A medical test that an insurance company could use to distinguish between high- and low-risk types would create an equilibrium in which both high- and low-risk types could have full insurance. Sketch a brief proof using a diagram. Why is this equilibrium not an equilibrium under the normal information asymmetry assumptions? Show which of the three equilibrium criteria does not hold.

In this simple insurance model, a company has a monopoly over a small market. There are 100K potential customers with a low risk profile, 60K potential customers with a medium risk profile, and 10K potential customers with a high risk profile.  A person’s risk profile is important as it determines how much insurance is worth to the customer and how much money the customer will cost on average to the insurance company. The following table summarizes the estimates put together by the company:   Low risk profile Medium risk profile High risk profile Number of potential customers 100,000 60,000 10,000 Expected expense per customer $2K $7K $15K Maximal price the customer isready to pay for insurance $3K $8K $16K Remark: Explaining where these numbers come from would require a subtler model that describes the risk covered by the insurance policy. While there is no need to do this for the purpose of this exercise, notice though how the maximal price…

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Use the figure below to answer the following question. Let In represent Income when health, let Is represent income when ill. Let E[I] represent expected income. Point D represents Utility Is у в an actuarially fair and full contract an actuarially fair and partial contract X E[1], the utility from Expected income with no insurance an actuarially unfair and full contract an actuarially unfair and partial contract с IH U(I) Prome