Pat owns a property worth $1 million. The probability of it being subject to fire and...

Transcribed Image Text:

Pat owns a property worth $1 million. The probability of it being subject to fire and becoming worthless is 1%. An insurance agency offers an insurance covering the property's full value of $1 million against an insurance premium of $ 12500. Assume that Pat's utility function is u(W)= We where W is her total net wealth in $ and a is a constant. a) Will Pat buy the insurance? b) For the remaining problem assume that a = 0.5, i.e., u(W) = W0.5, b1) The property is Pat's only asset. How much would she be willing to pay for a full insurance that gives her $ 1 million if the property goes up in flames? b2) Assume that there are no insurances available and that Pat has two properties instead of one. The two properties are identical in terms of worth. The risk of devastating fires occurring is 1% for each of them. How much does each of the new properties have to be worth in order for Pat to be better off than with the single apartment that is of worth $ 1 million? b3) As a final option she considers contacting an old acquaintance who operates a roulette wheel at a nearby casino. Assume for simplicity that the casino doubles the bet when winning, i.e., you get 2 times your bet back when you win on color (i.e., black or red). By manipulating the machinery the acquaintance can affect the outcome probabilities of the wheel. Which is the lowest probability of winning that would make Pat bet her property in b1) on a single bet on red? Pat owns a property worth $1 million. The probability of it being subject to fire and becoming worthless is 1%. An insurance agency offers an insurance covering the property's full value of $1 million against an insurance premium of $ 12500. Assume that Pat's utility function is u(W)= We where W is her total net wealth in $ and a is a constant. a) Will Pat buy the insurance? b) For the remaining problem assume that a = 0.5, i.e., u(W) = W0.5, b1) The property is Pat's only asset. How much would she be willing to pay for a full insurance that gives her $ 1 million if the property goes up in flames? b2) Assume that there are no insurances available and that Pat has two properties instead of one. The two properties are identical in terms of worth. The risk of devastating fires occurring is 1% for each of them. How much does each of the new properties have to be worth in order for Pat to be better off than with the single apartment that is of worth $ 1 million? b3) As a final option she considers contacting an old acquaintance who operates a roulette wheel at a nearby casino. Assume for simplicity that the casino doubles the bet when winning, i.e., you get 2 times your bet back when you win on color (i.e., black or red). By manipulating the machinery the acquaintance can affect the outcome probabilities of the wheel. Which is the lowest probability of winning that would make Pat bet her property in b1) on a single bet on red?