The figure below describes John's preferences over lotteries for three prizes- $1, $2, and $3, where p1 is the probability of winning $1, and p3 is the probability of winning $3. Assume that John is an expected utility maximizer.
a) Is John risk averse?
b) Suppose it is additionally known that John prefers a lottery that pays $2 with probability 1/2 and $3 with probability 1/2 to a certain payment of $2.50. Which of the following two lotteries will John prefer? Explain briefly.
• Lottery A: A payment of $2 with probability 1.
• Lottery B: A lottery that pays $2.50 with probability 0.35 and $1 with probability 0.65.
I can't seem to understand the above question. I first calculated the expected utilities. According to the statement since he prefers the former while he must be risk loving. However, when I calculate the EU of Lottery A and B, 2 and 1.525, respectively, I don know how to conclude in that case. He is a risk lover but since the expected utility of a lottery is higher than the lottery itself, he shouldn't choose Lottery B. I believe that the right answer is he chooses Lottery A.
Is it correct?
The screenshot of the exercise
