Health insurance and adverse selection. Insurance companies sells health insurance to two types of people: low—risk people and high-risk people The probability that a random

Insurance companies sells health insurance to two types of people: low—risk people and high-risk people The probability that a random person is low-risk is 315 [and so the probability that a random person is high-risk
‘5 also 1].
2 Ir low-risk people: have on average \$4M of medical expenses each year, and are willing to pay mm for medical insurance o high-risk people: have on average 511001] of medical expenses each year, and are willing to pay
Slldﬂﬂ for medical insurance People lmow whether they are low-risk or high—risk, but insurance companies do not. [A] Let’s start by considering a scenario where everyone buys insurance. {i} is the highest price of health insurance for which both high—ml: and low—risk people will
buy the insurance? {ii} is an insurance company’s expected proﬁt per person1 at the price you found in {i}? {B} Now let’s consider a scenario where only high—risk people buy insurance {i} is the highest price of health insurance for which high-risk people will buy the insurance? {ii} is thc insurance company’s expected proﬁt per person, if it charges the price in [i]? (C) Finally, let’s analyze the equilibrium.
(i) We haven’t considered the case where only low-risk people buy insurance. Why isn’t this a possible
equilibrium?
(ii) The scenarios considered in (A) and (B) can only be an equilibrium if it is possible for the
insurance company to not lose money. Based on your previous answers, in equilibrium who will
buy insurance? Will that equilibrium be Pareto efficient?
(iii) Suppose the government subsidizes health insurance (i.e. imposes a negative tax on all consumers).
How large must the subsidy be, in order for there to exist a price for which everyone chooses to
buy health insurance and the insurance company doesn’t lose money? me im new to economics

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