The questions concerns Health Economics

Your utility over income is U=sqrt(I ) and you have a 10% chance of getting sick. Your income when sick is $0 and your income when healthy is $100.

1. Graph your utility and income with income on the x-axis and utility on the y-axis. Show your income/utility when healthy and sick on the graph.

2. Calculate your expected income. Show on graph.

3. Calculate your expected utility. Show on graph.

Now you are offered health insurance by Prof. Grossman's Totally Full and Fair Insurance Company. For a premium of $20, you will get a payout of $50 if you get sick.

1. Is the insurance company's name accurate (is this actuarially fair and full)?
2. What is the expected payout from this insurance?
3. What is the Income when sick and income when healthy under insurance? Show on your graph
4. What is the expected income and expected utility under this insurance? Show each on your graph
5. Propose a full and fair insurance given your 10% chance of getting sick and your healthy and sick incomes.
6. What is the premium and payout, show on the graph your utility in this situation.