Suppose there is a set of patients whose expected costs are uniformly distribute

Suppose there is a set of patients whose expected costs are uniformly distributed between $2000 and $7000and each of these patients is willing to pay up to $1000 above their expected costs for the insurance.The insurance market is perfectly competitive and the price of insurance will be equal to the average cost of consumers who purchase the insurance. The insurance company do not observe costs from individual consumers.
a What is the price of insurance in the equilibrium?
b Who buy insurance in equilibrium?
Now, suppose the insurance company can tell if an individual patient’s cost is above or below $5000 and can provide two different insurance plans for these two groups of patients (those with costs above $5000 and those with costs below $5000).
c What is the price of the insurance for low-cost patients?
d What is the price of the insurance for high-cost patients?
e Who benefit from the provision of two different types of insurance and who suffer? Why

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