Key takeaways:
• A risk-neutral agent has linear utility (u = x): they care only about expected value.
• A risk-averse agent has concave utility (u = √x): they'd accept a guaranteed amount less than the expected value to avoid the gamble. The gap is the risk premium.
• A risk-loving agent has convex utility (u = x²): they prefer the gamble to the sure thing.
• The certainty equivalent (CE) is the guaranteed amount that gives the same utility as the lottery.
⚠ Note on Risk Attitudes
We assumed the student is
risk neutral (the usual assumption in this course).
However, if the student is
risk loving, the more competitive option may become relatively more attractive.
If the student is instead
risk averse, the safer options may become more attractive.
Different risk attitudes correspond to different utility functions, which can lead to different choices—even when the probabilities and outcomes are the same.
How to use: Uni A pays $80k (risky), Uni B pays $40k (moderate), Uni C pays $20k (safe).
Toggle between utility functions to see how risk attitudes change the optimal choice.
Drag the probability sliders to explore different scenarios.