2 Scenario Your client, InsureCorp, is an insurance company considering launching an \"income insur ance' product in the island nation of Autarka. Income insurance is a product that fully insures a household against changes in income caused by a major injury or illness. At present, no businesses are selling income insurance producE in Autarka. Initial mar ket research suggesE that there are l households in Autarka interested in purchasing income insurance. Your client expects that the fixed cost of launching the income insurance product will be $20,0 per year1 and that each policy issued to a customer will cost the company an additional $1.5 in sales commissions. 2.1 Your task Your client wants you to analyse the potential market for income insurance and report on the following: o What is the maximum price the company can charge a household for an income insurance policy? I: What is the expected profit [or loss) for the company if it becomes a monopoly provider of income insurance? o Is there a risk that rival insurance companies will also enter the market, selling identical income insurance products? If so, what would be the expected profit of your client? (You should assume that any competitor's would face the same costs as your client.) 2.2 Household welfare A typical household in Autarka has an income of $160,00 per year. which they spend on food (good x) and clothing [good y). Their preferences oyer consumption baskets are represented by the utility function, U = Xlyl. The associate marginal utilities are, FIIM x134 l'yl'lblx 4x3\" and MU, 4?\" The price of food is F;r = $8 per meal, and the price of clothing is P, = 128 per item. Each household has a 10% probability of experiencing a major injury or illness in any given year. If a household experiences a major injury or illness, its income is reduced to $6,400 per year