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Why do the “sickly” individuals choose the more expensive insurance option when there is a separating...

Why do the “sickly” individuals choose the more expensive insurance option when there is a separating equilibrium?

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Answer #1

An equilibrium in which agents with different characteristics choose different actions is separating equilibrium.

To avoid losses, insurance typically will offer only a restricted coverage-premium combination. (Only low-coverage/high coinsurance plans at the cheap price and the expensive plan)
Sickly people will choose "sick-people" plan (the expensive plan) to remain equally well off as with perfect information.
Healthy people will choose "healthy-people" plans,but since they have only low-coverage options, they will be worse off than with perfect information.It cannot maximum utility without imperfect information.

in competitive markets with imperfect information on accident probabilities, if equilibrium exists it entails separate contracts with the high-risk individuals

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