A tax on healthy people. Consider the basic Rothschild-Stiglitz model with asymmetric information and robust and frail customers.

a. Suppose the government imposes a Wellness Tax > 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 > 0, is imposed on all customers in both sick and healthy states? Again, support your answer graphically.

c) Consider an individual whose utility function over income I is U(I), where U is increasing smoothly in I (U' > 0) and convex (U" > 0). a.Draw a utility function in U - I space that fits this description.