Each customer in the health insurance market has an initial wealth W = $40,000 and utility function U = W05. If a person contracts a deadly disease, they will lose $1,440. A vaccinated customer has a 10% chance of contracting a deadly disease. An unvaccinated customer has a 20% chance of contracting a deadly disease. Assume that the insurance market is a competitive market in which the price is driven down to the expected cost. There are no administrative costs of providing insurance, so an insurer's only costs are its expected benefit payments. (A) Calculate the maximum price that a vaccinated customer is willing to pay for full insurance against their loss. (3 marks) (B) Calculate the maximum price that an unvaccinated customer is willing to pay for full insurance against their loss. (3 marks) For questions (C) and (D), assume that 70% of customers are vaccinated. The remaining 30% of customers are unvaccinated. (C) Assume that it is impossible for an insurer to discover whether a customer is vaccinated. Will vaccinated customers be willing to insure against their loss? (3 marks) (D) The government has introduced vaccine certificates, which an insurer can use to discover whether a customer is vaccinated. However, some unvaccinated customers illegally create fraudulent certificates. If a customer says they are vaccinated, the probability that they really are vaccinated is x where x