Assume both people have $100.

70% they are healthy and all income goes to consumption

30% they are sick and health costs are $75 therefore only $25 left for consumption

Person A has utility function of U = C

Person B has utility function U = sqrt(C)

Assume insurance companies earn zero profits and offer actuarily fair full insurance. Calculate the premium and benefits an actuarily fair full insurance plan would offer each person and their expected utility if they bought that plan

Utility function U = c U = Vc Insurance Premium Paid when Healthy Insurance Payment Received when Ill Expected Utility with full insurance Increase in Utility due to insurance