2. Suppose that Sarah is an Expected lltility Decision maker and her utility over outcomes {wealth r. [measured in million :L'] is given by u{z} = l. Sarah is a houseowner which is worth to and knows that with probability 1,32 her house is damaged reducing the value to m, such that n a: m. c: a: while with 13'? probability no damage will occur. Additionally she has an amount of it on her bank account. {a} 1'Write down the lottery, its expected value and the expected utility for this lottery over wealth for general n, w, m. {b} Now, assume it = 2 , m = T and m = 2 {all measured in million E}. Write down the certainty equivalent of this lottery. Compare and interpret your nding with respect to Sarah's risk attitude. {c} Suppose an insurance company oers full insurance to Sarah at a price of 1.- {measured in million B}. What is the maximal price Sarah would pay for this insurance'.Tl How does this willingness to pay compare to the expected loss? Interpret this relationship. {d} Suppose now that no insurance is available, but Sarah has a neighbour. Tom. Tom is in a similar situation as Sarah and it is common knowledge that Tom's house is damaged with probability 1 If 4. The probabilities with which Tom's and Sarahsls house are damaged are independent. Tom oiTers the following contract to Sarah: if none of their houses or both of their houses are damaged, then neither helps the other. If however, only Tom's house is damaged, then Sarah helps Tom repair the house by giving him s = 1.!) [measured in million E}, while if only Sarah's house is damaged, then Tom helps Sarah by giving her I = [15 [measured in million E}. Write down the new lottery, its expected value and discuss whether Sarah should accept the contract. {e} Is the contract specied in d} fair?r Would Sarah also accept worse contracts, i.e. contracts in which she compensates Torn with an even higher amount s' 2: .s than she already does while Tom still pays I {all other conditions being equal}? Explain