Expected Utility

Background

Expected utility is a fundamental concept in economics concerning decision-making under uncertainty. It represents the anticipated or projected utility derived from potential outcomes in a scenario involving risk. The concept is grounded in the expected utility theory, a precursor to modern risk analysis used to quantify decisions where outcomes are uncertain.

Historical Context

The concept of expected utility was popularized through the mid-20th century by economists such as John von Neumann and Oskar Morgenstern. Their pivotal work, “Theory of Games and Economic Behavior,” laid the groundwork for this idea, forming a key part of game theory as well as decision theory.

Definitions and Concepts

Expected utility is defined as the sum of the products of the utility of each possible outcome and the probability of each outcome occurring. Formally, if a risky prospect has \( n \) potential outcomes, the expected utility (EU) can be described with the following formula:

\[ EU = \sum_{i=1}^{n} p_i \cdot U(X_i) \]

where:

• \( p_i \) is the probability of outcome \( i \) occurring,
• \( X_i \) is the payoff if outcome \( i \) occurs,
• \( U(X_i) \) is the utility derived from payoff \( X_i \).

Major Analytical Frameworks

Classical Economics

Classical economics, focusing on markets and consumer behavior, did not deal extensively with expected utility. The decisions were often modeled without explicit consideration of uncertainty.

Neoclassical Economics

Neoclassical economics incorporated expected utility as a central element in modeling consumer behavior under uncertainty. It assumes rational consumers who maximize their expected utility.

Keynesian Economics

While Keynesian economics focuses on aggregate demand and government intervention in the economy, it employs expected utility in more microeconomic contexts to understand individual investor behavior under uncertainty.

Marxian Economics

Marxian economics largely does not engage directly with expected utility. The framework typically focuses on class struggles and surplus value rather than individual decision-making under risk.

Institutional Economics

Institutional economics examines how institutions influence economic behavior, including decision-making under uncertainty. Expected utility is applied to understand how institutions mitigate risk and shape choices.

Behavioral Economics

Behavioral economics challenges the rationality assumed in expected utility theory, emphasizing cognitive biases and psychological influences on decision-making under risk.

Post-Keynesian Economics

Similar to Keynesian economics, the post-Keynesian approach factors in more of a macro perspective but can integrate expected utility concepts at the micro level, particularly in financial markets and investment decisions.

Austrian Economics

Austrian economics may view expected utility within the broader theory of entrepreneurial risk-taking and subjective value. They emphasize the dynamic nature of decisions under uncertainty.

Development Economics

In development economics, expected utility can analyze the impact of risky investments and policies on different communities, assessing which strategies maximize societal welfare under uncertain conditions.

Monetarism

Monetarism, focused on the role of governments and central banking in managing money supply, can incorporate expected utility to understand broader economic decisions under risk, especially in financial markets.

Comparative Analysis

Horizontally comparing the relevance and integration of expected utility across various economic theories provides insight into its strengths and limitations. While remaining a foundational tool under neoclassical perspectives, critiques from behavioral economics and institutional economics reveal practical deviations from perfect rationality.

Case Studies

Empirical cases employing the expected utility theory range from determining the optimal stock portfolio balances to public policy assessments in healthcare, where policy outcomes are uncertain but impactful on welfare.

Suggested Books for Further Studies

1. “Theory of Games and Economic Behavior” by John von Neumann and Oskar Morgenstern
2. “Expected Utility Hypotheses and the Allais-Paradox” edited by Maurice Allais and Ole Hagen
3. “Choices under Risk and Uncertainty: Theories and Empirical Evidence” by Louis Eeckhoudt

Related Terms with Definitions

• Risk Aversion: The tendency of individuals to prefer outcomes with lower uncertainty.
• Utility Function: A mathematical representation of how different outcomes provide satisfaction to an individual.
• Prospect Theory: A behavioral model that describes how people decide between alternatives that involve risk and uncertainty.
• Risk Premium: The additional return expected for taking on additional risk.
• Decision Theory: The study of an agent’s choices, combining the expected utility theory and other models.