Question 1: Suppose a risk-averse person, Anne has an asset valued at $400. With a probability equal to 0.20 an accident will happen, and she will lose all her asset, otherwise she will retain her asset. Anne's neighbour offers her a contract that provides full insurance which means that the neighbour compensates all her loss in the event of an accident. If Anne's utility function is () = .

(a) What is the maximum amount that she is willing to pay to her neighbour for this insurance? (4 marks) (b) Suppose the neighbour has a wealth equal to 400 with the same utility function. What is the minimum amount that the neighbour accepts to offer this insurance? (4 marks) Suppose now the individual can take an action (call it "care") and reduce the probability of the accident to 0.1. Her utility for any cost c is separable and is, () = . (c) At what value of c she becomes indifferent between taking "care" and not taking "care"? (4 marks) (d) Suppose c=1. If the neighbour provides full insurance what is the maximum premium that the individual is willing to pay now? (5 marks)