investor's uncertain wealth. Interpret.
7. Consider an individual whose utility function over money is u(w) = 1+2w. (a) Is the individual risk-averse, risk-neutral, or risk-loving? Does it depend on w? (b) Suppose the individual has initial wealth ¥W and faces the possible loss of Y. The probability that the loss will occur is . Suppose insurance is available at price p, where p is not necessarily the fair price. Find the optimal amount of insurance the individual should buy. You may assume that the solution is interior. (c) Is there a price at which the individual will not want to buy any insurance? If so, find it. If no, explain.
4. Kate has von Neumann-Morgenstern utility function U(x1,x2) = m7. 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 ? 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 your answer.