Assume there is a single private re insurance company in the city. Let's consider the decision to purchase re insurance from the perspective of the owner of a coffee shopwhom we will call Emily. Both Emily and the insurance company know that the risk of re in the coffee shop is equal to p, which is fairly high because of the large number of electrical appliances. Emily receives an income of W 'cm the business if there is no re, and would have no income (a nancial loss of the entire W) in the event of a re. Emily's expected utility (EU) depends on income (Y) in each of the two states as follows: EU=p x in(l'm) + (lp) X {ner-m} Because of the lack of competition, private re insurance is not offered at actuarially fair rates and the insurer makes a prot. Assume that the insurance firm sets its policy such that expected prots (that is, expected revenue minus expected costs) are equal to k times the premium collected. So, if a is the premium paid if there is no re and b is the net payout if there is a re, expected prots for the rm are equal to kn. a) Find the equation describing the set of re insurance contracts the rm offers Emily. Show graphically how the implied budget constraint compares to the budget constraint associated with actuarially fair insurance. Set up your graph so that income in the event of no re is shown on the x-axis and income in the case of a re is shown on the yaxis. b) Given the set of contracts offered by the re insurance company, how much insurance would Emily choose to buy":I Does she choose to buy less or more than full insurance? Why? Derive your answer algebraically and explain using a graph