# The expected utility

Your family is offering you your choice of two alternatives. The first alternative is to give you a money gift of $19,000. The second alternative is to make an investment in your name. This will quickly have the following two possible outcomes:

Outcome Probability

Receive $10,000 0.3

Receive $30,000 0.7

(a) Your utility for receiving M thousands dollar is given by the utility function u(M) = SQRT(M+6). Which choice should you make to maximize expected utility?

(b) You now are uncertain about what your true utility function for receiving money is, so you are in the process of constructing this utility function. So far, you have found that u(19) = 16.7 and u(30) = 20 are the utility of receiving $19,000 and $30,000 respectively. You also have concluded that you are indifferent between the two alternatives offered to you by your family. Use this information to find u(10).

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#### Solution Preview

a) u(M) = ?[M+6]

The expected utility with the first alternative is:

E(u)1 = u(19) = ?[19+6] = ?[25] = 5

The expected utility with the second ...

#### Solution Summary

The expected utility is clearly evaluated in this case.