Utility Theory and Its Assumptions

Utility theory is an economic theory that explains individuals’ behavior based on their preferences. It operates on several key assumptions:

Completeness of Preferences

• Individuals can rank order all possible consumption bundles.
• This implies that individuals can compare any bundle and rank them based on satisfaction.
• Real-World Example: Imagine you are at a restaurant, and the menu offers various combinations of meals, such as different types of appetizers, main courses, and desserts. If you can easily rank these options based on your preferences, even when there are many possible combinations, it demonstrates the completeness of your preferences. You can always choose the meal that you like the most, no matter how many options are available.

More-Is-Better

• If an individual prefers consumption bundle A to bundle B, they will also prefer a larger quantity of bundle A, represented as αA, to A itself, which is preferred to B.
• This assumption is called the monotonicity assumption.
• Real-World Example: Consider your preference for a popular brand of chocolate. If you prefer a large bar of that chocolate over a smaller one, it illustrates the more-is-better assumption. Even though you may not consume the entire large bar in one sitting, you would still choose it over the smaller one because having more of your preferred chocolate is better in your eyes.

Mix-Is-Better (Convexity)

• When an individual is indifferent between two stand-alone choices, combining them into a mix is preferred.
• For instance, a mix of half-week of food and half-week of clothing is preferred to one week of food alone or one week of clothing alone.
• This assumption is known as the convexity assumption.
• Real-World Example: Think of your choice between a plain hamburger and a plain hotdog. If you are indifferent between the two options, it represents the mix-is-better assumption. Now, if you find a combination that includes a half hamburger and a half hotdog (like a combo meal), and you prefer this mix to either the standalone hamburger or hotdog, it demonstrates the convexity of preferences. Mixing the two options is more satisfying for you.

Rationality

• The most crucial and controversial assumption.
• It implies that an individual’s preferences remain fixed regardless of the context and time.
• If A is preferred to B and B is preferred to C, then A will always be preferred to C.
• Real-World Example: Suppose you have ranked three vacation destinations: Beach (A), Mountains (B), and Desert (C). According to the rationality assumption, if you prefer the Beach (A) over the Mountains (B) and the Mountains (B) over the Desert (C), then you should always prefer the Beach (A) over the Desert (C), regardless of the context or time. This assumption assumes that your preferences remain consistent and rational.

Normative vs. Positive Aspects

• Economic theories can be either normative or positive.
• Normative theories prescribe how people should behave, while positive theories explain observed behavior.
• Utility theory falls under the positive category as it seeks to explain individuals’ actual choices and behavior, rather than dictating how they should behave.

Frequently asked questions about utility theory

Question 1: What is utility theory, and what does it aim to explain?

Answer 1: Utility theory is an economic theory that aims to explain individuals’ behavior based on their preferences. It seeks to provide insights into why people make certain choices and decisions.

Question 2: What are the four key assumptions of utility theory?

Answer 2: The four key assumptions of utility theory are completeness of preferences, more-is-better (monotonicity), mix-is-better (convexity), and rationality.

• Completeness. This entails that for all q, r: either qWr or rWq or both. If the answer is both, then I am indifferent between q and r.
• Transitivity. If qWr, rWs then qWs.
• Continuity. If qWr, rWs then there exists some p such that (q,p; s,1-p)~r.
• Independence. This requires that if qWr, then (q,p; s,1-p)W(r,p; s,1-p) This means that I prefer tacos to hamburgers for lunch, I will not change my preferences between tacos and hamburgers if I am offered a salad as well. This is the axiom most commonly relaxed when alternatives to EUT are examined.

Question 3: Can you provide a real-world example of the “completeness of preferences”?

Answer 3: Sure. Imagine you are at a restaurant, and the menu offers various combinations of meals. If you can consistently rank these options based on your preferences, even when there are numerous choices, it demonstrates the completeness of your preferences.

Question 4: Explain the “more-is-better” assumption with a real-world scenario.

Answer 4: Of course. Think about your preference for a specific brand of chocolate. If you prefer a larger bar of that chocolate over a smaller one, it illustrates the more-is-better assumption. Having more of your preferred chocolate is better in your eyes, even if you don’t consume it all at once.

Question 5: How does the “mix-is-better” assumption (convexity) apply to real-life decisions?

Answer 5: Consider your choice between a plain hamburger and a plain hotdog. If you are indifferent between the two options, it represents the mix-is-better assumption. Now, if you find a combination that includes a half hamburger and a half hotdog (like a combo meal) and prefer this mix to either the standalone hamburger or hotdog, it demonstrates the convexity of preferences. Mixing the two options is more satisfying for you.

Question 6: Explain the importance of the rationality assumption in utility theory.

Answer 6: The rationality assumption is crucial in utility theory because it ensures that individuals’ preferences remain consistent and avoid circularity. If someone prefers A to B and B to C, then the assumption dictates that they should always prefer A to C, regardless of the context or time.

Question 7: Utility theory is a preference-based approach that provides a rank ordering of choices. Explain this statement.

Answer 7: The statement “Utility theory is a preference-based approach that provides a rank ordering of choices” can be explained as follows:

1. Preference-Based Approach: Utility theory is built on the idea that individuals have preferences for various choices or outcomes. In other words, people have specific likes and dislikes, and they can express these preferences when faced with decision-making situations. For example, when choosing between different products, services, or experiences, individuals tend to have preferences for one over the other.
2. Rank Ordering of Choices: Utility theory takes these preferences and translates them into a systematic rank ordering of choices. It provides a structured way to compare and evaluate alternatives by assigning a numerical value or utility to each choice based on an individual’s preference. This ranking allows for a clear understanding of which choices are preferred, which are less preferred, and by how much.

Question 8: What is a “util” and what does it measure?

Answer 8:

A “util” is a hypothetical unit of measurement used in utility theory to represent the satisfaction or happiness derived from consuming goods and services. It is a non-standard unit of measurement specifically designed for understanding and quantifying the concept of utility.

The term “util” measures the level of utility or satisfaction that an individual derives from consuming a particular product or experiencing a specific outcome. In utility theory, it’s a way to assign a numerical value to the subjective preference or well-being associated with different choices. The higher the number of utils associated with a choice, the greater the satisfaction or utility derived from that choice.

It’s important to note that “utils” are not tied to any specific physical quantity or unit of measurement like kilograms, meters, or dollars; they are purely a theoretical construct used to compare and rank preferences. The main purpose of utils is to help economists and decision-makers analyze and model how individuals make choices and decisions based on their preferences and the relative levels of satisfaction or utility they assign to different options.