Intermediate Microeconomics · free preview

Risk Aversion and the Certainty Equivalent

A concave v makes the expected utility of any gamble fall below the utility of its mean, the certainty equivalent is the sure wealth matching the gamble, and the gap between mean and certainty equivalent is the risk premium.

1. The Jensen gap

The Jensen gap

2. Certainty equivalent and risk premium

Certainty equivalent and risk premium

3. Measuring curvature

Measuring curvature

4. Applications in sequence

Applications in sequence

5. The Jensen direction

For a risk-averse consumer, how does EU compare with v of EM?

6. The certainty equivalent

For v the square root, 50-50 states 225 and 25, EU equals 10. What is the certainty equivalent?

7. The risk premium

Same gamble, mean 125, certainty equivalent 100. What is the risk premium and what does it buy?

8. Curvature and wealth

For v the square root, what happens to absolute risk aversion as wealth grows?

9. A modest gamble's CE

For v the square root and 50-50 states 121 and 81, compute the certainty equivalent, and write the number.

10. The premium there

Same gamble, compute the risk premium, and write the number.

11. A third gamble's certainty equivalent

For v the square root and 50-50 states 49 and 169, the EU is 10. What is the certainty equivalent?

12. Risk aversion that fades

For v the square root, absolute risk aversion at wealth w is one over twice root w. What happens between 100 and 400?

13. The premium as a willingness to pay

For the 50-50 gamble over 100 and 36, the EU is 8 and the mean is 68. What is the risk premium?

14. The Jensen gap again

For the 50-50 gamble over 225 and 25, what is the gap between v of the mean and the EU of 10?

15. EU of the third gamble

For v the square root and 50-50 states 49 and 169, compute the expected utility, and write the number.

16. Premium of the third gamble

Same 50-50 gamble over 49 and 169, compute the risk premium, the mean minus the certainty equivalent, and write the number.

Practice this interactively

Free account · instant grading · spaced review that schedules itself.

Start this course for free