4 Adverse Selection - Rothschild and Stiglitz Attached is a graph of a consumer's Is-IH plot. There are two types of consumers: robust and frail, both with their own separate indifference

curves. Let E be the consumer's level of income without insurance. D₁₂ P₁₂₁₂ P₂ P₂ UF is the frail consumer's indifference curve and UR is the robust consumer's in- difference curve. Let the line that runs from point 2, to point E be the zero profit line for frail consumers and the line that runs from point 9₂ to point E be the zero profit line for robust consumers. a Let firms not have perfect information about the consumer's type; that is, they do not know if the consumer is a robust type or a frail type. Explain why a firm offering two insurance plans 2₁ and 23 is an equilibrium. b Let us now assume that the insurance companies can now perfectly distin- guish between both types of individuals. Explain why a firm offering 2₁ only to frail consumers and offering only to robust consumers is an equi- librium. c Would a private insurance mandate be necessary if insurance companies can perfectly distinguish between robust and frail consumers? Why or why not?