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Unformatted text preview: Problem Set 7 Answer Key 1 Problem 1 Question a: If the insurer knows each consumer’s type, he will charge each one a price equal to his/her willingness to pay: p = 1 . 5 Kh for type h All consumers buy the insurance, since the price is no more than their will- ingness to pay. This is e ﬃ cient because it maximizes the social surplus. The social surplus is the sum of the insurer’s pro f t and the consumer surplus: Z all h with insurance [(1 . 5 Kh − p ) + ( p − Kh )] dh where consumer surplus is 1 . 5 Kh − p for type h and the social surplus sums over all types that buy the insurance. Notice that the integrand is positive for all h , so the integral achieves the maximum when all consumers buy the insurance. Question b: When the insurer does not observe h , he charges price p. Type h consumer purchases the insurance i f p ≤ 1 . 5 Kh , that is: h ≥ p 1 . 5 K All consumers with their health levels between 1 . 5 K p and 1 will buy the insurance. Demand for the insurance is (which is simplyinsurance....
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This note was uploaded on 07/18/2008 for the course ECON 200 taught by Professor Philiphaile during the Spring '08 term at Yale.
- Spring '08