Last updated:

# Expected Utility Calculator

What is expected utility?How to calculate expected utility — Expected utility formulaThe role of expected utility in strategic decision makingFAQs

With our expected utility calculator, we aim to aid you in assessing the probable outcomes of different scenarios. To broaden your analytical toolkit, you may find our risk calculator and expected value calculator to be of interest.

• What expected utility is;
• Its importance in decision-making under uncertainty; and
• How to calculate expected utility for multiple events.

We will also present examples to elucidate the calculation process of expected utility.

## What is expected utility?

Expected utility theory is a concept in economics and decision theory that represents the average of all possible outcomes under uncertainty, weighted by their respective probabilities and the utility or value assigned to each outcome. It is used to model rational decision-making when outcomes are uncertain and quantify the desirability of different choices based on their potential benefits or drawbacks.

The expected utility of an action is calculated by multiplying the utility value of each possible outcome by the probability of that outcome occurring and then summing these products. The utility value assigned to each outcome is subjective and can vary from one individual to another, reflecting personal preferences, risk tolerance, and individual circumstances.

In essence, expected utility helps determine the best course of action when faced with multiple choices with uncertain results. It provides a way to make consistent choices by considering not only the likelihood of each outcome but also the relative importance, or utility, of those outcomes to the decision-maker.

## How to calculate expected utility — Expected utility formula

To understand how to calculate expected utility theory, let’s consider an example with two possible investment outcomes:

• Investment A:
• Probability: 40%
• Monetary value: $10,000 • Investment B: • Probability: 60% • Monetary value:$20,000

You can calculate the expected utility using the following steps:

1. Assess the probability and monetary value of event 1.

First, determine the likelihood of Investment A occurring and its potential payoff. Here, Investment A has a 40% chance of happening, and its monetary value is $10,000. To facilitate this calculation, you can also check out our probability calculator. 2. Evaluate the probability and monetary value of event 2. Next, establish the probability of Investment B and its corresponding payoff. Investment B has a 60% probability and a monetary value of $20,000.

3. Compute the expected utility.

Now, you can calculate the expected utility using the expected utility formula, where the utility of the monetary value is the square root of the monetary value (to represent utility in this example):

expected utility = (probability of event 1 × (monetary value 1 ^ 0.5)) + (probability of event 2 × (monetary value 2 ^ 0.5))

For the given example:

expected utility = (0.4 × ($10,000 ^ 0.5)) + (0.6 × ($20,000 ^ 0.5)) = 124.85

By calculating expected utility, individuals or firms can make informed decisions that maximize their overall satisfaction or return based on the utility derived from different financial outcomes.

## The role of expected utility in strategic decision making

The concept of expected utility is vital for strategic decision-making in uncertain environments. It allows businesses and individuals to make choices aligned with their objectives and risk preferences. Here's how the expected utility can guide strategic decisions:

• Incorporating risk into planning

Decision-makers use expected utility to factor in the risk associated with various outcomes. By assigning probabilities and utilities to different scenarios, they can evaluate which decision will likely yield the best adjusted-for-risk result.

• Optimizing portfolio management

In finance, expected utility is used to balance portfolios by assessing the risk-reward trade-off of various investments. Investors might choose a mix of assets that maximizes expected utility, which may not necessarily be the mix with the highest expected return due to differing risk profiles.

Companies often face investment decisions with uncertain returns. Expected utility allows them to choose investments that best align with their financial strategies and risk tolerance levels, potentially avoiding choices that, while lucrative, could jeopardize the company's financial stability if risks materialize.

• Negotiations and contracts

In negotiations, understanding the expected utility of different contract terms can help negotiators to prioritize which terms to push for and which to compromise on, based on the relative value and likelihood of each outcome.

• Market analysis and product development

Expected utility can inform decisions about entering new markets or developing new products by helping to predict whether the potential gains outweigh the risks and costs.

• Utility as a driver of value creation

Beyond financial metrics, expected utility highlights that value creation for a company also depends on qualitative factors, such as customer satisfaction or brand reputation, which can be integrated into decision-making through utility functions that capture more than just monetary gain.

In conclusion, calculating expected utility provides a structured approach to decision-making when outcomes are uncertain. It can inform a broad range of strategic decisions by quantifying the desirability of different choices in accordance with the decision-maker's goals and risk appetite.

FAQs

### How can I calculate the expected utility of a single event?

You can calculate the expected utility in three steps:

1. Determine the probability of the event.

2. Determine the utility value of the outcome.

3. Apply the expected utility formula:

expected utility = probability × utility value

### What is the expected utility for a 50% event with a utility value of \$100?

The expected utility of this event will be 50. You can calculate this using this formula:

expected utility = probability × utility value

### Can expected utility be negative?

Yes, if the outcomes are undesirable and the utility values assigned are negative, the expected utility can be negative, indicating a loss or negative impact.

### How does risk aversion affect expected utility?

Risk aversion can shape the utility function, typically resulting in a concave function that reflects the principle of diminishing marginal utility, meaning the more we have of something, the less additional units of it are worth to us.