In economics, an index of risk aversion is defined as: I(m) = -U" (m) U'(m) where m measures how much of a commodity is owned and U(m) is a utility function. Find the index of aversion, I(m), for both utility functions U₁(m) = √m and Ut(m) = m5/8, and determine which indicates a greater aversion to risk.

In economics, an index of risk aversion is defined as: I(m) = -U" (m) U'(m) where m measures how much of a commodity is owned and U(m) is a utility function. Find the index of aversion, I(m), for both utility functions U₁(m) = √m and Ut(m) = m5/8, and determine which indicates a greater aversion to risk.

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

6. An analyst is assessing a DM's utility function for profit Y, in dollars, ranging from -400,000 to 2,000,000, and wishes to use a function: U(Y) : = Y+400,000 B 2,400,000 9 -400,000 ≤ y ≤ 2,000,000 She determined that the DM is indifferent between Alternative A and Alternative B: Alternative A: Probability 0.5 of making profit $2,000,000 Probability 0.5 of making profit -$400,000 Alternative B: Probability 1.0 of making profit of $800,000 (a) What would you use for the DM's utility function? Show your work. 6 (b) Why could you use Expected Value when analyzing problems involving profit for this DM?
2. Alice believes that her car would cost £12500 to replace if it was stolen or damaged. Based on crime statistics for the area she lives in, she believes that the probability of her car being stolen or damaged is 0.15. (i) Alice's utility function is given by U(w) = ln(w) for w > 0 and she as £35000 in the bank. Calculate how much Alice would be prepared to pay (in a single payment) to insure her car against theft or damage (ii) Repeat the calculation in the previous part but now assume Alice has £500000 in the bank.
1. A standard model of choice under risk is Expected Utility Theory (EUT) in which preferences over lotteries that pay monetary prizes (x₁, x2, ..., xs) with probabilities (P1, P2, ..., Ps) with Eps = 1 are represented by the function L S (a) What does it mean to say that a function represents the consumer's prefer- ences? Σpsu(xs) Choice 1 8=1 (b) State and briefly comment on the axioms required for the EUT representation. (c) Consider the following experiment of decision making under risk in which sub- jects are asked which lottery they prefer in each of the following two choices: Lottery B 0 with prob. 0.01 10 with prob. 0.89 50 with prob. 0.10 Lottery D Choice 2 Lottery A 0 with prob. 0 10 with prob. 1 50 with prob. 0 Lottery C 0 with prob. 0.90 10 with prob. 0 50 with prob. 0.10 Suppose that the modal responses are Lottery A in Choice 1 and Lottery D in Choice 2. Assume that utility of zero is equal to zero and illustrate why it is not possible to reconcile these experimental…
2. A small college is trying to predict enrolment for the next academic year. Thevice president for business states that enrolment has tended to follow apattern described by E = 18,000 – 0.5P, where E denotes total enrolment andP is yearly tuition.a) If the school sets tuition at €20,000, how many students can it expect to enrol?b) If the school wants to maximize total tuition revenue, what tuition should itcharge?c) As the vice president for business, what tuition would you recommend? Explainbriefly.d) Due to a strong post-COVID-19 recovery, the income conditions in the regionimprove substantially. Explain in one sentence how this could affect the college’senrolment pattern and the enrolment level maximizing its tuition revenue.
4. Show how to construct the reference dependent utility function for two friends Kate and Mary whose gains and losses are listed as follows : Kate's net worth is $ 4.5 million ( decreased from $ 5.5 to $ 4.5 million ) Mary's net worth $ 3.2 million ( increased from $ 3 to $ 3.2 million ) ( First determine the reference point ( use a parameter ) and then derive reference utility function for each ) .
Adam has just purchased a new car and has to decide whether to buy insurance to cover his new car in the event of a loss. Assume that Adam knows the probability (p) of him having an accident and losing his new car. The car is valued at L and the amount of insurance to purchase for this value is X. Adam’s entire wealth after buying the car is W. Let r be unit price of insurance. Briefly explain the problem of the insurance company and show that for insurance to be actuarially fair, the premium must equal the probability of accident.
1. Show if the following utility functions represent risk averse, risk neutral or risk loving preferences. u(c) = 10° + 3 u(c) = C2 + 3C i. ii. ii. u(c) = e4C iv. u(c) = 1 – e-C
3. Consider a home energy storage (battery) system that can store up to 2 units of energy. At every time step, there is a demand for energy in the home which is drawn from 0,1,2 units with equal probability independent of the demands in the previous time steps. At every point in time, you have to satisfy the demand either by discharging the needed energy from the battery or purchasing power from the grid (or a combination of the two). You could also choose to purchase power from the grid to charge your battery. The grid energy price is either H(igh) or L(ow) according to a Markov chain (Price moves from H to L with probability p, and from L to H with probability q). (a) Model the decision making as an infinite horizon MDP where the objective is to minimize the discounted cost of energy purchased over an infinite horizon. (b) Write down a policy a of your choosing. Perform two steps of the operator T, for your policy, followed by one step of T..
Oliver takes $2500 with him to a camp and there is 50% chance he will lose $900 on his way. Suppose Oliver can buy an insurance policy that will totally cover his loss, what maximal amount will he be willing to pay for such insurance? Oliver’s utility function is given by the function U(E) = E0.5 where E is the amount that he spends on the camp without any saving. a. $325 b. $475 c. $650 d. $535
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.
4. The BestElect electronics store is having a sale on November 8th on any new electronics purchased. Every customer will receive $50 off their purchase of a new electronic item. They are also offering a student discount on every item in the store for the whole month of November. If you can prove you are a student, you will receive 15% off any item. Let x be the price of any new electronic item in the store. a. Write a function P(x) that represents the price of a new electronic item on November 8th for any customer. b. Write a function D(x) that represents the price you will pay for an item after the student discount is applied during any day in November. Now, we have two functions P and D that depend on the price of the item, x. P is a rule that says "take the price of the item, then subtract $50." D is a rule that says "take the price, then take 85% of it." If you want to take advantage of both sales, a composition of functions is necessary! But is there a difference between P(D(x))…
2) Explain how utility could be used in a decision where performance is not measuredby monetary value.