Expected Utility Calculator
Calculate expected utility to make rational decisions under uncertainty and assess risk preferences
Calculate Expected Utility
Choose the utility function that best represents risk preferences
Event 1
Event 2
Expected Utility Results
Calculation Breakdown
Event 1:
Probability: 0% (0.000)
Value: $0
Utility: 0.00
Weighted Utility: 0.00
Event 2:
Probability: 0% (0.000)
Value: $0
Utility: 0.00
Weighted Utility: 0.00
Formula: EU = (p₁ × U(x₁)) + (p₂ × U(x₂))
Result: 0.00 = (0.000 × 0.00) + (0.000 × 0.00)
Decision Analysis
Example Calculation
Investment Decision
Investment A:
• Probability: 40%
• Value: $10,000
Investment B:
• Probability: 60%
• Value: $20,000
Utility Function: Square root
Calculation
EU = (0.4 × √10,000) + (0.6 × √20,000)
EU = (0.4 × 100) + (0.6 × 141.42)
EU = 40 + 84.85
EU = 124.85
Utility Functions
Square Root
U(x) = √x
Risk-averse behavior
Linear
U(x) = x
Risk-neutral behavior
Logarithmic
U(x) = ln(x)
Highly risk-averse
Quadratic
U(x) = x²
Risk-seeking behavior
Decision Making Tips
Consider all possible outcomes and their probabilities
Choose utility function based on risk tolerance
Higher expected utility indicates better choice
Account for diminishing marginal utility
Understanding Expected Utility Theory
What is Expected Utility?
Expected utility is a metric used to help make rational decisions when facing uncertain outcomes. It combines the probability of each outcome with its utility (subjective value) to determine the most desirable choice.
Why Use Expected Utility?
- •Accounts for risk preferences and attitudes
- •Provides consistent decision-making framework
- •Incorporates diminishing marginal utility
- •Better than simple expected value for large amounts
Formula Explanation
EU = Σ(pᵢ × U(xᵢ))
- EU: Expected Utility
- pᵢ: Probability of outcome i
- U(xᵢ): Utility of outcome i
- xᵢ: Monetary value of outcome i
Note: The utility function reflects risk preferences. Square root function models risk aversion, while linear function represents risk neutrality.
Applications in Strategic Decision Making
Portfolio Management
Balance risk-reward trade-offs by assessing expected utility of different investment combinations.
Business Investments
Evaluate projects with uncertain returns while considering company risk tolerance and financial stability.
Contract Negotiations
Assess different contract terms based on their expected utility to each party in the negotiation.