Risk Aversion and Income

- Variability in potential payoffs increases risk premium.

- Example:

• A job has a .5% probability of paying $40,000 (utility of 20) and a 5 percent chance of paying 0 (utility of 0).

* The expected income is $20,000, but expected utility falls to 10.

Expected utility = .5u($) + .5u($40,000)

         = 0 + .5(20) = 10

* The certain income of $20,000 has a utility of 16.

*  If person is required to take the new position, the utility of them will fall by 6.

* The risk premium is $10,000 (that is they would be willing to give up $10,000 of the $20,000 and have same E(u) as the risky job.

*  Thus, it can be said that greater the variability, greater the risk premium.

*  Indifference Curve

- Combinations of the3 expected income & standard deviation of income which yield the same utility.