Problem set # 2. Risk, expected utility, and loss aversion Due date: March 7I. Assume a household whose utility is neo-classical, U(x). Therealized income is random, high or low:probability 0.5[x₁ = Y(1+),x₁ = {x₂ = Y(1-8), probability 0.5'where & > 0 is the realized shock.Find the cost of volatility, measured by insurance that the household iswilling to pay, r, such that U(Y(1-7)) = E(U(x)),where E(U(x)) is the expected utility in the absence of insurance.Hint: this question can be solved graphically by looking at a chart of U'(x), themarginal utility as a function of income x, see the chart below. To simplify notation,assume normalized utility such that U(1) = U'(1) = 1.U'(x)1-1 1+X II Redo question I for the case of a loss-averse household -- when thebad shock happens, the utility weight associated with the loss is magnifiedby the rate of disappointment, B. Thus, the 'expected utility' of a loss-averse household is V=0.5U[Y(1+ɛ)] +0.5(1+B)U[Y (1–ɛ)].Hint: the hint of question 1 applies also to question 2; one can solve theabove graphically, or assume that U(x) = ln (x).III. Assume that B= 2, &=0.05, Y = 1. Calculate the cost ofvolatility for risk-averse and loss-averse consumer described in the firsttwo questions.

Given information Realized High income with 0.5 probability=Y(1+e)--- e>0 realized shock Realized…

Problem set # 2. Risk, expected utility, and loss aversion Due date: March 7 I. Assume a household whose utility is neo-classical, U(x). The realized income is random, high or low: x = Y(1+E), probability 0.5 x₂ , where & > 0 is the realized shock. x₂ = Y(1-8), probability 0.5' Find the cost of volatility, measured by insurance that the household is willing to pay, T, such that U(Y(1-7)) = E(U(x)), where E(U(x)) is the expected utility in the absence of insurance. Hint: this question can be solved graphically by looking at a chart of U'(x), the

Problem set # 2. Risk, expected utility, and loss aversion Due date: March 7 I. Assume a household whose utility is neo-classical, U(x). The realized income is random, high or low: x = Y(1+E), probability 0.5 x₂ , where & > 0 is the realized shock. x₂ = Y(1-8), probability 0.5' Find the cost of volatility, measured by insurance that the household is willing to pay, T, such that U(Y(1-7)) = E(U(x)), where E(U(x)) is the expected utility in the absence of insurance. Hint: this question can be solved graphically by looking at a chart of U'(x), the

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Related questions

Q: Assume that two investment opportunities have identical expected values of $100,000. Investment A…

A: Given, E(A) = E(B) = 100,000

Q: A decision maker is risk averse with current wealth equal to $90,000 and the utility functionu = w2.…

A: Wealth = $90,000 Utility Function - w1/2 Probability of accident = 0.2 Damage due to accident =…

Q: You've estimated the following expected returns for a stock, depending on the strength of the…

A: Investors look at the expected return to gauge what they might make from an investment. It's…

Q: Uncertainty The Utility function is U = W1/3 Flood occurs with Probabilities=1/25. The Value of a…

A: Expected utility is a weighted average of utilities of each of the possible events.

Q: Question 1) An expected utility maximiser owns a car worth £60000 and has a bank account with…

A: Note:- “Since you have asked multiple question, we will solve the first question for you. If you…

Q: Define Expected Shortfall (ES), which is also called "Conditional Value at Risk "Expected Tail…

A: Conditional Value at Risk (CVaR), otherwise called the expected shortfall.

Q: Beta and volatility differ as risk measures in that beta measures only non‑systematic risk, while…

A: Risk is the possibility of future profits or outcomes deviating from expectations. It is the level…

Q: Suppose one uses the single-index model to estimate characteristics of securities.Which of the…

A: It can be defined as a concept that shows how much currency of one nation is valuable in terms of…

Q: Please show how to solve this in excel for 1 - 6 below Consider an investment for which the expected…

Q: Given the following information, what is the standard deviation of the returns on a portfolio that…

A: According to the given information:

Q: An investor with initial wealth $20000 and utility function U(x) = ln(x) is considering an…

A: Utility refers to the benefit that a consumer gains by consuming any goods or service.

Q: Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with…

A: The Von Neumann-Morgenstern (VNM) utility index is an index that measures an individual's preference…

Q: b) Explain why, in general, the problem of moral hazard makes full insurance contracts impractical.…

A: Insurance firms attempt to reduce moral hazard by designing policies that reward conduct that does…

Q: 10. Karl's utility function is U(w) where w is wealth. His initial wealth %3D w+200 300. He…

A: If Karl gambles and wins, he gets 200 and if he gambles and lost, he loses 200. So The total wealth…

Q: 2. A consumer has utility function for wealth U(W) = Ws, wealth W $1,000, and faces a 50% chance of…

A: Utility function for wealth: U(W) = W1/3 --------------------- W is wealth. ---------------------…

Q: Problem Solving. Solve the following problems completely. 2. You have identified two risks with…

A: Expected Monetary Value is a necessary piece of risk for the executives and is utilized in the…

Q: A risk-averse expected-utility maximizer has initial wealth w0 and utility function u. She facesa…

A: The objective of the question is to determine the expected utility of a risk-averse individual who…

Q: Suppose Firm B is selling 1-year insurance contracts for houses. Suppose Firm B's customers are…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Suppose that you have a job paying $50,000 per year. With a 5% probability, next year your wage will…

A: Given The income per year =$50,000 There is a 5% chance that the next year the wage is reduced to…

Q: Suppose that the probability of low demand is 0.75. (a) What is the maximum Expected Monetary…

A: The law of demand is a basic rule of economics that states that at a higher price consumers will…

Q: A risk-averse individual experiences an adverse event with probability of 2% (0.02) that costs…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Please explain briefly the concepts of risk aversion, utility, and certainty equivalent. What is the…

A: The concept of risk refers to that situation where an individual is uncertain about the outcome of…

Q: 1. Assume the following smooth production function: Q = Q(K,L) with positive marginal…

A: A production function is a numerical function that shows the connection between the inputs utilized…

Concept explainers

Unemployment and Cost of Unemployment

Unemployment is the state of being unemployed, even when an individual is actively seeking work opportunities. The unemployment rate refers to the percentage of the workforce that is currently unemployed.

Question

Problem set # 2. Risk, expected utility, and loss aversion Due date: March 7
I. Assume a household whose utility is neo-classical, U(x). The
realized income is random, high or low:
probability 0.5
[x₁ = Y(1+),
x₁ = {
x₂ = Y(1-8), probability 0.5'
where & > 0 is the realized shock.
Find the cost of volatility, measured by insurance that the household is
willing to pay, r, such that U(Y(1-7)) = E(U(x)),
where E(U(x)) is the expected utility in the absence of insurance.
Hint: this question can be solved graphically by looking at a chart of U'(x), the
marginal utility as a function of income x, see the chart below. To simplify notation,
assume normalized utility such that U(1) = U'(1) = 1.
U'(x)
1-1 1+
X

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.

Similar questions

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.
Hugo has a concave ubility function of U(W)=√W. His only asset is shares in an Internet start-up company. Tomorrow he will learn the stock's value. He belleves that it is worth $225 with probability 80% and $256 with probability 20%. What is his expected utsty? What risk premium would he pay to avoid bearing this risk? The stock's expected utility (EU) is EU = (Enter a numeric response using a real number rounded to two decimal places.) han fro
solve d please
None
advanced microeconomics, uncertainty
‘Lottery A’ refers to a lottery ticket that pays $2,000 with a probability of 0.3, $8,000 with a probability of 0.4, $12,000 with a probability of 0.2, and $18,000 with a probability of 0.1.What is the expected value of Lottery A?A) $7200B) $8000C) $9000D) $7900E) None of the above
Millicent’s utility function is U(w) = W0.5 , where W is her wealth. She owns a “pure water” producing firm that will be worth GH100 or 0 Ghana cedis next year with equal probability. a. Suppose her firm is the only asset she has. What is the lowest price at which she will agree to sell her pure water? (Hint: price=amount that will give her the same expected utility) b. Assume that she has GH200 safely stored under her mattress, find the new lowest price at which she will agree to sell her “pure water” producing firm c. From your answers in parts (a) and (b), what is the relationship between her wealth and her degree of risk aversion?