2. Cloneville is a town consisting on 100,000 identical citizens. Each citizen has a current total wealth of $160,000 and has a utility function given by u (w) = w². In any given year, 10% of the citizens will lose 75% of their wealth to a fire. Since the citizens are identical, they are all equally likely to experience a fire. (a) Calculate the actuarially fair premium for complete fire insurance in Cloneville. How many citizens of Cloneville would purchase insurance if it cost this much? (b) Do you think insurance companies in Cloneville are likely to offer actuarially fair insur- ance? Why or why not? (c) Nearby Simville also has 100,000 citizens with the same initial wealth and risk of fire. While no citizens in Simville are risk-loving, some are more risk-averse than others. In fact, there are even a few citizens in Simville who are risk-neutral. i. Suppose insurance is supplied by a competitive industry made up of identical in- surance companies. Costs of providing insurance include covering losses that occur ith

2. Cloneville is a town consisting on 100,000 identical citizens. Each citizen has a current total wealth of $160,000 and has a utility function given by u (w) = w². In any given year, 10% of the citizens will lose 75% of their wealth to a fire. Since the citizens are identical, they are all equally likely to experience a fire. (a) Calculate the actuarially fair premium for complete fire insurance in Cloneville. How many citizens of Cloneville would purchase insurance if it cost this much? (b) Do you think insurance companies in Cloneville are likely to offer actuarially fair insur- ance? Why or why not? (c) Nearby Simville also has 100,000 citizens with the same initial wealth and risk of fire. While no citizens in Simville are risk-loving, some are more risk-averse than others. In fact, there are even a few citizens in Simville who are risk-neutral. i. Suppose insurance is supplied by a competitive industry made up of identical in- surance companies. Costs of providing insurance include covering losses that occur ith

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question 2 A person has a wealth of $20,000 but faces an accident that results in a loss of S12,000 with probability, p. Suppose that Bermoulli utility is given by u(x) = -1/x. 1. Determine the maximum amount of money the person is willing to pay for complete coverage (as a function of p). 2. Now suppose that an insurance company offers an insurance contract with a deductible of $2,000. Again, determine the maximum amount of money a person is willing to pay for this insurance contract.
Kindly solve 3rd question only
Donna just paid $800 for a new iPhone. Apple offers a two year extended warranty for $200 and Donna is considering purchasing it. She has utility given by U(X)=√X. Without the extended warranty, the iPhone becomes worthless if it breaks. What is the minimum probability, p, that the iPhone breaks in the next two years that will cause Donna to prefer to purchase the extended warranty? p=_____________ If the probability that her phone breaks is p=0.25, will Donna will prefer to buy or not buy the warranty?
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?
You have a house worth 300,000. A fire will burn everything to the ground and leave $0 in value. Assume full coverage in the case of a fire. In every given year, there is a 5% probability that your home burns. If your Utility function is U=Wealth/2 How much would you be willing to pay (the premium) for insurance? 15,800 O 45,850 O 15,000 29,250
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.
Shane just bought a house worth $360,000 in an area that is known for floods. A flood occurs with a 5% chance and if it occurs, his home is reduced in value to $202,500. Shane has utility function given by U(X)=√X. He would be willing to pay a maximum of ___________ for flood insurance. The fair insurance premium for flood insurance is ___________ Shane's risk premium is ___________ Suppose, instead, that Shane's utility function is given by U(X)=X2 . Then, the maximum he would be willing to pay for flood insurance is ___________
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:
A risk-averse consumer with $100,000 in wealth faces 0.1 probability of losing half of his wealth within the next year. a. What is the consumer's expected wealth one year from now? b. An insurance company offers our consumer full insurance against the possible loss. What premium must the consumer be charged for the insurance company to expect to break even? c. Suppose our risk-averse consumer is indifferent between getting $85,000 wealth with certainty and facing the above described uncertain situation. What is the maximum premium that the insurance company will be able to charge this consumer for its full insurance policy?
Question 5 (1 point) Suppose that Jim has a von Neumann-Morgenstern utility function: U(c) = c². %3D Based on his utility function, we can tell that Jim is There is not enough information to determine his risk preference. risk averse. risk neutral. risk loving.
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?