🎲 Expected Utility Calculator
Outcomes × probabilities with risk aversion
How to Use This Calculator
1
Enter Outcomes
Monetary outcomes for each state.
2
Enter Probabilities
Must sum to 1.0.
3
Set Risk Aversion
a = 0 is risk-neutral; higher a → more risk averse (CRRA).
Formula
EU = Σ p_i · u(x_i)
CRRA u(x) = (x^(1−a) − 1)/(1−a), a ≠0; u(x)=x if a=0
Example: x=[1000,−500], p=[0.6,0.4], a=1 → u(x)=ln(x); negative outcomes not defined for CRRA — shift outcomes or use risk‑neutral approximation.
Frequently Asked Questions
What if outcomes are negative?
CRRA is defined for positive wealth. Model outcomes as final wealth (baseline + gain/loss), or use a utility that handles negatives.
What values for a are typical?
Commonly between 1 and 5 in economic applications; a=0 is risk‑neutral.
Does EU pick the best choice?
Choose the option with the highest expected utility among alternatives.