How does expected utility theory explain decision-making under uncertainty?

Expected utility theory explains decision-making under uncertainty by proposing that individuals choose between risky options by comparing the expected utilities of their possible outcomes. A decision-maker calculates expected utility by weighting each outcome's utility by its probability and selects the option with the maximum expected utility.

What are the criticisms of expected utility theory?

Criticisms of expected utility theory include its assumptions of rationality and consistency, which may not align with real human behavior. It fails to account for emotions and other cognitive biases. Additionally, paradoxes such as the Allais and Ellsberg paradoxes highlight inconsistencies in actual decision-making versus theoretical predictions.

What are the main assumptions underlying expected utility theory?

The main assumptions underlying expected utility theory are: completeness (all choices can be ranked), transitivity (consistent ranking of choices), independence (preference between two options should be unaffected by a third), and continuity (preferences smoothly adjust to changing probabilities of outcomes). These assumptions enable consistent decision-making under uncertainty.

How is expected utility calculated in practice?

Expected utility is calculated by multiplying the utility of each possible outcome by its probability, then summing these products. This process involves first quantifying the utility values and probabilities based on a decision-maker's preferences and available information.

How does expected utility differ from expected value?

Expected utility considers individual preferences and their subjective attitudes towards risk, incorporating utility values for outcomes. Expected value calculates the weighted average of possible outcomes, focusing only on monetary gains or losses without accounting for varied risk preferences.

What does the expected utility of 4 indicate in the investment example?

The investment aligns with your risk preferences.

How does the expected utility theory account for risk preferences?

By focusing solely on the highest probability outcomes.

In the given game example, how is the expected utility calculated?

$E(U) = (1.0 \times 50) + (0.0 \times (-20)) = 50$

What historical problem did the expected utility theory aim to solve?

The Nash Equilibrium, related to strategic interactions.

Which of the following is an application of expected utility in microeconomics?

Legal ramifications of monopoly practices.

Expected Utility: Theory & Calculation

expected utility

Expected utility is a key concept in decision theory and economics, representing the sum of all possible utility outcomes of a decision, each weighted by the probability of its occurrence. It provides a framework for individuals to make rational choices by comparing the expected benefits of different actions. By focusing on maximizing expected utility, decision-makers aim to select the option that yields the highest forecasted satisfaction or value.

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Expected Utility Definition

Expected utility is a crucial concept in microeconomics, especially in understanding decision-making under uncertainty. It provides a framework for evaluating options when future outcomes are uncertain. The basic idea is to choose the action that maximizes the expected value of the utility, which is a measure of satisfaction or preference.

Understanding Expected Utility

In decision-making, you often face uncertainty, which could involve risk, incomplete information, or unpredictable outcomes. The expected utility theory helps you make rational decisions by considering all possible outcomes and their probabilities. For instance, when investing in stocks, the outcome isn't certain, but you can calculate the expected utility to choose the best stock that aligns with your risk preference. The expected utility is mathematically represented by the formula:\[E(U) = \sum P_iU(x_i)\]Where:

$E(U)$ is the expected utility.
$P_i$ is the probability of outcome $i$.
$U(x_i)$ is the utility of outcome $x_i$.

Expected Utility: A concept in microeconomics that quantifies the anticipated satisfaction or value derived from an uncertain event, incorporating the probabilities of different outcomes.

Consider a simple gamble where you can win \$10 with a probability of 0.5, or lose \$5 with a probability of 0.5. Using the expected utility formula, if you assign a utility value of 10 for a win and -5 for a loss, the expected utility would be:\[E(U) = (0.5 \times 10) + (0.5 \times (-5)) = 2.5\]This calculation shows how you would evaluate the gamble's utility by attaching probabilities to the possible monetary gains and losses.

The expected utility theory originates from the work of Daniel Bernoulli in the 18th century when he sought to provide a solution to the St. Petersburg Paradox, a problem involving seemingly infinite expected value. To understand more, consider how the foundational aspects of expected utility link with the subjective probability, which allows for preferences to be mapped to numerical representations. This model ultimately resolved many critiques of the expected value theory by incorporating varying degrees of risk aversion. Through the lens of expected utility, you can see how nuanced traditional economic models become when intersecting with psychological elements of decision-making.

The expected utility not only aids in financial decisions but also plays a role in daily choices, like deciding whether to carry an umbrella when the weather forecast is uncertain.

Expected Utility Theory

Expected utility theory is integral to making decisions under conditions of uncertainty. It enables you to evaluate different options by considering the potential outcomes and their likelihood. This theory essentially helps in deciding the option that provides the greatest overall benefit.

Core Concepts of Expected Utility Theory

When applying expected utility theory, you incorporate elements of probability to measure the anticipated satisfaction from various outcomes. This requires understanding several core concepts:

Probability: The likelihood of an outcome occurring.
Utility: The satisfaction or value derived from an outcome.
Expected Utility: The weighted average of all possible utilities, considering their probabilities.

The formula to compute expected utility is:\[E(U) = \sum P_iU(x_i)\]Where $P_i$ is the probability of outcome $i$ and $U(x_i)$ is the utility of outcome $x_i$.

Imagine you are playing a game where you can win \$50 with a probability of 0.6 or lose \$20 with a probability of 0.4. To calculate the expected utility, if you assign a utility of 50 for a win and -20 for a loss, the calculation would be:\[E(U) = (0.6 \times 50) + (0.4 \times (-20)) = 24\]This result implies that, on average, playing the game provides a positive utility of 24 units.

The expected utility theory is more than just a mathematical calculation; it provides deeper insights into behavioral economics. Economists often expand on this model by integrating additional factors like risk aversion, where individuals may prefer certain outcomes over uncertain ones, even if the expected utility is higher for the latter. To further explore, consider the concept of von Neumann-Morgenstern utility functions, which extend the notion of expected utility into the real-world considerations of human behavior under risk. This concept contributes to understanding anomalies like insurance purchase, where individuals pay a premium beyond rational calculations to avoid potential negative outcomes.

Expected utility theory is not solely for economists. It's a valuable tool that can help improve decision-making in everyday life, from simple choices like menu selections to complex financial investments.

How to Calculate Expected Utility

Calculating expected utility involves determining the anticipated satisfaction or value from potentially uncertain events by considering all possible outcomes and their probabilities. This helps you to make informed decisions under uncertainty.

Steps to Calculate Expected Utility

To calculate expected utility, follow these essential steps:

Identify all possible outcomes of the decision.
Assign a probability to each outcome, representing the likelihood of its occurrence.
Determine the utility value for each outcome, indicating your preference or satisfaction level.
Use the expected utility formula to calculate the anticipated utility.

The mathematical formula for expected utility is given by:\[E(U) = \sum P_iU(x_i)\]This equation sums the products of each outcome's probability $P_i$ and its corresponding utility $U(x_i)$.

Suppose you are deciding whether to invest in a risky stock with the following outcomes:

Outcome	Probability	Utility
Gain \$100	0.3	15
No Gain/Loss	0.5	0
Loss \$50	0.2	-10

Calculate the expected utility:\[E(U) = (0.3 \times 15) + (0.5 \times 0) + (0.2 \times (-10)) = 4\]The expected utility of 4 suggests this investment aligns with your preferences under risk.

Expected utility theory plays a central role in understanding human behavior regarding risk. It is often contrasted with expected value, which doesn't account for the individual's risk preferences. By considering how utilities are assigned subjectively, economists can better depict real-life choices. For instance, two individuals with different risk tolerances may face the same decision yet select different options based on their expected utility calculations. Additionally, utility scales can be considered ordinal, meaning they reflect order or preference rather than quantity, adding another layer of depth to decision-making analysis.

To gain greater accuracy in determining expected utility, ensure that probabilities are well-calibrated and utilities are precisely defined according to personal or economic preferences.

Expected Utility Function

The expected utility function is a mathematical representation used in microeconomics to explore how decision-makers respond to uncertainty. It forms the basis for analyzing choices when outcomes are not guaranteed, offering insights into preferences and risk behavior.

Applications of Expected Utility in Microeconomics

Expected utility plays a pivotal role in various aspects of microeconomics. Here are some common applications:

Consumer choice under uncertainty: Helps predict purchasing decisions when products have uncertain attributes, like durability or future benefits.
Asset pricing: Assists in valuing financial assets by considering the expected returns and associated risks.
Insurance: Explains why individuals purchase insurance by weighing the utility of potential losses against the cost of premiums.
Game theory: Utilizes expected utility to analyze strategic interactions where players' outcomes depend on others' actions.

These applications highlight the versatility of the expected utility concept in addressing real-world economic scenarios.

Consider the decision to buy insurance for a car valued at \$15,000. The probabilities are:

Outcome	Probability	Utility
Accident (Loss of \$15,000)	0.03	-150
No Accident	0.97	0

The expected utility calculation for not buying insurance would be:\[E(U) = (0.03 \times -150) + (0.97 \times 0) = -4.5\]This negative utility suggests a strong incentive to purchase insurance.

The expected utility theory goes beyond simple probabilities by integrating risk preferences. For example, Von Neumann-Morgenstern utilities consider people's psychological tendencies towards risk — known as risk aversion. This concept is crucial in constructing utility functions where decision-makers derive satisfaction not only based on outcomes but also on their individual risk tolerance.A practical extension of this theory is Prospect Theory by Kahneman and Tversky, which critiqued the limitation of expected utility in explaining anomalies in economic behavior. Through this lens, economic agents are observed to behave irrationally, often overvaluing certain gains over probable outcomes, a phenomenon called the certainty effect. Understanding these models allows economists to adapt and predict economic trends with a higher degree of accuracy.

Incorporate expected utility analysis when considering long-term investments. It provides a comprehensive view of potential risks and rewards, aiding in smarter financial planning.

expected utility - Key takeaways

Expected Utility: A concept in microeconomics that measures the anticipated satisfaction from uncertain events, based on probabilities of different outcomes.
Expected Utility Theory: A framework for decision-making under uncertainty, aiming to select the option with the highest expected utility.
Formula: Expected utility is calculated as E(U) = \sum P_iU(x_i), where P_i is the probability of outcome i and U(x_i) is its utility.
Calculation Example: In a game of probability, you might calculate expected utility using potential winnings and losses weighted by their probabilities.
Application in Microeconomics: Used in consumer choice, asset pricing, insurance, and game theory to evaluate decisions under uncertainty.
Expected Utility Function: A mathematical tool to model decision-making, reflecting preferences and risk behavior when outcomes are uncertain.

expected utility

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