1. Aria is risk neutral. His initial wealth is $4,000. Ben is risk averse. Her initial wealth is 3,600 and she is facing the possibility of losing $1,200 with a probability 25%. Aria tells Ben: "Let us sign a contract agreeing to the following: you give me now $x (for me to keep, no matter what happens), and then if you suffer the loss I will give you $y (note: I will still keep the $x you gave me, but I will give you $y)". Find values of x and y such that Ben is better off if they sign the contract (relative to not signing the contract) and Aria is indifferent between signing the contract and not signing it.

2.Ann's initial wealth is $400 and she is facing a potential loss $120 with probability 20%. For each of the following contracts, calculate the premium and deductible as well as the expected profit of the insurance company if Ann purchases the contract. Note that each contract is given as a pair ( , )x y where x is Ann's wealth in case the loss occurs and y is her wealth in case the loss does not occur. (a) A = (370,370), (b) B = (350,390), (c) C = (330,380)