Identify the type of information asymmetry involved in each case as either adverse selection or the principal$-$agent problem.

Adverse Selection

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A doctor sees on X$-$rays that a patient$$s injury is fully healed but orders one more office visit in three months, with fresh X$-$rays, $$to confirm that it$$s all healed.$$

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An insurance company denies coverage for a treatment that is essential for full recovery. The insurer approves a cheaper alternative, which leaves the patient with a degree of permanent disability.

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In a discussion about cholesterol, a patient tells his doctor he has already cut fatty food out of his diet, when in fact he hasn$$t$.$

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A doctor knows she has been sued for malpractice far more often than her colleagues. Her patients don$$t know this.