Suppose you own a luxury flat which is valued at $20mm. You figure that the chance of a fire is 0.1 and the damage in case of a fire would be $8 million. Assume the utility of wealth of overall homeowners is represented by Vw. (a) What is the optimal amount of insurance you would buy? (b) What is the insurance premium per unit of protection to be charged by the insurance company if the insurance market is competitive? (c) What if the insurance premium is charged differently, say equal to "fair premium plus $0.1m"? Would you be better off without insurance? (d) Why do actual insurance policies cost more than the actuarially fair premium?