Your client, InsureCorp, is an insurance company considering launching an income insurance product in the nation of Avalon. 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 products in Avalon. Initial market research suggests that there are 12,000 households in Avalon interested in purchasing income insurance. Your client expects that the fixed cost of launching the income insurance product will be $10,000,000 per year, and that each policy issued to a customer will cost the company an additional $4,000 in sales commissions.

In the analysis section you must complete each of the steps detailed below. When completing the steps you must: Type all equations using the Insert Equation function (or equivalent). Show all of your working and include sufficient written description for the reader to follow your process. Note that hand draw figures and equations are not acceptable. There is no word/page limit for the analysis section.

Step 1: Derive an expression for the typical households marginal rate of substitution.

Step 2: Find the typical households optimal consumption basket when its income is $160,000. What is the households associated level of utility?

Step 3: Find the typical households optimal consumption basket when its income is $20,000. What is the households associated level of utility?

Step 4: What is the typical households expected utility if it does not purchase insurance?

Can you help me answer the above question, thank you

2.2 Household welfare A typical household in Avalon has an income of $160,000 per year, which they spend on food (goodx ) and clothing (good y ). Their preferences over consumption baskets are represented by the utility function, U=x1/3y1/3 The associate marginal utilities are, MUx=3x2/3y1/3andMUy=3y2/3x1/3. The price of food is Px=$8 per meal, and the price of clothing is Py=$100 per item. Each household has a 20% probability of experiencing a major injury or illness in any given year. If a household experiences a major injury or illness, its income will be reduced to $20,000 per year. 2.2 Household welfare A typical household in Avalon has an income of $160,000 per year, which they spend on food (goodx ) and clothing (good y ). Their preferences over consumption baskets are represented by the utility function, U=x1/3y1/3 The associate marginal utilities are, MUx=3x2/3y1/3andMUy=3y2/3x1/3. The price of food is Px=$8 per meal, and the price of clothing is Py=$100 per item. Each household has a 20% probability of experiencing a major injury or illness in any given year. If a household experiences a major injury or illness, its income will be reduced to $20,000 per year