nd tConsider an indiv idual whose utility function over income I is U ( I ) , where U is increasing smoothly in I and is concave (in other words, our basic assumptions throughout this section of the module ). Let I S be this person's income if he is sick, let I H be his income if he is healthy ( I H > I S ), let p be his probability of being sick, let E [ I ] be expected income, and let E [ U ] be his expected utility when he has no insurance

(a) Assume (for part a only) that I S = 0 and I H > 0 . Write down algebraic expressions for both E [ I ] and E [ U ] in terms of the other parameters of the model.

Answer:

E [ I ] = ( 1 - p ) I H + pI S = ( 1 - p ) I H

The second equality above follows from the fact that I S = 0.

E [ U ] = ( 1 - p ) U ( I H ) + pU ( I S )

I have the answers but do not understand them. Can you explain the answers? where is (1-p) coming from ?