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. 1. Considering that Monty Burns actually buys insurance from Miss b, express the wealth of Monty Burns and the income of Miss b as functions of q and r. You have of course to consider the associated probabilities of the two possible states of the world, i.e. damage v. no damage! Use only the information you have, i.e. do NOT consider Burns' other sources of wealth, nor Miss b 's other sources of income.
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. 1. Considering that Monty Burns actually buys insurance from Miss b, express the wealth of Monty Burns and the income of Miss b as functions of q and r. You have of course to consider the associated probabilities of the two possible states of the world, i.e. damage v. no damage! Use only the information you have, i.e. do NOT consider Burns' other sources of wealth, nor Miss b 's other sources of income.
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.7P
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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.
1. Considering that Monty Burns actually buys insurance from Miss b, express
the wealth of Monty Burns and the income of Miss b as functions of q and r.
You have of course to consider the associated probabilities of the two possible
states of the world, i.e. damage v. no damage! Use only the information you
have, i.e. do NOT consider Burns' other sources of wealth, nor Miss b 's other
sources of income.
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