Consider the basic Rothschild-Stiglitz model with asymmetric information and two types on consumers. A policymaker who has taken this class suggests that is might be beneficial to impose a flat tax on healthy people and distribute the tax revenue to sick people, providing partial insurance to people.

a. Since the tax will only offer partial insurance, there will still be a private competitive market for additional insurance. Will a separating equilibrium be possible in the insurance market if this tax is implemented? Draw a diagram to justify you answer.

b. After the tax is implemented a recession hits and a new policymaker decides to make up for a tax revenue shortfall by expanding the tax to include sick people as well as healthy people. Will a separating equilibrium be possible in the insurance market under this policy?