Rik and Claire, a couple residing in Lincolnshire, own a house valued at 200,000. The probability of a fire is p = 0.01. An insurance company offers insurance at a premium y per insured sum K. The couple's preferences can be represented by the utility function u(x) = x. If there is a fire, it will destroy the house and reduce its value to zero (we assume that the couple's land without a house has no value). (a) How large is the insurance premium at which the insurance company makes zero profit? (5 marks) (b) What is the couple's optimal choice of K if the insurance is actuarially fair, and how much wealth will they own in each state? (5 marks)