Problem 1: Insurance Markets. Every person has $3,000 to spend. There are two groups of people:...

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Problem 1: Insurance Markets. Every person has $3,000 to spend. There are two groups of people: 150 sick people and 250 healthy people. A sick person visits the hospital with probability p = 0.2. A healthy person visits the hospital with probability p 0.1. Any hospital visit costs $1,200. All individuals have the following expected utility function: = EU = (1 − p)√√/C₁ + P√√Co 1. First, assume that the insurance company can distinguish between sick and healthy individuals and can charge each individual their actuarially fair premium. a) What the actuarially fair price for a person? b) What is the actuarially fair price for a healthy person? 2. Suppose the insurance company cannot distinguish between sick and healthy people. a) If they charge one price to everyone for full insurance, what price x do they need to charge to make zero expected profits when everyone buys? (Hint: It is somewhere in between the actuarially fair prices, but not halfway since groups are of different sizes.) b) Will the sick buy full insurance at the price x? c) Will the healthy buy full insurance at the price x? 3. Now, suppose the insurance company offers two insurance packages: 1) full insurance at a price of $240; and 2) partial insurance with $150 of coverage at a price of $15 a) Will the sick buy full or partial insurance? b) Will the healthy buy full or partial insurance? c) Is this a successful separating equilibrium? Briefly explain your reasoning. Problem 1: Insurance Markets. Every person has $3,000 to spend. There are two groups of people: 150 sick people and 250 healthy people. A sick person visits the hospital with probability p = 0.2. A healthy person visits the hospital with probability p 0.1. Any hospital visit costs $1,200. All individuals have the following expected utility function: = EU = (1 − p)√√/C₁ + P√√Co 1. First, assume that the insurance company can distinguish between sick and healthy individuals and can charge each individual their actuarially fair premium. a) What the actuarially fair price for a person? b) What is the actuarially fair price for a healthy person? 2. Suppose the insurance company cannot distinguish between sick and healthy people. a) If they charge one price to everyone for full insurance, what price x do they need to charge to make zero expected profits when everyone buys? (Hint: It is somewhere in between the actuarially fair prices, but not halfway since groups are of different sizes.) b) Will the sick buy full insurance at the price x? c) Will the healthy buy full insurance at the price x? 3. Now, suppose the insurance company offers two insurance packages: 1) full insurance at a price of $240; and 2) partial insurance with $150 of coverage at a price of $15 a) Will the sick buy full or partial insurance? b) Will the healthy buy full or partial insurance? c) Is this a successful separating equilibrium? Briefly explain your reasoning.

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The question refers to an insurance market situation where individuals are considering purchasing health insurance and the insurance company is setting prices Lets go step by step 1 Actuarially fair p... View the full answer