8.9 Investment in risky assets can be examined in the state-preference framework by assuming that W * dollars invested in an asset with a certain return, r, will yield W *(1 r) in both states of the world, whereas investment in a risky asset will yield W *(1 rg ) in good times and W *(1 rb) in bad times (where rg  r  rb).

a. Graph the outcomes from the two investments.

b. Show how a “mxied portfolio” containing both risk-free and risky assets could be illustrated in your graph. How would you show the fraction of wealth invested in the risky asset?

c. Show how individuals’ attitudes toward risk will determine the mix of risk-free and risky assets they will hold. In what case would a person hold no risky assets?

d. If an individual’s utility takes the constant relative risk aversion form (Equation 8.62), explain why this person will not change the fraction of risky asset held as his or her wealth increases.20