Eli owns a social media site that is worth 44 million. There is a 25% chance that the value of shares will become worth 20 million. Eli is hoping to convince an insurance company to provide cover at a fair rate of 0.25 per 1 of cover. Eli's utility function is = 1/2 (a) Prove that at a 'fair rate', Eli will purchase full insurance coverage. (8 marks)

(b) Sketch the utility of wealth diagram for Eli with wealth on the x-axis and utility on the y-axis. Ensure that you indicate the total cost of the insurance to Eli and the maximum amount that Eli would be willing to pay for the insurance. (8 marks)

(c) If the insurance premium is , where is the coverage, then a fair rate of insurance is when = , where is the probability of the insurance company having to pay out. Show what would happen to Eli's optimal insurance coverage if the insurance company opted to charge a rate of above the fair rate. (6 marks)

(d) Do you think that an insurance company would provide full cover at the fair rate? Explain. (8 marks)