pls help me with steps 1-3, thanks! (provide proper and correct working)

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 products in Autarka. Initial mar- ket research suggests that there are 10,000 households in Autarka interested in purchasing income insurance Your client expects that each policy issued to a customer will cost the company $2.000 in sales commissions. 2.2 Household welfare A typical household in Autarka has an income of $90,000 per year, which they spend on food (good x) and clothing (good y). Their preferences over consumption baskets are represented by the utility function. U = x1/41/4 The associate marginal utilities are, y! *2/4 443/6 MU, and MU, 4y34 The price of food is P. = 59 per meal, and the price of clothing is P, = 36 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 is reduced to $14,400 per year 3.2 Analysis In the analysis section you must complete each of the steps detailed below. When com- pleting 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 household's marginal rate of substitution (4 marks) Step 2: Find the typical househoid's optimal consumption basket when its income is $90,000. What is the household's associated level of utility? (10 marks) Step 3. Find the typical household's optimal consumption basket when its income is $14,400. What is the household's associated level of utility? (10 marks)