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**Subject 1. Utility Theory**

**Utility**refers to the total satisfaction received by a person from consuming a good or service.

**Completeness**. A person can compare any two bundles, A and B, in such a way that it leads to one of the three following results: (i) A is preferred to B, (ii) B is preferred to A, or (iii) A and B are the same (they are indifferent).**Transitivity**. Consider any three bundles A, B, and C. If a person prefers A to B and also prefers B to C, she or he must prefer A to C.**Nonsatiation**. Consider two bundles, A and B. A has more than B in every commodity and yet all these commodities are not economic "bads"; then a person will rank A higher than B.

Utility theory is a quantitative model of consumer preferences and is based on the above axioms. Consumer preferences can be represented by an ordinal utility function:

This is a mathematical expression that shows the relationship between utility values and every possible bundle of goods.

This

*ordinal*- not

*cardinal*- utility captures only ranking and not strength of preferences.

#### Practice Question 1

A person can compare any two bundles using the utility theory. This refers to the axiom of ______.A. completeness

B. transitivity

C. nonsatiationCorrect Answer: A

This axiom of completeness does not permit a person to say, "I just cannot decide."

#### Practice Question 2

A person who is indifferent between A and B and is also indifferent between B and C must be indifferent between A and C.A. This assumption is referred to as the axiom of transitivity.

B. This assumption violates the axiom of transitivity.

C. This assumption has nothing to do with the axiom of transitivity.Correct Answer: A

The axiom of transitivity holds for indifference and strict preference.

#### Practice Question 3

Which axiom means "the more, the better"?A. The axiom of completeness

B. The axiom of transitivity

C. The axiom of nonsatiationCorrect Answer: C

For economic "goods" (which means these commodities can give you positive satisfaction), the axiom of nonsatiation simply means "the more, the better." You may think of a counter-example; after you have eaten 10 ice cream cones, you will not want even a single one. But don't forget that in a market you can always trade those additional ice cream cones for money and then purchase other goods. Thus "the more, the better" generally holds.

#### Practice Question 4

Suppose a cup of orange juice has utility of 120 utils, a cup of tea has a utility of 80 utils, and a cup of water has a utility of 40 utils. A utility function would conclude that the cup of orange juice is better than the cup of tea by exactly the same amount by which the cup of tea is better than the cup of water.True or False?Correct Answer: False

Cardinal utility is not supported in the reading. Ordinal utility is the core assumption of consumers' preferences and utility functions.

### Study notes from a previous year's CFA exam:

1. Utility Theory