Please show all the work and how you calculate these. The answers need to be at least two decimal places. *\"H' You are considering whether to buy health insurance. Your utility is given by the square root of your monthly income: UU)=\\/7 Your monthly income is $6000, but there is a oneinten chance [10%) that you will get sick and have $3000 in medical bills. 1. What is your expected utility (NOT income} for this month if you don't buy insurance? 2. You find an insurance company that will provide full insurance {that is, the insurer will pay all $3000 of your medical bills if you get sick) for a premium of $100. What is the expected utility from buying insurance? 3. Will you buy the insurance? Why or why not? 4. Suppose the insurance company reduces its coverage from full insurance to partial insurance by saying it will only pay half ($1,500) of your medical bills if you get sick. The premium is still 5100. Will you still buy the insurance? Why or why not