Insurance Premium Question for Public Economics Class

3. (20 points) Consumption-Smoothing Benefits of Insurance. Amy's utility function is U = VC, where C is consumption and is given by C = Income - Expenses. Amy's income is $10,000 and there is a 5% chance that she will get sick, which would cost $3,600 in medical expenses. (a) (5 points) What is Amy's expected utility if she doesn't have insurance? (b) (5 points) What is the actuarially fair premium for a full-coverage insurance plan? What is the actuarially fair premium for an insurance plan that provides 50% coverage? Page 3(c) (5 points) What is the maximum premium that Amy would be willing to pay for a full-coverage insurance plan? (d) (5 points) Suppose now there's a government mandate: everyone must either buy full-coverage health insurance at a premium of $200, or pay a fine of $150 and stay uninsured. Would Amy purchase the health insurance or not