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? 3 (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? (

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