Jim Whitney Economics 250

Monday, April 22, 2013

Incomplete information and health insurance

Assumptions:

  1. Consumers will buy insurance as long as the pricedoes not exceed their expected medical expenses. (In the real world, they will pay even more due to risk aversion.)
  2. The only costs for insurance companies are payouts to cover medical expenses
  3. The insurance is competitive: insurers charge expected breakeven prices ("actuarially fair")
Case 1: Imperfect information: No one knows their own health prospects, only general probabilities.
1 Health status Healthy Unhealthy
2     Probability (Percent of population) 75% 25%
3     Average annual expenses $4,000 $12,000
4 Expected annual health costs = insurance price:  
 

Case 2: Asymmetric information: Buyers know if they are at risk for poor health, but sellers can't tell.

1

   Group N: Not at risk Group R: At risk
2 Percent of population 50% 50%
3 Health status Healthy Healthy Unhealthy
4 Buyers' perspective: Probability of health status given their risk group 100% 50% 50%
5     Average annual expenses $4,000 $4,000 $12,000
6     Expected annual health costs for each risk group:    
7 Sellers' perspective: Probability of health status 75% 25%
8 Expected annual expenses = initial price $6,000
9     Will consumers in each risk group buy insurance?    
10     Initial average earnings per policy sold:  
11 Expected annual expenses for insurers after adverse selection = final price:  
 

Case 3: Asymmetric information: Scientists discover a test to determine whether or not you will be unhealthy. The test is free and confidential. It is up to the buyers whether or not to disclose their test result.

1

   Group N: Not at risk Group R: At risk
2 Percent of population 50% 50%
3 Health status Healthy Healthy Unhealthy
4     Probability 100% 50% 50%
5     Average annual expenses $4,000 $4,000 $12,000
6 Expected annual expenses before testing $6,000
7 Will buyers in each risk group take the test?    
8     Will tested buyers disclose their test result to insurers?      
9     What price will sellers charge consumers who disclose results?      
10     What price will sellers charge consumers who do not disclose results?