Consider the basic Rothschild–Stiglitz model with asymmetric information and robust and frail customers.

a. Suppose the government imposes a Wellness Tax, τ > 0, on robust and frail types but collects on this tax only when they are healthy (that is, there is no tax if they turn out to be sick). Will a separating equilibrium still be possible? Draw a version of the Rothschild–Stiglitz diagram to support your answer.

b. Will a separating equilibrium be possible if the tax τ > 0 is imposed on all customers in both sick and healthy states? Again, support your answer graphically.