Expected utility without insurance Lottery scenario similar to case of insurance customer She gains a high income IH if healthy,and low income Is if sick. Uncertainty about which outcome will happen, though she knows the probability of becoming sick is p Expected utility E[U(I)]is: E[U(0)]=pU(s)+(1-p)U(IH) Bhattacharya,Hyde and Tu-HealthEconomics
Bhattacharya, Hyde and Tu – Health Economics Expected utility without insurance Lottery scenario similar to case of insurance customer She gains a high income IH if healthy, and low income IS if sick. Uncertainty about which outcome will happen, though she knows the probability of becoming sick is p Expected utility E[U(I)] is: E[U(I)] = p U(IS ) + (1- p) U(IH )
E[U(I)]and probability of sickness Consider a case where the person is sick with certainty(p=1): E[U]=U(Is)equals the utility from certain income Is(Point S) Consider case where person has no chance of becoming sick(p=o): E[U]=U(IH)equals utility from certain income I(Point H) U UWh U ( EU(]o.25 EU01o.75 U(ls)- E00.75 E00.25 月 Bhattacharya,Hyde and Tu-HealthEconomics
Bhattacharya, Hyde and Tu – Health Economics Consider a case where the person is sick with certainty (p = 1): E[U] = U(IS ) equals the utility from certain income IS (Point S) Consider case where person has no chance of becoming sick (p = 0): E[U] = U(IH) equals utility from certain income IH (Point H) E[U(I)] and probability of sickness