Monty Burns, the owner of the Springfield Nuclear Power Plant, owns many real estate properties. His last acquisition is a house worth €1,000, 000. Monty Burns considers purchasing an insurance for this new property. With probability 0.1, he will face damage reducing his property' value to €640, 000 while with probability 0.9 his property will not be damaged and thus will remain at its current value. Burns' vNM utility for wealth is given by u°(w) = Vw. Miss b runs an insurance company in Springfield and is willing to insure Monty Burns. The insurance contract says the following: if Burns' new property is damaged, she will pay an amount q (the coverage) to Monty Burns in exchange for a payment r (the premium) that is due independently from the occurence of the damage. Miss b's vNM utility over her income y is u'(y) = y.

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
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Chapter7: Uncertainty
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Problem 7.7P
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Monty Burns, the owner of the Springfield Nuclear Power Plant, owns many real
estate properties. His last acquisition is a house worth €1,000, 000. Monty Burns
considers purchasing an insurance for this new property. With probability 0.1, he
will face damage reducing his property' value to €640,000 while with probability 0.9
his property will not be damaged and thus will remain at its current value. Burns'
vNM utility for wealth is given by u°(w) = Vw.
Miss b runs an insurance company in Springfield and is willing to insure Monty Burns.
The insurance contract says the following: if Burns' new property is damaged, she
will pay an amount q (the coverage) to Monty Burns in exchange for a payment r
(the premium) that is due independently from the occurence of the damage. Miss b's
vNM utility over her income y is u°(y) = y.
Transcribed Image Text:Monty Burns, the owner of the Springfield Nuclear Power Plant, owns many real estate properties. His last acquisition is a house worth €1,000, 000. Monty Burns considers purchasing an insurance for this new property. With probability 0.1, he will face damage reducing his property' value to €640,000 while with probability 0.9 his property will not be damaged and thus will remain at its current value. Burns' vNM utility for wealth is given by u°(w) = Vw. Miss b runs an insurance company in Springfield and is willing to insure Monty Burns. The insurance contract says the following: if Burns' new property is damaged, she will pay an amount q (the coverage) to Monty Burns in exchange for a payment r (the premium) that is due independently from the occurence of the damage. Miss b's vNM utility over her income y is u°(y) = y.
2. What is the expected utility of Monty Burns when he does NOT purchase
insurance from Miss b? What is the certainty equivalent for this level of expected
utility?
3. Will Miss b provide full coverage (q = €360, 000) in case of damage? Explain.
4. Suppose Miss b provides full coverage in case of damage. If Burns buys the
insurance, he will have the same amount of wealth regardless of whether there
is damage or not. Monty Burns wants to be at least as well off as in the case he
does not buy insurance. Compute the maximum premium r* that he is willing
to pay.
Transcribed Image Text:2. What is the expected utility of Monty Burns when he does NOT purchase insurance from Miss b? What is the certainty equivalent for this level of expected utility? 3. Will Miss b provide full coverage (q = €360, 000) in case of damage? Explain. 4. Suppose Miss b provides full coverage in case of damage. If Burns buys the insurance, he will have the same amount of wealth regardless of whether there is damage or not. Monty Burns wants to be at least as well off as in the case he does not buy insurance. Compute the maximum premium r* that he is willing to pay.
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