The Assumptions of Cardinal Utility:

1. Measurability: Cardinal utility assumes that utility can be measured numerically. Under this assumption, individuals are able to assign precise numerical values to the satisfaction they derive from consuming different goods or services. This allows for the comparison of utility levels across individuals and goods.

2. Ordinal Utility: Cardinal utility assumes that individuals can rank their preferences in a consistent and meaningful way. This means that individuals are able to determine which combinations of goods or services provide them with higher levels of utility and which ones provide lower levels.

3. Independence of Marginal Utility: Cardinal utility assumes that the marginal utility derived from consuming additional units of a good or service is independent of the initial level of consumption. This means that the satisfaction gained from each additional unit remains constant, regardless of the individual's initial level of consumption.

4. Diminishing Marginal Utility: Cardinal utility assumes that the marginal utility derived from consuming additional units of a good or service diminishes as the individual consumes more of it. This reflects the idea that the more of a particular good or service an individual consumes, the less satisfaction they derive from each additional unit.

The Assumptions of Ordinal Utility:

1. Preference Ranking: Ordinal utility assumes that individuals can rank their preferences, but does not require them to assign precise numerical values to the satisfaction they derive from consuming different goods or services. Instead, individuals simply need to be able to determine which combinations of goods or services provide them with higher levels of utility and which ones provide lower levels.

2. Transitivity of Preferences: Ordinal utility assumes that individuals have consistent and transitive preferences. This means that if an individual prefers bundle A to bundle B, and bundle B to bundle C, then they must also prefer bundle A to bundle C. This assumption ensures that individuals make rational choices based on their preferences.

3. Completeness of Preferences: Ordinal utility assumes that individuals have complete preferences, meaning that they are able to compare and rank all possible combinations of goods or services. This assumption allows for the construction of indifference curves, which represent different combinations of goods that provide the individual with the same level of utility.

4. Non-Satiation: Ordinal utility assumes that individuals always prefer more of a good to less. This means that individuals always strive to increase their overall level of utility and are never satisfied with their current level of consumption.

Overall, the assumptions of cardinal and ordinal utility provide the foundation for understanding how individuals make choices and allocate resources based on their preferences and the satisfaction they derive from consuming goods and services. While cardinal utility assumes precise numerical measurement of utility, ordinal utility focuses on the ranking and comparison of preferences.