Question

Anne faces an uncertain World with two possible states, good and bad. In the good state she has money holding MG and in the bad state, she has money holdings MB. We will write the money bundle M = (MG,MB). The good state is realized with probability ? and the bad state is realized with probability 1 - (pi). Anne’s preferences are characterized by expected utility function, U(M)=(pi)(MG)^(1/2) + (1-pi)(MB)^(1/2). Let pi=3/4.

1) How does Anne rank the following three bundles M1 = (100,100), M2 = (50,250), M3 = (120, 40)?

2) What is Anne’s expected money holdings for the three bundles? (that is, weighted average money holdings over the two states).

3) Draw Anne’s indifference curve for expected utility, U (M) = 10.

4) In the same graph, draw the constant expected money holdings line for expected money holding of 100 (that is, money bundles M that all have the same expected money holdings).

5) Is Anne risk loving, neutral, or averse?

6) Determine the certainty equivalent of each of the three bundles M1, M2, and M3.

7) In the same graph as above, draw Anne’s indifference curve for U(M) = 10, but now set pi = 1/2.

Answer 1

1)

Utility from M1 =  

Utility from M2 =

Utility from M3 =

Anne's ranking preference would be in order of her utility from high to low: M1>M3>M2

2)

Let expected money holding = E(M)