You start an insurance company as your first entrepreneurial venture after graduation. Your main product line is malpractice insurance for dentists. After exhaustive research, you learn that settling malpractice claims against careful dentists costs $2,000 and settling malpractice claims against reckless dentists costs $7,500.
Individual dentists know whether they are reckless or careful, and your research shows that approximately 20% of dentists are reckless. How much do should you charge for malpractice insurance to break even? Why?