Question

There are four consumers, whose health care costs are expected to be $1000, $2000, $3000, and $4000 if they are enrolled in a generous, PPO plan. Call these consumers types I, II, III, and IV frespectively. Their health costs are expected to be 10% less if they are enrolled in a restrictive, HMO plan. Each type obtains a value of $5000 from the HMO plan. A type of consumer obtains some incremental value from the PPO plan, and these incremental values for the four types are, respectively, $1000, $ 2000, $3000, and $4000. The following table summarizes the costs and values: Consumer Cost at PPO Cost at HMO Value at HMO Value at PPO Type I Type II Type III Type IV $2000 $3000 $4000 $1000 * 0.9 $2000 * 0.9 $3000 * 0.9 $4000 * 0.9 $5000 $5000 $5000 $5000 $6000 $7000 $8000 $9000 The health plan markets are competitive, so that each health plan's premium must be equal to the expected cost of its enrollees. For example, if all four types of consumers enroll in the PPO, the premium is the average of $1000, $2000, $3000 and $4000, or $2500. If all four types of consumers enroll in the HMO, the premium becomes $2500*0.9 due to the 10% cost savings at an HMO.