Monty Burns, the owner of the Springfield Nuclear Power Plant, owns many real estate properties. His last acquisition is a house worth EUR1, 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 EUR640, 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 ^a (w) = w. 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 bs vNM utility over her income y is u^ b (y) = y. 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.