Question

A. If a population has two kinds, high and low. risk. Let the expected annual health care costs for the high risk be $5,000, and for the low risk, half that. If there are twice as many low risk as high-risk individuals, and if the one insurer’s administrative load is 20%, what would the premium be if everyone will buy health insurance?

B. Now if a new insurer (B) enter this marketplace and be allowed to exclude the high risk due to pre-existing condition exclusions while the other incumbent insurer (A) is forced to still charge the same rate. Assuming loads remain at 20% in long run equilibrium, what would the premiums be in each market, (low risk, high risk)?

Answer 1

A) High risk costs 5000 Nos. 1/3

Low risk costs 2500 Nos. 2/3

Overall costs per person 5000*1/3 + 2500*2/3 = 3333.33

Loading of 20%=666.67

Total premium 4000

B) Only low risks

Costs 2500 loading 20% so premium per person 2500*1.2 = 3000

Only high risks

Costs 5000 loading 20% so premium per person 5000*1.2= 6000