Alice and Ben are both expected utility maximizers. Alice's vNM utility is u1 (x) = x while Ben's vNM utility is u2 (x) = x where both and are strictly between 0 and 2. Consider the following lotteries:

Lottery P : (25%, $2; 75%, $0) Lottery Q: (q, $1; 1q, $0)

For any lottery Q where q is between 0 and 1, if Alice prefers P to Q then Ben also prefers P to Q.

1. What is the relationship between and ? Do we know which is larger?

2. Suppose Alice is risk-loving. Do we know if Ben is risk-averse or risk-loving?

3. Suppose Ben is risk-loving. Do we know if Alice is risk-averse or risk-loving?