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?

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?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.3P

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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?
a) (3) Consider two investments X and Y, where X pays $0 and $10 with equal probability and Y pays 0 with probability 0.75 and $20 with probability 0.25. What investment would an investor choose if her utility function is u(x) = x? u(x) = x u(x) = 1-e 10 () (i) (ii)
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.
Alice would be willing to pay up to £15 for a gamble giving a 35% chance of £50 and a 65% chance of £10. (a) What is the expected value of this gamble? Represent Alice's preference over risk in a large, suitably labelled graph. The graph should include Alice's expected utility from the gamble described above (b) Represent on the same graph the maximum amount that Alice would pay to remove the risk from this gamble.
To go from Location 1 to Location 2, you can either take a car or take transit. Your utility function is: U= -1Xminutes -5Xdollars +0.13Xcar (i.e. 0.13 is the car constant) Car= 15 minutes and $8 Transit= 40 minutes and $4 What is your probability of taking transit given the conditions above? What is your probability of taking transit if the number of buses on the route were doubled, meaning the headways are halved? Remember to include units.
Choice under uncertainty Alice would be willing to pay up to £15 for a gamble giving a 35% chance of £50 and a 65% chance of £10. 5. (a) What is the expected value of this gamble? Represent Alice's preference over risk in a large, suitably labelled graph. The graph should include Alice's expected utility from the gamble described above. (b) Represent on the same graph the maximum amount that Alice would pay to remove the risk from this gamble.
(a) Given a utility function of an individual is U(x) = x² - 4x, determine his risk attitude. (b) With a utility function of U(x) = x - 3x², where x is the amount invested. (i) determine if this function satisfy the two properties of utility functions. (ii) compute the utility when the amount invested is 3 and 5 respectively.
Suppose that Bill's utility function of wealth is given by u(w) = √w, where w represents his total wealth in dollars. Bill's total wealth is $360,000. If an earthquake happens, his wealth will be reduced to $250,000 with the loss of his house. Suppose the probability of an earthquake happening is 10%. (a) Is Bill risk-averse, risk-loving, or risk-neutral? Explain. (b) If Bill could buy insurance to completely avoid the loss, how much would he be willing to pay for this insurance at most? Explain.
Consider a city where everyone commutes to the city center and commuting cost per mile per month is $40. Each household occupies a 1,000-square-foot dwelling and has $7,000 worth of possessions in its dwelling. The probability that any particular household will be burglarized (involving the uninsured loss of all possessions) is 0.10 at the city center and decreases by 0.01 per mile (to 0.09 at one mile, 0.08 at two miles, and so on). The housing price is $1.00 per square foot at the city center. a) Draw the housing-price curve for locations up to five miles from the city center.
Consider a city where everyone commutes to the city center, and the commuting cost per mile per month is $50. Each household occupies a 1,500-square-foot dwelling and has $10,000 worth of possessions in its dwelling. The probability that any particular household will be burglarized and lose all its possessions (no insurance) is 0.2 (per month) at the city center and decreases by 0.01 per mile (to 0.19 at one mile, 0.18 at two miles, and so on). The price of housing is $2 per square foot at the city center. 1. Starting from the center, a one-mile move outward changes the expected value of the loss from crime from_______ to _______, a change of _________ per square foot. 2. The slope of the housing-price curve is _________, computed as __________ 3. Draw the housing-price curve for locations up to five miles from the city center. The price changes from ________ at the city center to _________ five miles away.
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 .
The promoter of a football game is concerned that it will rain. She has the option of spending $14,040 on insurance that will pay $39,000 if it rains. She estimates that the revenue from the game will be $65,040 if it does not rain and $30,040 if it does rain. What must the chance of rain be if buying the policy has the same expected return as not buying it? Write expressions showing the expected returns if the promoter does and does not purchase the insurance, using p to represent the probability of rain. Without insurance, E(return) = With insurance, E(return) = The chance of rain must be _%.