Expected Utility Calculator

Expected utility measures the anticipated satisfaction or value of a decision that has uncertain outcomes. Instead of simply multiplying probabilities by raw monetary amounts—which reflects risk-neutral behavior—expected utility applies a concave utility function (such as the square root function, representing risk aversion) to each monetary payoff.

The mathematical formula used by this calculator is: EU = (P1 * U(M1)) + (P2 * U(M2)), where P1 and P2 represent the probabilities of each respective event, and U(M1) and U(M2) represent the utility derived from monetary values M1 and M2. In this model, U(M) is calculated as the square root of the monetary value, demonstrating diminishing marginal utility of wealth.

Imagine you are evaluating a financial investment with two possible scenarios:

Scenario 1: A 60% chance (P1 = 0.60) of receiving a monetary payoff of $10,000 (M1).

Scenario 2: A 40% chance (P2 = 0.40) of receiving a monetary payoff of $2,500 (M2).

Step 1: Compute the utility for each monetary outcome using the square root function. For M1, the square root of $10,000 is 100. For M2, the square root of $2,500 is 50.

Step 2: Multiply each utility value by its corresponding probability. For Scenario 1: 0.60 * 100 = 60. For Scenario 2: 0.40 * 50 = 20.

Step 3: Sum the weighted utility values together to find the total expected utility. EU = 60 + 20 = 80.

Reflect Your Risk Profile: The square root utility model assumes a standard level of risk aversion. If you are analyzing corporate decisions where entities behave differently toward risk, ensure the underlying utility function matches your specific risk tolerance.

Verify Probabilities: Always ensure that all mutually exclusive probabilities in your calculation sum up precisely to 1.0 (or 100%). Even a minor discrepancy in probability inputs can skew the final expected utility score.