# Expected utility

Expected utility is a decision-making theory that states that people make decisions based on the expected outcomes of their choices. It suggests that people look at the potential outcomes of a decision and then weigh them against each other to determine which option is most likely to provide the greatest benefit. This theory is commonly used in management decision-making, as it allows for the evaluation of different options based on their expected utility and the potential costs and benefits associated with each. Expected utility theory can be used to help managers make decisions that optimize resources, reduce risk, and maximize gain.

## Example of expected utility

• A manager needs to decide which of two potential suppliers to use for a new project. He can use expected utility theory to compare the cost and quality of the two suppliers, and then decide which one is most likely to provide the greatest benefit to the company.
• A business owner needs to decide whether to expand their operations into a new market. They can use expected utility theory to estimate the potential costs and benefits of entering that market and then decide which option is most likely to provide the greatest profit.
• An investor needs to decide which stocks to invest in. They can use expected utility theory to evaluate the potential returns of each stock and then decide which one offers the greatest expected return on their investment.

## Formula of expected utility

The expected utility formula is a mathematical expression used to determine the most optimal course of action given a set of available options. It is defined as the sum of all the products of the probability of each option multiplied by the utility associated with that option. The formula is expressed as:

$$$$EU = \sum_{i=1}^{n} P_i \cdot U_i$$$$

where EU is the expected utility, P is the probability of option i occurring, and U is the utility for that option.

The expected utility formula can be used to make decisions in situations where the outcomes are uncertain. By assigning a probability to each option and a utility value to each outcome, the expected utility of each option can be calculated and the most optimal decision can be made. The expected utility formula can also be used to compare different decisions to determine which one is the most beneficial.

## When to use expected utility

Expected utility theory is a useful tool for decision-making in many different contexts. It can be used to help managers weigh potential outcomes of decisions and determine which option is most likely to provide the greatest benefit. Specifically, expected utility theory can be used in the following situations:

• To compare the costs and benefits of different business strategies.
• To help organizations manage risk by evaluating potential outcomes and their associated probabilities.
• To assess the financial viability of different investments.
• To assess the cost-effectiveness of different marketing strategies.
• To evaluate different projects and prioritize resources.
• To assess the likelihood of success for different projects and initiatives.
• To determine the optimal pricing strategy for a product or service.
• To evaluate different suppliers and optimize supplier relationships.
• To assess the expected return on investment for different projects.

## Types of expected utility

Expected utility is a decision-making theory that states that people make decisions based on the expected outcomes of their choices. There are several types of expected utility which can be used to help managers make decisions that optimize resources, reduce risk, and maximize gain. These include:

• Risk Neutral Utility: This is a type of expected utility which considers the potential outcomes of a decision without taking into account potential risks. This type of expected utility assumes that all outcomes have the same probability and will therefore be treated equally.
• Risk Averse Utility: This form of expected utility takes into account the potential risks associated with a decision and assigns a higher probability to outcomes that are less risky. This type of expected utility is used when decisions involve a greater degree of uncertainty.
• Risk Seeking Utility: This type of expected utility is the opposite of risk averse utility and assigns a higher probability to outcomes that involve greater risk. This type of expected utility is typically used when decisions involve high-reward investments.
• Expected Value Utility: This form of expected utility focuses on the expected value of a decision, rather than the probability of a particular outcome. This type of expected utility is typically used when decisions involve large sums of money or a long-term investment.

Expected utility theory provides a reliable and robust way of making decisions that can be beneficial in a variety of situations. The main advantages of using expected utility theory include:

• Its ability to weigh potential outcomes, allowing decision-makers to identify the best option with the greatest expected value;
• Its ability to account for risk and uncertainty, as decision-makers can take into account potential costs and benefits associated with different options;
• Its ability to optimize resources, as decision-makers can identify the option that gives the greatest return on investment;
• Its ability to reduce risk, as decision-makers can identify the option with the least potential downside;
• Its flexibility, as it can be used in a variety of situations and can be tailored to different organizational goals.

## Limitations of expected utility

Expected utility theory has several limitations that should be considered when making decisions. These include:

• Ignoring risk aversion: Expected utility theory assumes that people are risk-neutral, meaning that they are indifferent to risk. However, in reality, people may be risk-averse, meaning they are more likely to choose options with lower risks and higher rewards.
• Uncertainty: Expected utility theory assumes that all the information needed to make a decision is known, which is not always the case in the real world.
• Limited scope: Expected utility theory applies only to decisions that involve a single option and does not account for situations where multiple options are available.
• Complexity of decisions: The assumptions of expected utility theory may not hold for complex decisions, as the assumptions may not accurately reflect the real world.
• Self-interest: Expected utility theory assumes that people make decisions based solely on their self-interest, without taking into account the interests of others.

## Other approaches related to expected utility

Expected utility theory is one approach to decision-making; however, there are also several related approaches. These include:

• Prospect Theory: This theory suggests that people make decisions based on the level of risk involved in an option. It states that people are more likely to take risks when the potential rewards are greater.
• Subjective Expected Utility: This theory states that people make decisions based not only on the expected value of an option, but also on the subjective value they place on it. This approach takes into account both personal preferences and cultural values.
• Risk Aversion: This theory suggests that people are more likely to make decisions that minimize risk rather than maximize gain.
• Expected Value: This theory suggests that people make decisions based on the expected value of an option, which is the average outcome of a decision.

In summary, expected utility theory is one approach to decision-making, and there are several related approaches that take into account different factors such as level of risk, personal preferences, and expected value. Each of these approaches can help managers make more informed decisions that optimize resources and reduce risk.

 Expected utility — recommended articles Expected utility theory — Maximin criterion — Risk-return tradeoff — Theory of transaction costs — Expected monetary value — Indifference point — Analytic network process — Minimax criterion — Selection process in conditions of certainty and uncertainty