Expected Utility Calculator

The Expected Utility Theory is a fundamental concept in economics and decision theory that helps in assessing the desirability of various uncertain prospects. It combines probabilities and outcomes into a single measure to guide decision-making under uncertainty.

Historical Background

Expected Utility Theory was formally introduced by John von Neumann and Oskar Morgenstern in their book "Theory of Games and Economic Behavior" (1944). It has since become a cornerstone in the fields of economics, finance, and risk management, guiding individuals and organizations in making rational choices under uncertainty.

Calculation Formula

The expected utility of an outcome is calculated by summing the products of the utility values of outcomes and their respective probabilities:

\[ EU = (p_1 \times u_1) + (p_2 \times u_2) \]

where:

• \(EU\) is the expected utility,
• \(p_1\) and \(p_2\) are the probabilities of events 1 and 2, respectively,
• \(u_1\) and \(u_2\) are the utility values (often monetary) associated with events 1 and 2.

Example Calculation

If the probability of Event 1 is 40% with a monetary value of $100 and the probability of Event 2 is 60% with a monetary value of $150, the expected utility is calculated as:

\[ EU = (0.4 \times 100) + (0.6 \times 150) = 40 + 90 = 130 \]

Importance and Usage Scenarios

Expected utility is used to model behavior when faced with decisions like investments, insurance, and gambling, where outcomes are uncertain. It helps in choosing the option with the highest expected utility, thereby rationalizing choices under risk and uncertainty.

Common FAQs

1. What is the difference between expected utility and expected value?

   • Expected utility considers the desirability or utility of outcomes to the decision-maker, whereas expected value is a mathematical average of all possible outcomes.

2. How does risk aversion affect expected utility?

   • Risk-averse individuals value certain outcomes more than uncertain ones, even if the uncertain outcomes have a higher expected value. This is reflected in their utility functions, which are concave, indicating diminishing marginal utility of wealth.

3. Can expected utility theory explain all decision-making under uncertainty?

   • While expected utility theory provides a robust framework for decision-making under risk, it has limitations and may not account for all behaviors, such as loss aversion and the overweighting of unlikely events, described by prospect theory.

This calculator makes the concept of expected utility approachable and applicable, providing a practical tool for individuals and professionals to assess the desirability of various uncertain outcomes.