Principles of Microeconomics - Utility Functions

These flashcards cover key concepts and definitions related to utility functions in microeconomics, focusing on ordinal preferences, utility functions, and relationships in consumer theory.

What do ordinal preferences indicate?

Ordinal preferences indicate the ranking of choices rather than the magnitude of differences between them.

What are the symbols for preference relations in ordinal preferences?

x ≻ y means x is preferred strictly to y, x ≼ y means x is preferred at least as much as y, and x ~ y means x and y are equally preferred.

Who are some philosophers that considered 'utility' as a measure of happiness?

Bentham, J.S. Mill, and other utilitarians.

What does cardinal utility imply?

Cardinal utility implies that something with twice the utility is considered twice as good.

What is the definition of a utility function u(x)?

A utility function u(x) represents a preference relation if and only if certain equivalences hold for ordered options.

What assumption is made regarding continuity in utility functions?

Small changes to a consumption bundle cause only small changes to the preference level.

What is represented by an indifference curve (IC)?

An indifference curve represents all bundles that give the same utility level.

What mathematical relationship exists for marginal utility (MU)?

MU is defined as the rate of change of total utility as the quantity of a commodity consumed changes.

What is the importance of monotonic transformations in utility functions?

Monotonic transformations ensure different utility functions can represent the same preference relation without altering the ordering.

What are perfect substitutes in terms of utility functions?

Perfect substitutes are described by a utility function where only the total amount of goods consumed matters, typically represented as V(x,y) = x + y.

What is the implication of perfect complements in utility functions?

Perfect complements are represented by a utility function like W(x,y) = min{x, y}, where the value of the bundle is determined by the good in the least quantity.

What does a quasi-linear utility function look like?

A quasi-linear utility function has the form u(x,y) = f(x) + y, allowing for linear behavior in one good.

What characterizes Cobb-Douglas utility functions?

Cobb-Douglas utility functions are always monotonic, convex, and can be easily expanded for more than two goods.

How is marginal rate of substitution (MRS) calculated?

MRS is calculated using the ratio of marginal utilities: MRS = -MU1/MU2.