Suppose there are two types of people, high risk (H) and low risk (L) with utility function U(c) = c0.5 Each has income (=consumption) of $100. The high risk people are 10% of the population and have a 75% chance of getting cancer in which case their income would be zero. The low risk people are the remainder of the population and have a 25% chance of getting cancer and hence zero income. The private insurance industry is perfectly competitive. Insurers are afraid the government will take over the industry and decide to price in a different way. Mindful of the social consequences they will price so that the high risk is fully insured. What condition must be placed on the low-risk for this to be an equilibrium? What is the expected utility of the low-risk given the condition?

Suppose there are two types of people, high risk (H) and low risk (L) with utility function U(c) = c0.5 Each has income (=consumption) of $100. The high risk people are 10% of the population and have a 75% chance of getting cancer in which case their income would be zero. The low risk people are the remainder of the population and have a 25% chance of getting cancer and hence zero income. The private insurance industry is perfectly competitive. Insurers are afraid the government will take over the industry and decide to price in a different way. Mindful of the social consequences they will price so that the high risk is fully insured. What condition must be placed on the low-risk for this to be an equilibrium? What is the expected utility of the low-risk given the condition?

EBK HEALTH ECONOMICS AND POLICY

7th Edition

ISBN:9781337668279

Author:Henderson

Publisher:Henderson

Chapter4: Economic Evaluation In Health Care

Section: Chapter Questions

Problem 3QAP

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Suppose there are two types of people, high risk (H) and low risk (L) with utility function U(c) = c0.5 Each has income (=consumption) of $100. The high risk people are 10% of the population and have a 75% chance of getting cancer in which case their income would be zero. The low risk people are the remainder of the population and have a 25% chance of getting cancer and hence zero income. The private insurance industry is perfectly competitive. (a) Suppose private insurers are able to distinguish the two types. What market price would emerge for each risk type? How much insurance would each type purchase?
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