Microeconomic Expected Utility & Risk Premium Calculator

Expected Utility Theory models decision-making under uncertainty, explaining why risk-averse individuals pay insurance premiums to avoid volatile financial gambles.

To use the Microeconomic Expected Utility & Risk Premium Calculator, enter your Risk Preference Utility Function U(w), State 1 Wealth Outcome (w1), State 1 Probability (p1) and other values. The calculator instantly computes Expected Utility EU, Expected Wealth EW and more. Results update in real time as you change any input — no submit button needed.

How to Use This Calculator

Enter your Risk Preference Utility Function U(w) — choose from Square Root U(w) = √w (Risk Averse -- Diminishing Marginal Utility), Natural Log U(w) = ln(w) (Risk Averse), Linear U(w) = w (Risk Neutral), State 1 Wealth Outcome (w1) (e.g. 10000 in ), State 1 Probability (p1) (e.g. 50 in %), and State 2 Wealth Outcome (w2) (e.g. 40000 in ). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Expected Utility EU = p1 × U(w1) + p2 × U(w2)

Expected Wealth EW = p1 × w1 + p2 × w2

Certainty Equivalent CE = U⁻¹(EU)

Risk Premium = Expected Wealth (EW) - Certainty Equivalent (CE)

Worked Example

50% chance of 10,000 vs 50% chance of 40,000 under U(w) = √w:

Expected Wealth EW = + = 25,

000.

Expected Utility EU = + = 150 utils.

Certainty Equivalent CE = 150^2 = 22,500.

00.

Understanding Your Result

Evaluate your result in the context of your specific use case and relevant industry standards or reference values. A single calculated result is a starting point — test two to three scenarios to understand how sensitive the outcome is to your key input assumptions. For high-stakes decisions, verify your result against a secondary source or subject-matter expert before acting.