Expected Utility is a fundamental economic concept that quantifies the anticipated utility an individual or an entire economy is projected to achieve under various potential conditions. This measurement helps in decision-making processes where outcomes are uncertain.
Calculating Expected Utility
Basic Formula
The calculation of expected utility, \(EU\), can be expressed mathematically as:
- \(p_i\) is the probability of outcome \(i\),
- \(U(x_i)\) is the utility derived from outcome \(i\),
- \(n\) represents the total number of possible outcomes.
Step-by-Step Calculation
- Identify Possible Outcomes: Define all potential outcomes \((x_1, x_2, \ldots, x_n)\).
- Assign Probabilities: Assign a probability \(p_i\) to each outcome such that \(\sum_{i=1}^n p_i = 1\).
- Determine Utility: Calculate or estimate the utility \(U(x_i)\) for each outcome.
- Multiply and Sum: Multiply each probability by its corresponding utility and sum the results to get the expected utility \(EU\).
Types of Expected Utility
Objective Probability
Objective probabilities are derived from statistical data or historical records, providing a more precise basis for calculating expected utility.
Subjective Probability
Subjective probabilities depend on personal belief or judgment, often used when statistical data is unavailable or when dealing with unique events.
Special Considerations
Risk Aversion
Risk-averse individuals prefer outcomes that minimize uncertainty, even at the expense of potentially higher utility. This often translates into choosing options with lower variance in outcomes.
Risk Neutrality
A risk-neutral decision-maker evaluates options solely based on the expected utility, showing indifference to the variability of outcomes.
Risk Seeking
Risk-seeking individuals favor options with higher variability, even if the expected utility remains constant or lower, due to the potential of achieving significantly higher utility.
Practical Examples
Insurance Decisions
In deciding the purchase of insurance, individuals use expected utility to weigh the guaranteed utility loss (insurance premium) against the potential but uncertain financial loss due to adverse events.
Investment Choices
Investors apply expected utility to choose between different investment portfolios, balancing expected returns against the risks associated with each.
Historical Context
The concept of expected utility came to prominence with the works of Daniel Bernoulli in the 18th century, particularly through his paper “Exposition of a New Theory on the Measurement of Risk.” This seminal work laid the groundwork for modern decision theory and risk management.
Applicability
Expected utility theory is widely used in:
- Economic Policy Making: To assess the impact of policy decisions under uncertainty.
- Corporate Strategy: For strategic business decisions that involve risk and uncertainty.
- Behavioral Economics: To understand how real-world decisions often deviate from the theoretical model due to cognitive biases.
Related Terms
- Utility Function: A function that assigns numerical values to different outcomes representing the satisfaction or benefit derived from them.
- Stochastic Dominance: A concept used in decision theory to compare different prospects based on their expected utilities.
- Probability Distribution: A statistical function that describes all the possible values and likelihoods that a random variable can take within a given range.
FAQs
What is the significance of expected utility in decision-making?
How do risk preferences affect expected utility?
Can expected utility be applied to non-financial decisions?
References
- Bernoulli, Daniel. “Exposition of a New Theory on the Measurement of Risk.” Econometrica, 1738.
- Von Neumann, John, and Morgenstern, Oskar. “Theory of Games and Economic Behavior.” Princeton University Press, 1944.
Summary
Expected utility serves as a cornerstone for understanding decision-making under uncertainty. By combining probabilities of outcomes with their associated utilities, this theory aids in making rational choices that balance risk and reward. The practical application spans various fields, from economics to finance, enhancing our ability to navigate through uncertain environments.
