4. [10 Marks] Suppose that you have a wealth w = 4 and face a risk q of damages d = 3. Fortunately, you have access to insurance contracts of the form (P, R), Where P is the premium you make to the insurance company and R is the reimbursement the insurance company delivers to you if you suffer damages. Suppose further that your preferences over your net consumption in each state have the expected utility property, and that your utility is given by the function u(c) 2 V5. (a) (2 marks) Write down an expression representing your expected utility from the lottery (i.e. the probability distribution) corresponding to not being insured. (b) (2 marks) Suppose now that you have access to a fair insurance contract with full insurance. Derive your expected utility from the lottery corresponding to this contract. (c) (3 marks) Suppose that the decision-maker has access to an insurance contract (P, R) = (1, 2). Is this contract fair? Derive the decision-maker's expected utility from the lottery corresponding to this contract. ((1) (3 marks) Assume that q = 1/2. Describe your preferences over the lotteries from questions (a) to (c) above