Expected Utility Calculator

1. What is Expected Utility?

Definition: Expected Utility is a concept in economics and decision theory that measures the anticipated benefit or satisfaction from a decision, considering the probabilities and outcomes of different events.

Purpose: This calculation helps in evaluating decisions under uncertainty by quantifying the expected satisfaction derived from monetary outcomes, adjusted for risk preferences.

2. How Does the Expected Utility Calculator Work?

The calculator uses the following formula for Expected Utility, as shown in the image above:

\[ EU = (p_1 \times (v_1^{0.5})) + (p_2 \times (v_2^{0.5})) \]

Where:

$ p_1 $: Probability of Event 1 (in percentage)
$ v_1 $: Monetary Value of Event 1 (in dollars)
$ p_2 $: Probability of Event 2 (in percentage)
$ v_2 $: Monetary Value of Event 2 (in dollars)
$ EU $: Expected Utility

Steps:

Enter the Probability of Event 1 in percentage
Enter the Monetary Value of Event 1 in dollars
Enter the Probability of Event 2 in percentage
Enter the Monetary Value of Event 2 in dollars
The calculator converts probabilities to decimal form
Applies the square root to the monetary values to reflect diminishing marginal utility
Multiplies each transformed value by its probability
Sums the results to compute the Expected Utility

3. Importance of Expected Utility Calculation

Calculating Expected Utility is essential for:

Decision Making: Helps individuals make rational choices under uncertainty
Risk Assessment: Accounts for risk aversion by using a utility function (square root in this case)
Investment Analysis: Compare investment options with uncertain outcomes
Economic Modeling: Used in models to predict behavior in uncertain environments

4. Using the Calculator

Example 1: Calculate the Expected Utility of two investments

Probability of Event 1: 40%
Monetary Value of Event 1: $10,000
Probability of Event 2: 60%
Monetary Value of Event 2: $20,000
Expected Utility: $ EU = (0.4 \times (10000^{0.5})) + (0.6 \times (20000^{0.5})) ≈ 124.85 $

Example 2: Calculate the Expected Utility of a lottery

Probability of Event 1: 30%
Monetary Value of Event 1: $5,000
Probability of Event 2: 70%
Monetary Value of Event 2: $15,000
Expected Utility: $ EU = (0.3 \times (5000^{0.5})) + (0.7 \times (15000^{0.5})) ≈ 106.88 $

5. Frequently Asked Questions (FAQ)

Q: Why use the square root in the utility function?
A: The square root reflects diminishing marginal utility, meaning additional money provides less additional satisfaction as wealth increases.

Q: When would I need to calculate expected utility?
A: When making decisions under uncertainty, such as choosing between investments or evaluating risky options.

Q: What does a higher expected utility mean?
A: A higher expected utility indicates indicates a more desirable option, considering both the outcomes and their probabilities.

Q: How does this differ from expected value?
A: Expected Value calculates the average monetary outcome, while Expected Utility adjusts for risk preferences using a utility function.