Consider a risk loving agent who has a utility function that takes the form U = I², where I is income. Imagine that this agent can make $100 with 90% probability and $0 with 10% probability. What is ?

To find the expected utility for the risk loving agent, we first need to calculate the expected value of income:

Expected income = (0.9 * $100) + (0.1 * $0) = $90

Now, we can plug the expected income into the utility function:

U = $90² = $8100

Therefore, the expected utility for the risk loving agent is $8100.