There is a consumer who has a utility function from income U1(W) = W3/4. This person gets her income from the following uncertain situation: There is a 80% chance they have an income of $256 and a 20% chance of getting $81. There is a different consumer that has utility U2(W) = W1/4 and her income has a 18% chance of being $625 and a 82% chance of being $150.0625.
a) Find the expected income for each person.
b) Find the expected utilty for each person
c) Show that if these to people trade income situations, both will be better off and explain why this makes sense.