The worth of consumer's house is 160, and her utility function is u(w) = √w. The probability of outbreak of fire is p = 1/2, and the fire will make 120 amount of loss of worth of house. Under the given conditions, consumer can join insurance that pay insurance money as B by pay insurance fee qB. (a) Find the amount of insurance that consumer will join. (b) Derive the condition that consumer will not join insurance. (c) Derive the condition that make consumer join full insurance. (d) Find the B, when the q is given as q = 3/5

The worth of consumer's house is 160, and her utility function is u(w) = √w. The probability of outbreak of fire is p = 1/2, and the fire will make 120 amount of loss of worth of house. Under the given conditions, consumer can join insurance that pay insurance money as B by pay insurance fee qB. (a) Find the amount of insurance that consumer will join. (b) Derive the condition that consumer will not join insurance. (c) Derive the condition that make consumer join full insurance. (d) Find the B, when the q is given as q = 3/5

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.5P

See similar textbooks

Similar questions

↑ Consider the following FIRE INSURANCE PROBLEM where fire destroys a $300 (thousand) house.< INSURANCE PAYOUT INSURANCE PREMIUM 200 0 EVENT FIRE → NO FIRE PROBABILITY 0.02 0.98 OUTCOME 100 300 10 10 (a) What do we mean when we say an agent is Risk Averse? (b) Assume utility is U(x) = √(x). What is the expected payoff and expected utility of having no insurance? Show your work. (c) Suppose the Insurance Premium was $10. Would this risk averse agent buy insurance? Show your work and explain. (d) Suppose the probability of a fire rose to 5%. Would the agent buy insurance now? Show your work and explain.
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.
1. A dealer decides to sell a rare book by means of an English auction with a reservation price of 54. There are two bidders. The dealer believes that there are only three possible values, 90, 54, and 45, that each bidder’s willingness to pay might take. Each bidder has a probability of 1/3 of having each of these willingnesses to pay, and the probabilities for each of the two bidders are independent of the other’s valuation. Assuming that the two bidders bid rationally and do not collude, the dealer’s expected revenue is approximately ______. 2. A seller knows that there are two bidders for the object he is selling. He believes that with probability 1/2, one has a buyer value of 5 and the other has a buyer value of 10 and with probability 1/2, one has a buyer value of 8 and the other has a buyer value of 15. He knows that bidders will want to buy the object so long as they can get it for their buyer value or less. He sells it in an English auction with a reserve price which he must…
1. A customer has utility function u(x) = log(x + 1000). The customer’scurrent wealth is $28,000. The customer’s car has a value of $14,700. Theprobability of the car being stolen is 0.016. How much would the customerbe willing to pay for insurance against the car being stolen?
2. Bob's wealth is $2500. However, he faces a 50% chance of suffering a S900 loss. He is an expected utility maximizer and his utility function is U(w) = vw , Where w is his wealth. (a) What is Bob's cost of risk? (b) If Bob can buy insurance against his loss for a price of $500, will he buy it? (c) What is the maximum amount Bob would be willing to pay for insurance?
Becky is deciding whether to purchase an insurance for her home againtst burglary. the payoff for her is shown as follow: Net worth of her Net worth of her home: $ 20000 burglary(10%) Net worth of her Net worth of her home: $50000 burglary (90%) The insueance would cover all the loss from burlary and the insurance fee is $8000. Her utility funtion is given as u=w ^0.3 Should Beck purchase the insurance Explain.
4. $1000 with of $325. (a) (b) Adam is risk averse. He is offered a choice between a gamble that pays a probability of 25% and $100 with a probability of 75%, or a sure payment What is the expected payment of the gamble? Will Adam prefer gamble over sure payment? Would he change his mind if the sure payment is $320 instead of $325? (c) If this individual has a utility function u(x) = lnx, would he prefer the payment of $320 or the gamble? (d) In the CRRA utility family u(x) = x¹-7. If this individual has a utility where y = 0.01, would he prefer the payment of $320 or the gamble?
A construction company needs to move lumber onto the roof of a building. If the lumber falls and hits someone it will cause $1,200,000 in damage. Assume that company must choose between the following levels of precaution: Spend $500 and the probability of an accident is .05 Spend $5,000 and the probability of an accident is .01 Spend $8,000 and the probability of an accident is .008 Spend $10,000 and the probability of an accident is .003 If the construction company is strictly liable for the costs of the accident, how much would they spend on precaution? A. $500 B. $5,000 C. $8,000 D. $10,000
for remain uninsured? S. Amanda has a utility of money function of u(w)-w4, Her initial wealth is w-$20,000 and she faces a .10 probability of a loss L $5,000; with probability 9 she suffers no loss. Calculate the amount of insurance Amanda will purchase if $1 of coverage costs $.10 per dollar of coverage. Would purchase any insurance if the cost per dollar of coverage was $.20.
An individual has 40,000 in income per year. The person will get sick with probability 0.1. If he does get sick, the medical bills will total 30,000. The following tables shows the utility derived from certain amounts of income: Income Utility40,000 20037,000 19535,000 19030,000 17020,000 14010,000 100Considering the probability of illness, what is the expected utility of income without insurance? Show your work.
8) Three decision makers have assessed utilities for the problem whose payoff table appearsbelow. probabilities and payoffs. S1 S2 S3 D1 500 100 -400 D2 200 150 100 D3 -100 200 300 Probability .2 .6 .2 Indifference Probability for Person Payoff A B C 300 .95 .68 .45200 .94 .64 .32150 .91 .62 .28100 .89…
Suppose that the buyers do not know the quality of any particular bicycle for sale, but the sellers do knowthe quality of the bike they sell. The price at which a bike is traded is determined by demand and supply.Each buyer wants at most one bicycle.(ii) Assuming that each buyer purchases a bike only if its expected quality is higher than the price,and each seller is willing to sell their bike only if the price exceeds their valuation, what is theequilibrium outcome in this market?