Expected Utility Formula

Definition

The expected utility formula is a mathematical representation used to calculate the anticipated satisfaction or benefit an individual derives from uncertain outcomes, factoring in both the probabilities of each outcome and the utility associated with them. This concept is central to understanding how people make choices under risk, as it allows for the comparison of different risky options by quantifying their expected values, thus providing a foundation for analyzing risk attitudes and decision-making behavior.

5 Must Know Facts For Your Next Test

1. The expected utility formula is typically expressed as $$E(U) = \sum p_i U(x_i)$$, where $$E(U)$$ is the expected utility, $$p_i$$ is the probability of outcome $$i$$, and $$U(x_i)$$ is the utility associated with that outcome.
2. This formula helps individuals weigh their options by considering both the desirability of outcomes and the uncertainty surrounding them, allowing for informed decision-making.
3. Individuals who are risk-averse will assign higher value to guaranteed outcomes compared to risky ones with higher potential rewards, leading to lower expected utility for high-risk options.
4. The concept of diminishing marginal utility suggests that as an individual consumes more of a good or outcome, the additional satisfaction gained from each additional unit decreases.
5. In real-life scenarios, the expected utility formula can be applied to decisions involving gambling, investments, insurance, and any situation where outcomes are uncertain.

Review Questions

• How does the expected utility formula help individuals make decisions under risk?
  • The expected utility formula aids in decision-making under risk by providing a systematic way to evaluate different options based on their potential outcomes and associated probabilities. By quantifying both the likelihood of various results and their respective utilities, individuals can compare choices more effectively. This allows them to choose options that align with their risk preferences, whether they are risk-averse, risk-neutral, or risk-seeking.
• Discuss how risk aversion influences the application of the expected utility formula in decision-making.
  • Risk aversion plays a significant role in how individuals use the expected utility formula to evaluate options. Risk-averse individuals tend to favor choices that offer guaranteed outcomes over those with higher expected utilities but greater uncertainty. As a result, when applying the expected utility formula, they might assign less weight to risky options even if those options have favorable probabilities. This leads them to select alternatives that minimize risk rather than maximize potential gains.
• Evaluate how diminishing marginal utility impacts an individual's assessment of expected utility in different scenarios.
  • Diminishing marginal utility affects how individuals assess expected utility by indicating that as they gain more of a particular outcome, each additional unit provides less satisfaction. This means that when calculating expected utilities for various choices, individuals may weigh large potential gains less heavily than smaller but more certain outcomes. Consequently, even if an option has a high expected value due to significant potential rewards, it may be less appealing if it also involves considerable risk. Understanding this relationship helps explain why people often prefer safer bets over those with higher returns but greater uncertainty.

Related terms

Utility:

A measure of the satisfaction or benefit that an individual derives from consuming goods or services or from particular outcomes.

Risk Aversion:

The tendency of individuals to prefer certain outcomes over uncertain ones, even if the uncertain option has a higher expected value.

Probability: A measure of the likelihood that a given event will occur, often expressed as a number between 0 and 1.