PROBLEM (4) A homeowner with expected utility preferences with u(x)= sqare root x owns a house worth $490k. There is a probability p that she will experience a house fire, in which case the damages will cost $240k. A risk-neutral insurance company asks for an insurance premium of $10k in return for covering the damages fully in case of a fire. (a) What should p be so that the homeowner is willing to insure her house? (b) What should p be so that the insurance company is willing to offer insurance?

PROBLEM (4) A homeowner with expected utility preferences with u(x)= sqare root x owns a house worth $490k. There is a probability p that she will experience a house fire, in which case the damages will cost $240k. A risk-neutral insurance company asks for an insurance premium of $10k in return for covering the damages fully in case of a fire. (a) What should p be so that the homeowner is willing to insure her house? (b) What should p be so that the insurance company is willing to offer insurance?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.8P

See similar textbooks

Similar questions

PROBLEM (4) A homeowner with expected utility preferences with ?(?) = √? (sqare root x) owns a house worth $490k. There is a probability p that she will experience a house fire, in which case the damages will cost $240k. A risk-neutral insurance company asks for an insurance premium of $10k in return for covering the damages fully in case of a fire. (a) What should p be so that the homeowner is willing to insure her house? (b) What should p be so that the insurance company is willing to offer insurance?
Utility Theory You live in an area that has a possibility of incurring a massive earthquake, so you are considering buyingearthquake insurance on your home at an annual cost of $180. The probability of an earthquake damagingyour home during one year is 0.001. If this happens, you estimate that the cost of the damage (fully coveredby earthquake insurance) will be $160,000. Your total assets (including your home) are worth $250,000. A. Apply Bayes’ decision rule to determine which alternative (take the insurance or not) maximizes yourexpected assets after one year.
A consumer has the following utility function u(x)= root x where x is the consumer’s total wealth. The consumer's total wealth is the consumer’s cash plus the value of her house. The consumer has $400 in cash (risk free) plus a house. The house is currently worth $756. With probability 70% nothing happens, and the value of the house stays the same. With probability 30%, high winds will cause $580 in damages to the house (in which case, the house value becomes $176). An insurance company offers to fully insure the house at an insurance premium p. What is the maximum insurance premium that the consumer is willing to pay? The consumer is willing to pay at most p=. The fair insurance premium is . In this example, the associated risk premium is .
could you answer part b to this question or if you have time part a and part b but part is more important. thank you 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?
Suppose that consumers have utility function U(C) = log(C) where C is the consumption level and log is the natural logarithm. Consumers have initial consumptionlevels of 100 and are exposed to the following risk of loss: lose 10 with probability0.4 and lose 5 with probability 0.6. They are considering buying insurance to coverthese losses. What is the fair price for the insurance?
Arielle is a risk-averse traveler who is planning a trip to Canada. She is planning on carrying $400 in her backpack. Walking the streets of Canada, however, can be dangerous and there is some chance that she will have her backpack stolen. If she is only carrying cash and her backpack is stolen, she will have no money ($0). The probability that her backpack is stolen is 1/5. Finally assume that her preferences over money can be represented by the utility function U(x)=(x)^0.5 Suppose that she has the option to buy traveler’s checks. If her backpack is stolen and she is carrying traveler’s checks then she can have those checks replaced at no cost. National Express charges a fee of $p per $1 traveler’s check. In other words, the price of a $1 traveler’s check is $(1+p). If the purchase of traveler’s checks is a fair bet, then we know that the purchase of traveler checks will not change her expected income. Show that if the purchase is a fair bet, then the price (1+p) = $1.25.
Suppose the equilibrium price for good quality used cars is $20,000. And the equilibrium price for poor quality used cars is $10,000. Assume a potential used car buyer has imperfect information as to the condition of any given used car. Assume this potential buyer believes the probability a given used car is good quality is .60 and the probability a given used car is low quality is .40. Assume the seller has perfect information on all cars in inventory. If the seller sells the buyer a poor quality car, what is the net-benefit to the seller? a. A net gain of $6,000. b. A net loss of $20,000. c. A net loss of $6,000. d. A net gain of $10,000.
Solve the following problem using an excel spreadsheet. A tobacco company isinterested in hiring a salesperson to promote smoking cigarettes in nightclubs. The position pays a flat salary of $50,000, regardless of sales levels. The firm has two applicants, Predictable Patty and Risky Ricky. Predictable Patty can produce with 100% certainty $100,000 a year in sales. Risky Ricky, on the other hand, can produce $300,000 with probability of 50%. But if he turns out to spend his time drinking and dancing in the nightclubs instead of making sales, he could actually cost the firm -$100,000 per year.a) During their first year on the job, what are the expected sales of Patty and Ricky? What are the firm’s expected profits on each worker?b) Now assume both workers are currently 25, and they will work until the retirement age of 65. The firm has the option to fire its new employee after one year based on sales, but can only hire one employee. Assume that it takes only one year to discover whether…
Q1) An expected utility maximiser owns a car worth £60000£60000 and has a bank account with £20000£20000. The money in the bank is safe, but there is a 50%50% probability that the car will be stolen. The utility of wealth for the agent is u(y)=ln(y)u(y)=ln⁡(y) and they have no other assets. Q2) Consider the setup from Question 1. A risk-neutral insurance company is willing to insure the car at the premium of π=£2/3π=£2/3 for every one pound of coverage. Q3) Consider the setup from Questions 1 and 2. How much profits, in expectation, does the insurance company earn on insuring the individual?
Exercise 3: Risky Investment Charlie has von Neumann-Morgenstern utility function u(x) = ln x and has wealth W = 250, 000. She is offered the opportunity to purchase a risky project for price P = 160, 000. 1 1 With probability p = 2 the project will be a success and return V > 160, 000. With probability 1 −p = 2 the project will fail and be worthless (i.e. it returns 0). For simplicity assume there is no interest between the time of the investment and the time of its return, that is r = 0 . How large must V be in order for Charlie to want to purchase the risky project? [Hint: What is Charlie’s expected utility is she does not purchase the project? What is Charlie’s expected utility is she purchases the project?]
You are considering a $500,000 investment in the fast-food industry and have narrowed your choice to either a McDonald’s or a Penn Station East Coast Subs franchise. McDonald’s indicates that, based on the location where you are proposing to open a new restaurant, there is a 25 percent probability that aggregate 10-year profits (net of the initial investment) will be $16 million, a 50 percent probability that profits will be $8 million, and a 25 percent probability that profits will be −$1.6 million. The aggregate 10-year profit projections (net of the initial investment) for a Penn Station East Coast Subs franchise is $48 million with a 2.5 percent probability, $8 million with a 95 percent probability, and −$48 million with a 2.5 percent probability. Considering both the risk and expected profitability of these two investment opportunities, which is the better investment? Explain carefully.
Scenario 2 Tess and Lex earn $40,000 per year and all earnings are spent on consumption (c). Tess and Lex both have the utility function (sqrt c) . Both could experience an adverse event that results in earnings of $0 per year. Tess has a 1% chance of experiencing an adverse event and Lex has a 12% chance of experiencing an adverse event. Tess and Lex are both aware of their risk of an adverse event. Refer to Scenario 2 If an insurance company knows the probability of Tess experiencing an adverse event, what is the actuarially fair premium charged to Tess per $1 of benefit? Round to two decimal places