a) If an individual is risk averse, which insurance contract will provide the most expected utility?

1. Actuarially fair and partial
2. Actuarially fair and full
3. Actuarially unfair and partial
4. Actuarially unfair and full

b) Using only the mathematical properties of a utility function with risk aversion, and the qualitative properties of each insurance contract (full vs partial, fair vs unfair), prove your answer algebraically (not numerically, you don't need to assume any functional form for the utility function!)