Preference Function A preference function is a mathematical function that represents an individual's or consumer's preferences. The utility function represe...
Preference Function
A preference function is a mathematical function that represents an individual's or consumer's preferences. The utility function represents the maximum satisfaction a consumer can obtain from consuming a good or service, while the preference function represents the relative ranking of different goods or services that a consumer compares when making a decision.
Utility Function
The utility function is a real-valued function that describes the level of satisfaction a consumer derives from consuming a good or service. The utility function must satisfy the following properties:
Non-negativity: U(x) ≥ 0 for all x ≥ 0. This means that the consumer's utility cannot decrease as they consume more of a good or service.
Additivity: U(x + y) = U(x) + U(y) for all x and y ≥ 0. This means that the consumer's utility increases linearly when they consume more of both goods or services.
Monotonicity: U(x) ≤ U(y) for all x ≥ y ≥ 0. This means that the consumer's utility is non-decreasing, meaning that their satisfaction increases as they consume more of a good or service.
Preference Function
The preference function is a real-valued function that describes the relative ranking of different goods or services that a consumer compares when making a decision. The preference function must satisfy the following properties:
Transitivity: P(x, y) ≥ P(x, z) if u(x) > u(y) and v(x) > v(z). This means that if one good is more preferred than another and one service is more preferred than another, then the consumer prefers the first good over the second and the service over the third.
Symmetry: P(x, y) = P(y, x). This means that the consumer's preference is the same for a good and a service that are equally preferred.
Non-negativity: P(x, y) ≥ 0 for all x and y ≥ 0. This means that the consumer's preference cannot decrease as they consume more of a good or service.
By combining the utility function and the preference function, we can understand how a consumer's preferences and utility change as they make decisions