# Clarifying question about utility theory and preferences

I am trying to solve this question about preferences and I got into an argument about it. I just want to make sure I am not overlooking something really simple.

What can you tell about the risk tolerance of someone who prefers a lottery C (pays 48,000 with 50% chance and 54,000 with 50%chance) over lottery B2 (pays 50,000 with 100% chance). Explain.

My answer: The information that a person prefers C over B2 by itself is insufficient to determine risk tolerance. This is because lottery C has higher expected payout (51,000) than the fixed payout of B2 (50000), and we are not able to deduce a preference between C and E(C) = 51000, i.e. its own expected payout. Indeed, a risk loving or risk neutral person would choose lottery C over B2. But a risk averse person with a sufficiently "flat"-ish utility curve would also choose C over B2, as shown in the image below (green is the utility curve).

• "Lotteries are a tax on people who are bad at math." Commented Mar 17 at 12:19
• Fyi Scott in economics, the term "lottery" is a general phrase that can refer to any situation where outcomes are uncertain, not just the lottery you buy tickets for. The decisions whether or not to buy insurance, speed on the highway, or bring your umbrella to work are all choices between lotteries. Commented Mar 19 at 15:15